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FOTD 29-12-12 (Faerie Fantasyland [7])
by Jim Muth 29 Dec '12

29 Dec '12

FOTD -- December 29, 2012 (Rating 7) Fractal visionaries and enthusiasts: On its surface, the Z^(-2)+C Mandeloid is not much to look at -- little more than a triangle consisting of flat overlapping disks. The disks can be made larger or smaller by changing the escape radius, but this has little effect on the worth of the fractal. All is not lost however. When the entire Julibrot is sliced in different directions, it shows some aspects that are more interesting. In today's image I have double rotated the slice 66 and 66 degrees toward the Julia orientation, and rendered it with the outside parts set to 'real'. In the image, we see that the flat disks have become organized into more attractive semi- chaotic spirals. (The parent fractal actually has buds, but this is a story for another day.) I named the image "Faerie Fantasyland". The odd spelling is kind of a trendy pseudo-magical way of spelling the word 'fairy', which is used by those who are into new-age stuff. The rating of a 7 includes a full point for the smooth GIF coloring, which I really did put an hour or so of effort into. Without the coloring, the underlying scene would rate only a 6. The image is very fast. It finishes in under one minute on all but the oldest and slowest units. The image may be viewed without the inconvenience of setting up and running the included parameter file. Simply surf over to the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> and view it there. High-definition variations are posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are posted to the venerable FOTD web site at <http://www.Nahee.com/FOTD/> Snow fell all day here at Fractal Central today, while the light winds and relatively mild temperature of 30F -1C actually made the snow enjoyable. At post time about 5 inches or 12cm had piled up, but it was still falling. I'll give a final report in the next FOTD. The fractal cat alternated between stretching out on the radiator and hunching on the shelf in the southwest window, watching the snowflakes drift down. The humans took it as easy as possible, but I am concerned with the sidewalk that will eventually need to be cleared. The next FOTD will be posted when it is ready, most likely in 24 hours. Until whenever, take care, and I see that two people have been pushed in front of subway trains within a month. These trains are dangerous. We must do something about the needless deaths caused by misused subway trains. We must pass tighter train-control laws to keep subway trains from the hands of those who would misuse them. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Faerie_Fantasyland { ; time=0:00:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=+1.49344425/\ +0.22623503/210/1/-90/0 params=66/0/66/0/0/0/0/0/\ -2/0 float=y maxiter=1500 inside=0 outside=real periodicity=6 colors=000CbFCcGDcGEcGEcHFcHGcHGcIHcIIcIIcJJcJKdJK\ eKLfKMgKMhLNiLOjLOkNPlNQmOQmPRmQSnQSnSToUUoWUoYVo_\ WoaWocVoeUogToiSokRomQnoQnqRnsRnuRmvQlwRkwRjvRitRg\ sSfqSdoSbnSalT_jTZiTXgTVeTUdUSbUR`UP_UNYVMWVKVVJTV\ IRVJQWJRXJSYKTZLUZMV_NV`OWaPXaQYbSZcT_dU_dV`eWafXb\ gYchZch_di`ejbfkcgkdhlehmfingjnhkoilpjlqkmrmnrnoso\ ptpquqqurrvsswttxuuxvuvututttstsrtrqtqpsposonsnmsm\ lslksjjriirhhrggrffreerddqccqbbqaaq``q__qYZpXYpWXp\ VWpUVpTUpSToRSoQRoPQoOPoNQrNOoNNmNMkNLiNKgNJeNHbNG\ `NFZNEXNDVNCTNAQN9ON8MN7KN6IN5GN4EM6HL8KKAMJCPJESI\ GUHIXGKZGLaFNdEPfDRiCTkCVnBXqAZs9`v9ax9cu9ds9ep9fn\ 9gk9hi9if9jd9ka9l_9mY9nV9oT9pQ9qO9rL9sJ9tG9uE8u99v\ CAvFBvIBvKCvNDvQDvSEvVFvYFvYHtYIrYJpYKnYMlYNjYOiZP\ g_Re`ScaTabU_cVZdXXeYVeZTf_RfaPfbNgcMgdKhfIhgGhhEi\ hCig9lgBifDfcFc_H`WJYTLVPNSMPPIRMETJBVG7XD4YB5ZC6Z\ C6_D7_D8`D8`E9aEAaEAaFBbF } frm:SliceJulibrot4 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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FOTD 28-12-12 (Into the Aether [8])
by Jim Muth 29 Dec '12

29 Dec '12

FOTD -- December 28, 2012 (Rating 8) Fractal visionaries and enthusiasts: Today's parent fractal came from the formula (-Z)^(2.003)+C rather than (+Z)^(2.003)+C. This negative Z parent resembles the more familiar positive Z, though it has no rectangles just east of the main minibrot, and the East Valley has split apart. Today's scene lies along the infinitely divided main stem, just east of a smaller minibrot that lies well east of the large minibrot. The name "Into the Aether" refers to that hypothetical all- pervading stuff that was once assumed to be the medium that transmits electromagnetic radiation. Nowadays we know that abstract waves of probablilty do the vibrating, though it's fun to think that the aether actually exists, interpenetrating the objects around us. (And who knows? Maybe something similar [a neutrino field] actually does interpenetrate our space.) The image rates an 8, which makes it the highest rated FOTD in quite some time. The parameter file finishes in 2 minutes on most SOTA units, which makes it about average. And the web sites are always available to make life easier. Get smart. View the image on the official FOTD web site without the need of calculating it. <http://www.crosscanpuzzles.com/Archives.html> And check the augmented variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are at: <http://www.Nahee.com/FOTD/> Clouds prevailed here at FC today, though the lack of sun and resulting chill was mitigated by the lack of wind and relatively mild temperature of 34F +1C. The fractal cat passed the day in the southwest window, watching the world go by. The fractal humans passed the day closing out the old year and preparing for another year. The next FOTD image will be posted in the proper time. Until whenever, take care, and the first step in solving a problem is to see that everyone agrees on what the problem is. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Into_the_Aether { ; time=0:06:37.05 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot5 center-mag=-1.621649157\ 158942/+0.00000020374490837/6.614526e+010/1/-155/0 params=0/0/0/0/0/0/0/0/2.003/0 float=y maxiter=3200 inside=0 logmap=392 periodicity=6 colors=00030441653865A77C89E9BGADICFKEHMGJOILQKNSM\ PUORWQTYSV`UXcWZfZaiaeldiohmtmqwpuzozzmwwjsthqqfon\ dmjdmhcmfcmdclbXgYQbTJYOCTJ6PFATHEWJL_KQbMUfNZiPcl\ RinSoqUssVwvXzxYnuZlr_jo`hmafjadgbbec`bdZ_eXYeWYeW\ YdWYdWZcVZbVZbVZaVZ`UZ`UZ_UZZUZZTZYTZXTZXTZWRVdSWc\ SWcSWcSWbCWNE`MGdMHiLJnLKrLInOHkQGgTFdVD`YCY_BUaAR\ d9Nf7Ki6Gk5Dn49p36r6Do9KmCRjFYhIdeLkcOr`QxZRtURqPS\ nKSkFShAJPEA6H9AJ9DL8GN8JP7MR7PS6SU6VW6ZY5a_5d`4gb\ 4jdzufnphYsi6ig8_fAQeCGdE6cK9dPCeUFeZIfdKfiNgnQgsT\ hxVhrOelHcfBaeDZdEXcFVbGSaHQ`IO_JLZKJYLHXMEWNCVOAU\ P7TQ5SR3RS1TV3UX5V_6Xa8Yd9ZfB`iDakEbnGdpHesJfuKbjH\ Z_FVPCSEAUDBWDBYCC_CCaCCcBDdBDfBDnAEjAEzAEn9Fp9Fq9\ FpHNoOVaI_PCdC6iL7dT8_`9WiARqBMyCIrQNlbSjaRhcRfcQd\ cQbmPamP_mPYmOWmOUmNSmNRmNcmJozFmzGkzHjzIhzzgzzezz\ czz`zzZzzWzzUzzSzzPzzNzzLzzIzzGzzEzzBzz9zz7zz8zz8z\ z9zzAzzBzzCzzDzzEzzFzzFzz } frm:SliceJulibrot5 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=(-z)^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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76531Z2 Circles-zoom
by Albrecht 28 Dec '12

28 Dec '12

Hi, as announced yesterday this is a zoom into one of the fractal miniatures building every second circle, a complete and pretty image with unusual structures. You may recall that there were previous postings with similar zooms, but these were not complete images, just the underlying image made visible. I?m going to explore border defined images further but it is not easy because every participating frm reacts differently and the border values must take care of that. But IF you get a usable image it?s always worth the effort. You may try and zoom into any miniatures even the smaller outside circles and you?ll see that every one is different and has it?s own structures. Here?s Hal?s link: http://www.emarketingiseasy.com/Albrecht/76531Z2.GIF Albrecht ---------------------------------start-par-------------------------------- 76531z2 { ; Inside View 2 ; time 0.08.26.25 1600/1200 ; newt-phoen-mmods-bees-sec reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=+0.10593790239912770/+0.00000000000026454/56.75406/1/90/3.885\ 78058618804789e-016 params=-0.05825983458967864/0.3785210730307932/76531.07595702022/14235.4\ 911030602/150512.0404808048/384.3204896048/384.00482000595/128.200000859\ 1/256.2000004001/512.3000008001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000220<4>110110000110<2>000KA4<7>gcOjgRmjT<3>zzc<9>UOFRKDOGA<3>A0\ 0<9>f0Ci0Dl0F<3>z0K<6>Z0EV0DR0C<3>A08004000<26>000<4>000<7>Q0UU0YX0a_0dc\ 0hf0l<2>p0w<4>_0dX0aU0Y<2>K0NH0JG0NE1R<3>7UX6`Z4h_2oa0wc<10>2WI2TG2RE<3>\ 4G54D36F5<16>kkammcpoe<3>zwm<3>mhZjdVfaS<3>VMCRI8OE4KA0000<43>000<4>0003\ 30<5>220 } frm:multifractal_10 { ; Albrecht Niekamp Jan2005 ;RP2 Left: 5 Digits_Channel:1_main 2_outside 3_inside1 4_inside2 5_inside3 ; Frms: 0_off 1_Sec 2_Mand(2) 3_Bees 4_Jul 5_Mmod 6_Phoen 7_Newt 8_Spid ; Right: 2 Digits_MMods_Number of sides 2 Dig_Phoenix 2 Dig_Spider ; 1 Dig_TransReset_main :0_no 1_dblmand 2_Iter-res 3_both +5_warp ; 4 Dig_TransReset_Ch2-5:0_no 1_z-reset 2_Iter-res 3_both +5_warp ;IP2 Left: 5 Digits_Bailout Number for Channels 1 to 5 ; Right: Variab: 4 Digits_Mand/Jul(2 var) 2 Digits_Secant 4 Digits_Bees ;RP3 Left: 2 Digits_Newtonvariable 4 Digits_Colour1 ; Right: 5 Digits_Colour2 5 Digits_Colour3 ;IP3 Left: Main: 5 Digits_Warp-factor (fn1 is used) ; Right: 5 Digits_Colour4 6 Digits_Colour5 ;RP4 Left: Outside: 5 Digits_Warp-factor (fn2 is used) ; Right: Outside: 4 Dig+1 fractaldig_bord-out 4 Dig+1 fractaldig_bord-in ;IP4 Left: Inside1_Maxiter ; Right: Inside1_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn2 used) 4 Dig+1 fractaldig_border1 ;RP5 Left: Inside2_Maxiter ; Right: Inside2_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn3 used) 4 Dig+1 fractaldig_border2 ;IP5 Left: Inside3_Maxiter ; Right: Inside3_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn4 used) 4 Dig+1 fractaldig_border3 ; Altnat: Left: 1_Lake effect enabled (Inside3 disabled) ; Right: 2 Digit_Frequency 2 Digit_Waterlevel 2 Digit_Amplitude ; le=0 z=pixel da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+11111 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==4)+(d==5)+(d==8)+(d==9) d4=d3==0 vb=d>5 sc=d==2 mo=d==6 px=d==7 ab=px+(d==3)+(d==5)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>1 sc1=d==2 mo1=d==6 px1=d==7 v1m=mo1+px1 v1j=d>7 dd1=v1j+(d==4)+(d==5) ab1=px1+(d==3)+(d==5)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=d>1 sc2=d==2 mo2=d==6 px2=d==7 v2m=mo2+px2 v2j=d>7 dd2=v2j+(d==4)+(d==5) ab2=px2+(d==3)+(d==5)+(d==9) d=trunc(dd/10) ex3=d>1 sc3=d==2 mo3=d==6 px3=d==7 v3m=mo3+px3 v3j=d>7 dd3=v3j+(d==4)+(d==5) ab3=px3+(d==3)+(d==5)+(d==9) d=dd-d*10 ba=imag(p5) mi3=trunc(ba) dd=(d>1)+(mi3>1) ex4=dd==2 sc4=d==2 mo4=d==6 px4=d==7 v4m=mo4+px4 v4j=d>7 dd4=v4j+(d==4)+(d==5) ab4=px4+(d==3)+(d==5)+(d==9) ; mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 dm=(d==2)+(d==4) ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex1+ex0+ex2+ex3+ex4 ; d=real(p3) dd=trunc(d) da=(d-dd)*10000000000 pp=trunc(dd/10000) ba1=dd-10000*pp ba2=trunc(da/100000) ba3=da-100000*ba2 ; d=imag(p3) sfac=trunc(d) da=(d-sfac)*100000000000 ba4=trunc(da/1000000) ba5=da-ba4*1000000 ; d=real(p4) ofac=trunc(d) da=(d-ofac)*10000000000 bh=trunc(da/100000)/10 bl=(da-bh*1000000)/10 bs=bl/2 ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) da=round((d-dd)*10000000000) d=trunc(dd/10000) dd=dd-d*10000 bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/1000) dd=dd-d*1000 bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/100) dd=dd-d*100 bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/10) dd=dd-d*10 bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=round(dd) bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) ; d=da p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 dp=p6+p0/100 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=d==3 fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 ; d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=d==3 fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 ; if (mi3==1) d=(ba-mi3)*1000000 fr=round((trunc(d/10000))*10) ;lake effect by S.Gallet d=d-fr*1000 lv=(trunc(d/100))/100 d=d-lv*10000 am=d/100 u=real(rotskew*pi/180) t=exp(-flip(u)) bo=1/real(magxmag) q=bo/0.75*imag(magxmag) dd=tan(imag(rotskew*pi/180)) da=2*q*t rs=2*bo*(dd+flip(1))*t zz=center+(-q-bo*dd-flip(bo))*t z=z-zz d=imag(conj(da)*z)/imag(conj(da)*rs) le=d<=lv if (le) dd=lv-d z=z+2*dd*(1+am*sin(fr*dd^0.2))*rs endif z=z+zz else da=(ba-mi3)*100000000000 d=trunc(da/10000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=d==3 fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 endif ; if (vb) if (d3) if (ab) z=z*le+pixel*(le==0) ;Spider c=p1 else z=z*le+pixel*(le==0) c=p1 ;newton endif elseif (ab) c=z ;Phoenix z=z*le+pixel*(le==0) else c=0.4*log(sqr(z^mm)) ;many mods z=0 endif elseif (d3) if (ab) c=p1 ;Julia z=z*le+pixel*(le==0) else ;bees c=p1 z=z*le+pixel*(le==0) endif elseif (ab) c=z ;Mandel z=0 else c=z ;Secant z=z*le+pixel*(le==0) endif t=0 bo=|z| p=pp z0=p7 zold=(0.0,0.0) cb=p9 ba=bb0 : if (tt) t=t+1 if (ex0) ex0=t<mi1 if (bo>bs) u=2*(fn1(t/sfac)) ex0=0 if (ir0) t=0 endif if (d4) z=z*u if (mo) c=0.4*log(sqr(z^mm)) else c=pixel endif else z=z*le+pixel*(le==0) cb=p9*u c=p1*u p=pp*u endif tt=tt-1+ex0 endif elseif ((ex1)&&bo>bl) if (bo<bh) d3=dd1 ba=bb1 ab=ab1 ex1=0 tt=tt-1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif if (ir1) t=0 endif if (d3) vb=v1j if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif else vb=v1m if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo1) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) ab=ab2 d3=dd2 ba=bb2 ex2=0 tt=tt-1 if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif if (ir2) t=0 endif if (d3) vb=v2j if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v2m if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo2) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) ab=ab3 d3=dd3 ba=bb3 ex3=0 tt=tt-1 if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif if (ir3) t=0 endif if (d3) vb=v3j if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v3m if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) ab=ab4 d3=dd4 ba=bb4 ex4=0 tt=0 if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (d3) vb=v4j if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v4m if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo4) c=0.4*log(sqr(z^mm)) endif endif endif endif endif if (vb) if (d3) if (ab) z=z*z+c ;Spiderjul John Horner c=c*sp+z else z1=z^p-1 ;Quasinewton Puskas Istvan z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+0.56+ph/100-0.5*zold ;Phoenix Mike Wareman zold=z z=z1 else z2=fn1(z)+c ;Many_mods Linda Allison z1=cos(z2) z=c*(1-z1)/(1+z1) endif elseif (d3) if (ab) z2=z*z ;Julia Puskas Istvan z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb ;Bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) if (dm) z=z*z+c+c*c-dp ;Double Mandel else z2=z*z ;Mandel Puskas Istvan z=z2*z2+p6*z2+c-p0 endif else z3=z ;Secant Mike Wareman z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<ba } ------------------------------------------end------------------------------

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FOTD 27-12-12 (The End of the End [7])
by Jim Muth 28 Dec '12

28 Dec '12

FOTD -- December 27, 2012 (Rating 7) Fractal visionaries and enthusiasts: After a brief break during which the world did not end, the FOTD has returned with another fractal. Like all other fractals, today's has existed for all eternity but has never been seen by intelligent beings until today. The parent fractal shows what happens when 2 parts of Z^2 are mixed with 2 negative parts of Z^(-0.9) and straight C is added on each iteration. This parent consists of a rather distorted Mandeloid set with a large triangular area of chaos to the northwest and a much smaller Mandeloid set some distance to the southwest. Today's image lies in the triangular area of chaos. The name "The End of the End" points out that the latest end of the world has come and gone, and like all previous ends of the world, it was a total failure. Of course, true believers will claim that some hugely important but invisible thing, such as a 'harmonic convergence', did actually happen, but was not noticed or reported by the mass media, which is controlled by the big greedy corporations for their own benefit. The calculation time of 1-1/3 minutes will pass in less time than it takes for a harmonic convergence to manifest. But the web sites will remove all traces of harmonic convergency. The chore of calculation may be avoided by viewing the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> High definition variations are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images may be accessed at: <http://www.Nahee.com/FOTD/> 1-1/2 inches (4cm) of snow fell on Christmas Eve here at Fractal Central, not quite enough to make an honest white Christmas, but just enough to make the kids happy. The day after Christmas brought 5 inches (12cm) of heavy sleety snow to the area, making more of a nuisance than a post card scene. Today was cloudy with a temperature of freezing. The fractal cat kept busy watching for the occasional passing snowflake, while the humans recovered from the holiday. The next FOTD will be ready by this time tomorrow. Whether it is posted as soon as it is ready remains to be seen. Until whenever, take care, and we should not even think of passing futile laws to solve our current problems such as climate change or easy access to guns. Such laws will do nothing but create more division, more criminals, and increase overall contention. If a solution to our problems is to be successful, it must be accepted and acted upon by everyone from the far right to the far left. If no such solution is possible, then our problems have no solution, and it is time to stop wasting energy, to blame the other guy and prepare for the end. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_End_of_the_End { ; time=0:01:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+0.1098265398921243/-0.2191813687286491\ /2.018e+012/1/-27.5/0 params=-2/-0.9/2/2/-0.6/0/0/0 float=y maxiter=800 inside=0 logmap=96 periodicity=6 mathtolerance=0.05/1 colors=000OKfNHcKFZHCUE9PB6K83F502KD3ZQ3mb4sn4qdAd\ VFVHKTBMO1RGAAAA08A0PQAUhAZqRcwRZtVUpZWkbdgea_`ZSW\ UKSLDND5J02E00AA5XzZznZzjZzeZzbXzdYzf_zhmzjpzlsvzv\ xzzzzzzmYmkUmjQmiMmlOmnQgpSbrUXtWSvYMx_HsWFnTDiQBq\ N9rJ7wG5rS3tY1u_0ta0ni0Yl0Qo0Dw0iXZgYVfYSeYPdYMbZJ\ aZG`ZD_ZAa_Bc_Ce`Df`Eh`FjaGlaHmaHgjVbrhYzuTdqPcnOc\ rRcnUcjXcg_ccbc`emXhmUkmQnmNimMemMamMYmMTmMPmMLmMH\ mMDmMGmOJmPMmQPmRSmTVmUYmV_mWamVbmVcmVdmUfzUgzUhzT\ izTkzTlzSmzSnzSpzRqzRrzRszRpzPnzNlzLizKgzzezzczzbz\ zbzzbzzazzazzazz`zz`zz`zzczzezzhzzjzzlzzozzqzzszzo\ zzlzzizzfzzbzz_zzXzzUzzQzzNzzKzzHzzDzzAzz7zz4zzJzz\ Yzzkzzjzzizzhzzgzzfzzezzdzzczzbzzaqf`rh_rjZslYsnXs\ pWtrVttUuvTuxTuzStvRtrRtoQtkQthPzdPz`OzYOzUNzRNzNM\ zJMzGLzCLz9Oz9Rz9Uz9Xz9_z9bz9ez9hz9kz9gzNdz_`zmYzz\ XzyWzyWzyVzyUzyUzyTzySzxSzxRzxQzxQzxPzxPzxOzwNzvNz\ uMztLzsLzrKzqJzpJzpLznMzm } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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76531Z Circles
by Albrecht 27 Dec '12

27 Dec '12

Hi, I?m back again amd taking over. First a BIG Thank You! to Hal for his wonderful way of presenting the Multifractal_10 Images. Guess I have to improve to keep his standards. All images presented in the next days are new and created for this purpose. "Circles" shoes the Many Mods formula which is well known to all regular viewers with one big exception: This one uses the Newton Formula for outer structures, I haven?t seen anything like it myself and it forms a beautiful image. The reason is: This image is border defined, Newton is used as main shape. Three freely designed borders are used by Multifractal_10: outside-shape, inside 1 and 2, inside 2 and 3. The sequence of formulas used is: Newton-phoenix-manymods-bees-secant. Another thing is unique: Every second circle consists of fractal miniatures ready to explore!! The next presentation will show one of them. Here?s Hal?s link to the image: http://www.emarketingiseasy.com/Albrecht/76531Z.GIF ; ----------------start par------------------------------------------------- 76531z { ; Circles ; time 0.17.38.19 1600/1200 ; newt-phoen-mmods-bees-sec reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=-0.0575112/2.64538e-013/2.735546/1/90/3.88578058618804789e-01\ 6 params=-0.05825983458967864/0.3785210730307932/76531.07595702022/14235.4\ 911030602/150512.0404808048/384.3204896048/384.00482000595/128.200000859\ 1/256.2000004001/512.3000008001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000<3>000000000330<6>220220220<3>110000110<2>000KA4<7>gcOjgRmjT<3\ >zzc<9>UOFRKDOGA<3>A00<9>f0Ci0Dl0F<3>z0K<6>Z0EV0DR0C<3>A08004000<26>000<\ 4>000<7>Q0UU0YX0a_0dc0hf0l<2>p0w<4>_0dX0aU0Y<2>K0NH0JG0NE1R<3>7UX6`Z4h_2\ oa0wc<10>2WI2TG2RE<3>4G54D36F5<16>kkammcpoe<3>zwm<3>mhZjdVfaS<3>VMCRI8OE\ 4KA0000<42>000 } frm:multifractal_10 { ; Albrecht Niekamp Jan2005 ;RP2 Left: 5 Digits_Channel:1_main 2_outside 3_inside1 4_inside2 5_inside3 ; Frms: 0_off 1_Sec 2_Mand(2) 3_Bees 4_Jul 5_Mmod 6_Phoen 7_Newt 8_Spid ; Right: 2 Digits_MMods_Number of sides 2 Dig_Phoenix 2 Dig_Spider ; 1 Dig_TransReset_main :0_no 1_dblmand 2_Iter-res 3_both +5_warp ; 4 Dig_TransReset_Ch2-5:0_no 1_z-reset 2_Iter-res 3_both +5_warp ;IP2 Left: 5 Digits_Bailout Number for Channels 1 to 5 ; Right: Variab: 4 Digits_Mand/Jul(2 var) 2 Digits_Secant 4 Digits_Bees ;RP3 Left: 2 Digits_Newtonvariable 4 Digits_Colour1 ; Right: 5 Digits_Colour2 5 Digits_Colour3 ;IP3 Left: Main: 5 Digits_Warp-factor (fn1 is used) ; Right: 5 Digits_Colour4 6 Digits_Colour5 ;RP4 Left: Outside: 5 Digits_Warp-factor (fn2 is used) ; Right: Outside: 4 Dig+1 fractaldig_bord-out 4 Dig+1 fractaldig_bord-in ;IP4 Left: Inside1_Maxiter ; Right: Inside1_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn2 used) 4 Dig+1 fractaldig_border1 ;RP5 Left: Inside2_Maxiter ; Right: Inside2_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn3 used) 4 Dig+1 fractaldig_border2 ;IP5 Left: Inside3_Maxiter ; Right: Inside3_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn4 used) 4 Dig+1 fractaldig_border3 ; Altnat: Left: 1_Lake effect enabled (Inside3 disabled) ; Right: 2 Digit_Frequency 2 Digit_Waterlevel 2 Digit_Amplitude ; le=0 z=pixel da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+11111 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==4)+(d==5)+(d==8)+(d==9) d4=d3==0 vb=d>5 sc=d==2 mo=d==6 px=d==7 ab=px+(d==3)+(d==5)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>1 sc1=d==2 mo1=d==6 px1=d==7 v1m=mo1+px1 v1j=d>7 dd1=v1j+(d==4)+(d==5) ab1=px1+(d==3)+(d==5)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=d>1 sc2=d==2 mo2=d==6 px2=d==7 v2m=mo2+px2 v2j=d>7 dd2=v2j+(d==4)+(d==5) ab2=px2+(d==3)+(d==5)+(d==9) d=trunc(dd/10) ex3=d>1 sc3=d==2 mo3=d==6 px3=d==7 v3m=mo3+px3 v3j=d>7 dd3=v3j+(d==4)+(d==5) ab3=px3+(d==3)+(d==5)+(d==9) d=dd-d*10 ba=imag(p5) mi3=trunc(ba) dd=(d>1)+(mi3>1) ex4=dd==2 sc4=d==2 mo4=d==6 px4=d==7 v4m=mo4+px4 v4j=d>7 dd4=v4j+(d==4)+(d==5) ab4=px4+(d==3)+(d==5)+(d==9) ; mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 dm=(d==2)+(d==4) ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex1+ex0+ex2+ex3+ex4 ; d=real(p3) dd=trunc(d) da=(d-dd)*10000000000 pp=trunc(dd/10000) ba1=dd-10000*pp ba2=trunc(da/100000) ba3=da-100000*ba2 ; d=imag(p3) sfac=trunc(d) da=(d-sfac)*100000000000 ba4=trunc(da/1000000) ba5=da-ba4*1000000 ; d=real(p4) ofac=trunc(d) da=(d-ofac)*10000000000 bh=trunc(da/100000)/10 bl=(da-bh*1000000)/10 bs=bl/2 ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) da=round((d-dd)*10000000000) d=trunc(dd/10000) dd=dd-d*10000 bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/1000) dd=dd-d*1000 bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/100) dd=dd-d*100 bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/10) dd=dd-d*10 bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=round(dd) bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) ; d=da p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 dp=p6+p0/100 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=d==3 fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 ; d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=d==3 fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 ; if (mi3==1) d=(ba-mi3)*1000000 fr=round((trunc(d/10000))*10) ;lake effect by S.Gallet d=d-fr*1000 lv=(trunc(d/100))/100 d=d-lv*10000 am=d/100 u=real(rotskew*pi/180) t=exp(-flip(u)) bo=1/real(magxmag) q=bo/0.75*imag(magxmag) dd=tan(imag(rotskew*pi/180)) da=2*q*t rs=2*bo*(dd+flip(1))*t zz=center+(-q-bo*dd-flip(bo))*t z=z-zz d=imag(conj(da)*z)/imag(conj(da)*rs) le=d<=lv if (le) dd=lv-d z=z+2*dd*(1+am*sin(fr*dd^0.2))*rs endif z=z+zz else da=(ba-mi3)*100000000000 d=trunc(da/10000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=d==3 fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 endif ; if (vb) if (d3) if (ab) z=z*le+pixel*(le==0) ;Spider c=p1 else z=z*le+pixel*(le==0) c=p1 ;newton endif elseif (ab) c=z ;Phoenix z=z*le+pixel*(le==0) else c=0.4*log(sqr(z^mm)) ;many mods z=0 endif elseif (d3) if (ab) c=p1 ;Julia z=z*le+pixel*(le==0) else ;bees c=p1 z=z*le+pixel*(le==0) endif elseif (ab) c=z ;Mandel z=0 else c=z ;Secant z=z*le+pixel*(le==0) endif t=0 bo=|z| p=pp z0=p7 zold=(0.0,0.0) cb=p9 ba=bb0 : if (tt) t=t+1 if (ex0) ex0=t<mi1 if (bo>bs) u=2*(fn1(t/sfac)) ex0=0 if (ir0) t=0 endif if (d4) z=z*u if (mo) c=0.4*log(sqr(z^mm)) else c=pixel endif else z=z*le+pixel*(le==0) cb=p9*u c=p1*u p=pp*u endif tt=tt-1+ex0 endif elseif ((ex1)&&bo>bl) if (bo<bh) d3=dd1 ba=bb1 ab=ab1 ex1=0 tt=tt-1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif if (ir1) t=0 endif if (d3) vb=v1j if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif else vb=v1m if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo1) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) ab=ab2 d3=dd2 ba=bb2 ex2=0 tt=tt-1 if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif if (ir2) t=0 endif if (d3) vb=v2j if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v2m if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo2) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) ab=ab3 d3=dd3 ba=bb3 ex3=0 tt=tt-1 if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif if (ir3) t=0 endif if (d3) vb=v3j if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v3m if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) ab=ab4 d3=dd4 ba=bb4 ex4=0 tt=0 if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (d3) vb=v4j if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v4m if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo4) c=0.4*log(sqr(z^mm)) endif endif endif endif endif if (vb) if (d3) if (ab) z=z*z+c ;Spiderjul John Horner c=c*sp+z else z1=z^p-1 ;Quasinewton Puskas Istvan z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+0.56+ph/100-0.5*zold ;Phoenix Mike Wareman zold=z z=z1 else z2=fn1(z)+c ;Many_mods Linda Allison z1=cos(z2) z=c*(1-z1)/(1+z1) endif elseif (d3) if (ab) z2=z*z ;Julia Puskas Istvan z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb ;Bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) if (dm) z=z*z+c+c*c-dp ;Double Mandel else z2=z*z ;Mandel Puskas Istvan z=z2*z2+p6*z2+c-p0 endif else z3=z ;Secant Mike Wareman z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<ba }

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FOTD 21-12-12 (DOOMSDAY!!!! [No Rating])
by Jim Muth 22 Dec '12

22 Dec '12

FOTD -- December 21, 2012 (No Rating) Fractal visionaries and enthusiasts: It's come! It's the end of the world! This is it! There's no tomorrow! Today is doomsday! Armageddon! The Apocalypse! Nostradamus was right! All this doom rolled into one! . . . . . . etc. . . . Ah nuts! The hour has passed. It was all a media scare tactic. What a disappointment! I have seen nothing happen that could be considered out of the ordinary in even the slightest degree, except that darkness seems to be falling unusually early lately. I believe the precise moment of doom was 11:11am EST, or 16:11pm GMT. But that time has come and gone, and the world is still here. The apocalypse was a flop. The Mayans were wrong. So let's move on to the fractals. In today's image the strange rectangle has totally vanished as predicted. Only a few traces of yellow mark the spot where it was last seen. Actually, the rectangle still exists in its full glory -- elsewhere. It is we who have changed our view of it and moved on. The name explains itself. If I had rated the image, it would have had the lowest rating in FOTD history -- most likely a 2. Luckily, the image is very fast. It finishes in only 30 seconds. The finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> Hi-def variations are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are at: <http://www.Nahee.com/FOTD/> The parameter file for a second image is included with this FOTD. The name "One from Doomsday" shows the spirit of the departed rectangle happily floating through the ethers of whereever good fractals go when they die. Those who do not believe in spirits may bypass this second image. The day began wet and windy, with a temperature of 50F 10C. The rain ended during the morning, but the clouds remained and the temperature dropped fast in the afternoon, reaching freezing by 4pm. A few flurries of snow fell later in the day, though the ground remained only wet. The fractal cat passed the day watching the world go by; the humans spent the day thinking of the holidays. The next FOTD will be posted in around six days, around December 27. There is simply too much to do here at FC to keep the FOTD going uninterrupted through the holidays. Until whenever, take care, and the next doomsday (fiscal cliff) is only ten days off. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= DOOMSDAY!!!! { ; time=0:00:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=+0.001962114\ 25377242/+0.00121653453603809/107.7586/1.3369/0/\ -38.6598082540901018 params=99/98/79/82/-1.7435/\ -0.002/0.000175/0.073883/2.003/0 float=y maxiter=8000 inside=0 logmap=55 periodicity=6 colors=00022M22M22L22L22K22K22J22J12I12I12H12H12G1\ 2G11F11F11E11E11D11D11C41011C11B11B11A11A119019018\ 018007007006006005005004004003003002002001001000Lc\ nKbmKbmKalKalKakJ`kJ`jJ`jJ_iJ_iIZhIZhIZgIYgIYfHYfH\ XeHXeHWeHWdGWdGVcGVcGVbGUbFUaFUaFT`FT`FS_ES_ESZERZ\ ERYERYEQYDQXDPXDPWDPWDOVCOVCOUCNUCNTCMTBMSBMSBLRBL\ RBLQAKQAKPAKPAJPAJO9IO9IN9IN9HM9HM8HL8GL8GK8FK8FJ7\ FJ7EI7EI7EH7DH7DH6CG6CG6CF6BF6BE5BE5AD5AD5AC59C49B\ 48B48A48A479379378368368357257256246245045134134A2\ 3KA3UK2cU2mc1zm1zm0zm0xp7un6sl6qj6nh5zm5zm5zm5zm4z\ m4zm4zm4zm3zm3zm3zm3zm2zm2zm2zm2zm1zm1zm1zm1zm0zm0\ zm0zm3zm2zm2zm2zm2zm2zm2zm2zm2zm2zc2zc2zc2zc2zc2zc\ 2zc2zc2zc2zc2zcbzcdzcfzchzcjzckzcjzcizcizchzchzcgz\ cgzcfzcmzcmzcmzcmzcmzcmzcmzcmzczzczzczzczzczzczzcz\ zUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzU\ zzUzzUzzUzzUzzUzzUzzUzzUz } One_from_Doomsday { ; time=0:01:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=+0.007190875\ 14157552/+0.0019266285650588/3195327/0.5078/55.814\ 0458117172074/54.4657933543971922 params=99/98/79/\ 82/-1.7435/-0.002/0.000175/0.073883/2.003/0 float=y maxiter=1000 inside=0 logmap=130 periodicity=6 colors=00022M22M22L22L22K22K22J22J12I12I12H12H12G1\ 2G11F11F11E11E11D11D11C41011C11B11B11A11A119019018\ 018007007006006005005004004003003002002001001000Lc\ nKbmKbmKalKalKakJ`kJ`jJ`jJ_iJ_iIZhIZhIZgIYgIYfHYfH\ XeHXeHWeHWdGWdGVcGVcGVbGUbFUaFUaFT`FT`FS_ES_ESZERZ\ ERYERYEQYDQXDPXDPWDPWKOVKOVKOUKNUKNTKMTKMSKMSULRUL\ RULQUKQUKPUKPUJPUJOcIOcINcINcHMcHMcHLcGLcGKmFKmFJm\ FJmEImEImEHmDHmDHzCGzCGzCFzBFzBEzBEzADzADzKCzKCzKB\ zKBzKAzKAzK9zK9zU8zU8zU8zU7zU7zU6zU6zU5zc5zc4zc4zc\ 3zc3zc2zc2zc1zm1zm0zm0xp7un6sl6qj6nh5zm5zm5zm5zm4z\ m4zm4zm4zm3zm3zm3zm3zm2zm2zm2zm2zm1zm1zm1zm1zm0zm0\ zm0zm3zm2zm2zm2zm2zm2zm2zm2zm2zm2zc2zc2zc2zc2zc2zc\ 2zc2zc2zc2zc2zcbzcdzcfzchzcjzckzcjzcizcizchzchzcgz\ cgzcfzcmzcmzcmzcmzcmzcmzcmzcmzczzczzczzczzczzczzcz\ zUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzU\ zzUzzUzzUzzUzzUzzUzzUzzUz } frm:SliceJulibrot4 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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FOTD 20-12-12 (One to Doomsday [No Rating])
by Jim Muth 22 Dec '12

22 Dec '12

FOTD -- December 20, 2012 (No Rating) Fractal visionaries and enthusiasts: It's the day before the end of days here at Fractal Central, and nothing has happened so far. Our poor strange curious little rectangle has not been so lucky however. Very little of it is left in today's image. What *is* left appears as the mostly obscured yellow stuff near the center of the frame. Tomorrow will be the actual day of doom -- time to close the rectangular book. The rectangle will be gone and the remains won't make much of an image, but it's kind of hard to make a good picture of something that is not there. So say goodbye to the rectangle as you are saying goodbye to the rest of the world. With so little time left, the very brief 45-second calculation will seem to finish almost instantly. The finished image is posted online at: <http://www.crosscanpuzzles.com/Archives.html> Hi-def variations are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Back images are at: <http://www.Nahee.com/FOTD/> Clouds arrived just before sunrise here at Fractal Central today and thickened throughout the day, while the temperature hovered around 43F +6C. The approaching rain arrived at sunset. The fractal cat had a peaceful day; the humans' day was not quite as peaceful. Unless the end arrives sooner than expected, the next FOTD will be posted in 24 hours. If the predicted end fails to arrive (as I expect it will) the next FOTD after tomorrow's will be posted on December 27, one week from today, after a hiatus of 5 days. Until whenever, take care, and once again, we have met the enemy and found they is us. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= One_to_Doomsday { ; time=0:00:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=+0.001928538\ 67501304/+0.00075156576200417/107.7586/1.3369/0/\ -38.6598082540901018 params=99/98/79/82/-1.7435/\ -0.0008/0.000175/0.073883/2.003/0 float=y maxiter=8000 inside=0 logmap=55 periodicity=6 colors=00022M22M22L22L22K22K22J22J12I12I12H12H12G1\ 2G11F11F11E11E11D11D11C41011C11B11B11A11A119019018\ 018007007006006005005004004003003002002001001000Lc\ nKbmKbmKalKalKakJ`kJ`jJ`jJ_iJ_iIZhIZhIZgIYgIYfHYfH\ XeHXeHWeHWdGWdGVcGVcGVbGUbFUaFUaFT`FT`FS_ES_ESZERZ\ ERYERYEQYDQXDPXDPWDPWDOVCOVCOUCNUCNTCMTBMSBMSBLRBL\ RBLQAKQAKPAKPAJPAJO9IO9IN9IN9HM9HM8HL8GL8GK8FK8FJ7\ FJ7EI7EI7EH7DH7DH6CG6CG6CF6BF6BE5BE5AD5AD5AC59C49B\ 48B48A48A479379378368368357257256246245045134134A2\ 3KA3UK2cU2mc1zm1zm0zm0xp7un6sl6qj6nh5zm5zm5zm5zm4z\ m4zm4zm4zm3zm3zm3zm3zm2zm2zm2zm2zm1zm1zm1zm1zm0zm0\ zm0zm3zm2zm2zm2zm2zm2zm2zm2zm2zm2zc2zc2zc2zc2zc2zc\ 2zc2zc2zc2zc2zcbzcdzcfzchzcjzckzcjzcizcizchzchzcgz\ cgzcfzcmzcmzcmzcmzcmzcmzcmzcmzczzczzczzczzczzczzcz\ zUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzU\ zzUzzUzzUzzUzzUzzUzzUzzUz } frm:SliceJulibrot4 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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Albrecht Niekamp's "Strange Beauty" 1536705 (2012-12-21)
by Hal Lane 22 Dec '12

22 Dec '12

While Albrecht Niekamp is on vacation and away from a computer, he has asked me to put some of his images onto my server. I did not post a fractal for 2012-12-20. Here is a link to Albrecht's fractal "Strange Beauty" created using his multifractal_10 formula: http://www.emarketingiseasy.com/Albrecht/1536705.GIF Click the image in your browser for its full size, 1600 x 1200 pixels, and to prevent its being resampled by your browser. Albrecht's fractal "Strange Beauty" seems somehow 'royally' sinister to me. It has many very sharp, perhaps dangerous, features. Further, the spikes that don't sharpen to a point, but travel to other areas to merge with other features, split into three grasping "arms" that remind me of an actual animal, a type of tapeworm: http://carlzimmer.com/books/imgs/photo_03_big.gif A strangely beautiful fractal, but a very scary fractal! I've previously posted some variations I did on the Strange Beauty fractal. The version of color map used in the following images is a colorful, rather than royal, map -- previously posted by Albrecht: "Here are some zooms into Albrecht's Strange Beauty fractal that uses his Multifractal_10 formula. The fractal has quite a bit of nifty, colorful variety in it. All 640 x 480 non-anti-aliased. They're arranged in increasing zoom depth, with the 2nd and later fractals each a zoom into the previous one: Albrecht's original Strange Beauty fractal: http://www.emarketingiseasy.com/TESTS/FOTD/STRNGBUT.GIF And zooms into it: http://www.emarketingiseasy.com/TESTS/FOTD/STRNGBU2.GIF http://www.emarketingiseasy.com/TESTS/FOTD/STRNGBU3.GIF http://www.emarketingiseasy.com/TESTS/FOTD/STRNGBU4.GIF http://www.emarketingiseasy.com/TESTS/FOTD/STRNGBU5.GIF http://www.emarketingiseasy.com/TESTS/FOTD/STRNGBU6.GIF http://www.emarketingiseasy.com/TESTS/FOTD/STRNGBU7.GIF http://www.emarketingiseasy.com/TESTS/FOTD/STRNGBU8.GIF Has numerical loss of precision: http://www.emarketingiseasy.com/TESTS/FOTD/STRNGBU9.GIF Has extreme numerical loss of precision: http://www.emarketingiseasy.com/TESTS/FOTD/STRNGB10.GIF The parent fractal: http://www.emarketingiseasy.com/TESTS/FOTD/STRNGBUP.GIF And a zoom into the parent: http://www.emarketingiseasy.com/TESTS/FOTD/STRNGB11.GIF " Paul N. Lee also posted renders of some variations on this fractal using par files Albrecht previously posted: "1536704e { ; Inside_View 1536705 { ; Strange_Beauty 1536705d { ; The_Big_Ball You may find a 1024 x 768 image version of the above PARs uploaded to the following: http://www.nahee.com/Stuff/Albrecht_1536704e.GIF http://www.nahee.com/Stuff/Albrecht_1536705.GIF http://www.nahee.com/Stuff/Albrecht_1536705d.GIF " Here's "Strange Beauty's" color map: http://www.emarketingiseasy.com/Albrecht/1536705_map.jpg It has the four 'royal' colors in gradual shades from dark to light and back to dark again. This one starts with the color gold. This type of map allows fractals with the correct patterns in them to have smoothly-shaded three- dimensional metallic features. The Fractint parameter set is below. The ready-to-run full parameter file for the fractal, including the multifractal_10 formula, is here: http://www.emarketingiseasy.com/Albrecht/1536705.par - Hal Lane ######################## # hallane(a)earthlink.net ######################## ===== Start of par file ============================== 1536705 { ; Strange_Beauty ; secant-mmods-bees-phoen-newt ; time 0.05.49 XP Dos shell ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=mfr.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=-1.50137769253409600/+0.100910670672261\ 60/6855.058/1/165.000000000015433/-4.8305803801440\ 5611e-013 params=-0.05825983458967864/0.3785210730307932/153\ 67.64595767025/14235.4911030602/152048.0404808048/\ 384.1604894048/384.00482000595/256.1007683001/512.\ 1007683001/768.1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000000oNIzb0<2>zz1zzC<2>zzz<3>jqdfo_blU<3>M\ b8<3>LQ8KM8KJ8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBiOD\ jQF<3>qeBriAtm9vq8xu7zz5zz4zz3<8>zY4zV5zS5<3>zE6wE\ 6tD6<10>w8Px8Rx7S<3>z5_<3>f5Ma5IW4E<2>_4H<3>P3DN2C\ K2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0gy0h<3>u1mt1\ ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4KW0Qc<3>5Xc6\ Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<3>civflvinvlqvotv\ sww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI<4>XC\ AaB9fB7<3>zA0<13>SA1QA1NA1<3>D92<6>UXAW`BYcC<3>hrI\ <3>UnXRm_NlcJkgFfpAaz<6>_5fc0ce7_jFR } ==== End of par file ================================

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DOS Fractint "Restore" file list omits latest images
by Hal Lane 20 Dec '12

20 Dec '12

Does anyone know if the silent omitting of files from the "Restore" file list (see behavior below) is the result of a "compiled in" limitation in DOS Fractint or a memory limitation in the WinXP DOS environment? When I recently tried to "Restore" an image in my DOS Fractint Ver 20.04.4 under WinXP SP3, I discovered that I couldn't see the last few fractals that it had calculated in the directory listing of .gif images able to be Restored. The files were really there, and could be listed and viewed by other software -- but were just not presented in the Fractint "Restore" command's file list. I noted that I had 5 thousand and some-odd files in the /Fractint/ directory, and on a whim, moved 600 of my older images to a new folder. Lo and behold, the latest images appeared in the "Restore" command's file list! Any observations on this behavior would be appreciated. Fractint Developers, would you be kind enough to address any replies to the Fractint email list serve? Thanks! - Hal Lane ######################## # hallane(a)earthlink.net ########################

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Albrecht Niekamp's "Mandscape2" 20227MA (2012-12-19)
by Hal Lane 19 Dec '12

19 Dec '12

While Albrecht Niekamp is on vacation and away from a computer, he has asked me to put some of his images onto my server. Here is a link to Albrecht's fractal "Mandscape2" created using his multifractal_10 formula: http://www.emarketingiseasy.com/Albrecht/20227MA.GIF Click the image in your browser for its full size, 1600 x 1200 pixels, and to prevent its being resampled by your browser. In Albrecht's fractal parameter set he has a note: "asymmetrical inside." It does appear at first glance that the main features along the X-axis are symmetrical about the Y-axis, but closer inspection reveals that this is not so. The features along the X-axis are set in an electric, icy blue background appropriate for the current season in mid-to-high northern latitudes. I was tempted to cut Albrecht's fractal in half down the centerline and make an animated .GIF of the two superimposed halves repeatedly alternating in the image, so the differences between them would jump out at you, but, unfortunately, I don't have the time to do it right now. If someone reminds me next year, I'll try doing it then. In Albrecht's fractal "Mandscape2," the color map: http://www.emarketingiseasy.com/Albrecht/20227MA_map.jpg again has four colors in gradual shades from dark to light, but of four colors different from the color maps of the last few fractals I've posted for Albrecht. The Fractint parameter set is below. The ready-to-run full parameter file for the fractal, including the multifractal_10 formula, is here: http://www.emarketingiseasy.com/Albrecht/20227MA.par - Hal Lane ######################## # hallane(a)earthlink.net ######################## ===== Start of par file ============================== 20227ma { ;mandscape2 (2005) ; asymmetrical inside ; Time 0.14.07.06 reset=2004 type=formula formulafile=mfr10.frm formulaname=multifractal_10 function=exp/exp/exp/sin passes=t center-mag=-0.504822/4.44089e-016/0.9463538 params=-0.05825983458967864/0.3785210730307932/20227.32595710661/25255.1\ 111020602/151024.0204808192/384.32768524288/384.00482000595/128.10076800\ 01/512.10076800005/768.10076800002 float=y maxiter=1024 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=000376<2>121000001023025047049<5>0BL0DN0DP<4>0KZ0L`0Mb0Nd0Of0Qh<3\ >0Up4Yr8atCgvGkxKqz<3>4_s0Vq0Uo<12>0FQ0DO0DM<3>08E06C06A0480460240120001\ 00<12>R0LT0NV0PX0P<3>d0Wf0Yh0Z<3>p0e<3>xOtzUxyOuwIquCns6iq0g<2>k0bi0`g0_\ e0Z<3>Y0SW0RU0O<5>I0FG0EE0CC0A<3>304102010<4>0B10D10F10H20J20L20N2<2>0T4\ 0V40X3<3>0d40f50h5<3>0p6<3>WxZczeUyY<2>0s8<4>0i60g60e60c4<2>0Y40W30U4<5>\ 0I20G20E20C20A1081<3>0000101221532653863A84DA5EB5HB<2>7NG8PI8RJ9TKAVNAXM\ <3>DdTDfVEhWFjYFlYGn_Gp`Prd<3>zzz<2>_ulRsgHqaHo`GmZFkXFiX<5>BYOAWMAUL9SK\ <3>7KE6IC5GB5DA4B9497 } ==== End of par file ================================

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FOTD 19-12-12 (Two to Doomsday [No Rating])
by Jim Muth 19 Dec '12

19 Dec '12

FOTD -- December 19, 2012 (No Rating) Fractal visionaries and enthusiasts: What we are witnessing in today's image is the death of the cur- ious rectangle. No longer anywhere near perfect, the former quadrilateral has been twisted into a bent wet noodle. I began the destruction by altering the parameters, thereby changing both the orientation and location of the slice. The destruction will continue in the next two FOTD's, and then, who knows or cares what? The day of doom will be upon us, when the fate of an abstract fractal rectangle will have less significance than an ant trapped on a stick in the middle of the Pacific Ocean. But despite the hopelessness, the image is still worth a quick look. It calculates in only one minute, about as much time as is required to check the finished image on the web sites. The image is posted to the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> with high definition variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are online at: <http://www.Nahee.com/FOTD/> Mostly cloudy skies and a temperature of 45F +7C made today totally unremarkable. The fractal cat had an unremarkable day also. The humans' day was a bit more animated as we watched the midday news reports, frustrated that the current determination to see something done about the gun situation will soon fade away as people 'get over' their outrage. Despite my recent comments, both FL and I feel there are far too many guns in our culture, which is violent enough as it is; but like nearly everyone else, we haven't the slightest idea what to do about it. The next FOTD will be posted in 24 hours. Until then, take care, and let's get people who act different off the streets and into therapy. (Hey, wait a minute! That would include myself!) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Two_to_Doomsday { ; time=0:01:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=0/0/100 params=91.8376/90.7176/87.4531/89.1331/-1.7435/\ -0.0001/0.000175/0.073883/2.003/0 float=y maxiter=8000 inside=0 logmap=55 periodicity=6 colors=00022M22M22L22L22K22K22J22J12I12I12H12H12G1\ 2G11F11F11E11E11D11D11C41011C11B11B11A11A119019018\ 018007007006006005005004004003003002002001001000Lc\ nKbmKbmKalKalKakJ`kJ`jJ`jJ_iJ_iIZhIZhIZgIYgIYfHYfH\ XeHXeHWeHWdGWdGVcGVcGVbGUbFUaFUaFT`FT`FS_ES_ESZERZ\ ERYERYEQYDQXDPXDPWDPWDOVCOVCOUCNUCNTCMTBMSBMSBLRBL\ RBLQAKQAKPAKPAJPAJO9IO9IN9IN9HM9HM8HL8GL8GK8FK8FJ7\ FJ7EI7EI7EH7DH7DH6CG6CG6CF6BF6BE5BE5AD5AD5AC59C49B\ 48B48A48A479379378368368357257256246245045134134A2\ 3KA3UK2cU2mc1zm1zm0zm0xp7un6sl6qj6nh5zm5zm5zm5zm4z\ m4zm4zm4zm3zm3zm3zm3zm2zm2zm2zm2zm1zm1zm1zm1zm0zm0\ zm0zm3zm2zm2zm2zm2zm2zm2zm2zm2zm2zc2zc2zc2zc2zc2zc\ 2zc2zc2zc2zc2zcbzcdzcfzchzcjzckzcjzcizcizchzchzcgz\ cgzcfzcmzcmzcmzcmzcmzcmzcmzcmzczzczzczzczzczzczzcz\ zUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzU\ zzUzzUzzUzzUzzUzzUzzUzzUz } frm:SliceJulibrot4 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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Albrecht Niekamp's "Hades - The Gate to the Underworld" 21225LZ (2012-12-18)
by Hal Lane 19 Dec '12

19 Dec '12

While Albrecht Niekamp is on vacation and away from a computer, he has asked me to put some of his images onto my server. Here is a link to Albrecht's fractal "Hades - The Gate to the Underworld" created using his multifractal_10 formula: http://www.emarketingiseasy.com/Albrecht/21222HAD.GIF Click the image in your browser for its full size, 1600 x 1200 pixels, and to prevent its being resampled by your browser. In Albrecht's fractal "Hades - The Gate to the Underworld," the "Hades" color map: http://www.emarketingiseasy.com/Albrecht/21222HAD_map.jpg looks like it has the same *colors* in it as the "Many Mods" image's color map: http://www.emarketingiseasy.com/Albrecht/21225MM_map.jpg but, they're not shifted in location like the Many Mods" image's map. At the top of the fractal seems to be a red Sun and golden sands. At the bottom are perhaps symmetrical silver sand dunes. As one moves down closer to the central black Mandeloid, the sands get very much darker, and you come upon a ring of fire. Finally, you're confronted with the black, gaping maw of Hades, rimmed with fire. The Fractint parameter set is below. The ready-to-run full parameter file for the fractal, including the multifractal_10 formula, is here: http://www.emarketingiseasy.com/Albrecht/21222HAD.par - Hal Lane ######################## # hallane(a)earthlink.net ######################## ===== Start of par file ============================== 21222had { ;Hades (2005) ; The gate to the underworld ; Time 2.09.12.02 reset=2004 type=formula formulafile=mfr10.frm formulaname=multifractal_10 function=cos/sin/sin/sin passes=t center-mag=-0.188053/0.00113846/24.61324/1/-90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/21222.32595700021/22222.0\ 506020602/551024.0204808192/384.32768524288/384.0048000545/256.100768555\ 55/512.10076855555/768.10076855555 float=y maxiter=3072 inside=maxiter outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=200222<24>iiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0cq0es<3\ >0kz<25>09C08A068<2>022000211<21>icNkeOmfP<3>unTwpVxqWzsX<25>CB7A96875<3\ >000400<23>o00q00s00<3>z00<31>000 } ==== End of par file ================================

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FOTD 17-12-12 (Four to Doomsday [No Rating])
by Jim Muth 18 Dec '12

18 Dec '12

FOTD -- December 17, 2012 (No Rating) Fractal visionaries and enthusiasts: Wow! Only four more days until the end of time. Actually, if time really were to end in four days, I wonder what would come next. Most likely, it would be a fractal. And speaking of fractals, we have one today. The indescribable parent fractal came about when I combined 7 negative parts of Z^(-1.9) with 1.5 negative parts of Z^(-9.1) and added (1/C) on each iteration. This parent consists of three circular bays with a prominent minibrot lying some distance east of the main body. Today's scene lies in a triangular open area connected with the East Valley of this minibrot. The name "Four to Doomsday" indicates that the day of doom is growing near indeed. The calculation time of 9-1/2 minutes will use up a portion of this time. But saving time is where the web sites become most useful. Save time by checking the finished image at: <http://www.crosscanpuzzles.com/Archives.html> and don't forget the high-definition variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are at: <http://www.Nahee.com/FOTD/> The heavy clouds and temperature of 50F 10C that prevailed here at Fractal central today was so routine that it left nothing to comment on. The fractal cats had no comment either, though the humans were quite animated at lunch time as we heard the litany about the need for tougher gun laws being repeated for the ten- hundredth time on TV. We want to hear more about the need to change the culture than the plans for another gun-control law that will do little or nothing to reduce violence. The next FOTD will be posted in 24 hours. Until then, take care, and I wonder when technology will solve the problem of violence. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Four_to_Doomsday { ; time=0:09:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=t center-mag=+1.086781515365839/+0.0425852688913911/\ 1.885e+009/1/-20/0 params=-7/-1.9/-1.5/-9.1/0/0/0/0 float=y maxiter=4500 inside=0 logmap=536 periodicity=6 colors=000ajK_WK_WK_VK`lK`dK`jKahKaiKagKblKbfKbiKc\ aKchKccK`lKYjKVnKShKPoKMlKKmHIoFGoDErBCpAAoA8mA6mA\ 5mA5lA5k95j95i95i95h94g94f84f84e84d84c84b84b74a74`\ 74_74_73Z73Y73X63W63W63V63U63T63S53S53R52Q52P52P52\ O42N42M42L42L42K42J32I32I31H31G31F31E31E21D21C21P3\ 1B21A21A21910810710710610510400300300200100002pc1o\ b1na1m`1l`1k_1jZ1iZ1hY1gX1fX1eW1eV1dV1cU1bT1aS1`S1\ _R1ZQ1YQ1XP1WO1VO1VN1UM1TM1SL1RK1QK0PJ0OI0NH0MH0LG\ 0LF0KF0JE0ID0HD0GC0FB0EB0DA0C90B80A80A709608607506\ 4054043032A6AKEKUMUcUcmUmwTwvSruSqtRpsRorQnqQmpPlo\ PknOjmOilNhkNgjMfiMfhLegLdfKceKbdJacJ`bI_aIZ`HY_HX\ ZGWYGVXFUWFTVFTUESTERSDQRDPQCOPCNOUMNULMUKLUJKUIJU\ HIUGHUFGUEFUEEcDDcCCcBBcAAc99c88z77z66z55z44z33z22\ z11z0zzzzzxzzvzzuzzszzqzzpzznzzmzzkzzizzhzzfzzezzc\ zzazz`zzZzzXzzWzzUzzTzzRzzPzzOzzMzzLzzJzzHzzGzzEzz\ CzzBzz9zzKzzKzzKzzKzzKzzK } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 18-12-12 (Three to Doomsday [No Rating])
by Jim Muth 18 Dec '12

18 Dec '12

FOTD -- December 18, 2012 (No Rating) Fractal visionaries and enthusiasts: Today's fractal features another glance at the Z^(2.003)+C rectangle. This time I have adorned it with a lively blue-and- gold color scheme, and sliced it at an angle rotated -1,-1,-1,+1 degrees from the true Julia orientation. Actually, the image is one of the better apparitions of the rectangle. Unfortunately, if the predicted doom actually arrives in three days, this could be the final apparition. The name "Three to Doomsday" indicates that the end is near enough for knees to begin knocking in terror. But the calculation time of 1-1/3 minutes will squander little of the brief remaining time. The finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> with hi-def variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> and all the back images at: <http://www.Nahee.com/FOTD/> Heavy clouds and showers of rain put a damper on outdoor activities here at Fractal Central today. The temperature of 48F +9C was mild for the season however, and kept the unpleasant- ness at a minimum. The cats, always pleasant, slept through most of the day. A full-day's sleep might seem boring to humans but it is quite normal for cats. The humans continued to watch the TV news and continued to wonder why no one even recognizes the underlying cause of gun violence. The next FOTD, (due to doomsday, possibly the third to last), will be posted in 24 hours. Until then, take care, and some say the solution to gun violence is to enact sweeping legislation to protect us from such violence. Perhaps we must ban the private possession of all guns. (I actually heard it.) Of course, if such legislation were ever passed, the result in rural areas such as Central Pennsylvania would be to turn the farmers, who would not give up their guns, into criminals. And if anyone then tried to enforce the gun ban, the result would be civil war. (I heard this also.) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Three_to_Doomsday { ; time=0:01:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=0/0/100 params=89/89/89/91/-1.7435/0/0.000175/0.073883/\ 2.003/0 float=y maxiter=10000 inside=0 logmap=55 periodicity=6 colors=00022M22M22L22L22K22K22J22J12I12I12H12H12G1\ 2G11F11F11E11E11D11D11C41011C11B11B11A11A119019018\ 018007007006006005005004004003003002002001001000Lc\ nKbmKbmKalKalKakJ`kJ`jJ`jJ_iJ_iIZhIZhIZgIYgIYfHYfH\ XeHXeHWeHWdGWdGVcGVcGVbGUbFUaFUaFT`FT`FS_ES_ESZERZ\ ERYERYEQYDQXDPXDPWDPWDOVCOVCOUCNUCNTCMTBMSBMSBLRBL\ RBLQAKQAKPAKPAJPAJO9IO9IN9IN9HM9HM8HL8GL8GK8FK8FJ7\ FJ7EI7EI7EH7DH7DH6CG6CG6CF6BF6BE5BE5AD5AD5AC59C49B\ 48B48A48A479379378368368357257256246245045134134A2\ 3KA3UK2cU2mc1zm1zm0zm0xp7un6sl6qj6nh5zm5zm5zm5zm4z\ m4zm4zm4zm3zm3zm3zm3zm2zm2zm2zm2zm1zm1zm1zm1zm0zm0\ zm0zm3zm2zm2zm2zm2zm2zm2zm2zm2zm2zc2zc2zc2zc2zc2zc\ 2zc2zc2zc2zc2zcbzcdzcfzchzcjzckzcjzcizcizchzchzcgz\ cgzcfzcmzcmzcmzcmzcmzcmzcmzcmzczzczzczzczzczzczzcz\ zUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzU\ zzUzzUzzUzzUzzUzzUzzUzzUz } frm:SliceJulibrot4 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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Spirals... 38400 of them
by Tony Hanmer 18 Dec '12

18 Dec '12

Greetings, Some time (nearly a year) ago I, finally posted details of a huge set of beautiful IFS spirals which I have found to the Apophysis forum, at http://www.apophysis.org/forums/viewtopic.php?f=2&t=1352&p=0&e=0&sid=d88420… They were found using combinatorics methods, i.e. starting with a small set of holons and varying certain characteristics of these, such as rotation or relative position. The zip files include a text tile giving more details. These are also able to be rendered in Fractint, or adapted, I would imagine, to 3d versions in XenoDream. Also, in Apophysis, they could all be considered as keyframes for an endless animation, from any one of them to any other and so on. This might be the most profound way of using them. Hope someone finds a use for these. Tony Hanmer Tbilisi, Republic of Georgia

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Albrecht Niekamp's "Lite Zoom" 21225LZ (2012-12-17)
by Hal Lane 17 Dec '12

17 Dec '12

While Albrecht Niekamp is on vacation and away from a computer, he has asked me to put some of his images onto my server. Here is a link to Albrecht's fractal "Lite Zoom" created using his multifractal_10 formula: http://www.emarketingiseasy.com/Albrecht/21225LZ.GIF Click the image in your browser for its full size, 1600 x 1200 pixels, and to prevent its being resampled by your browser. Albrecht's fractal, "Lite Zoom" is related to the 21225MM.GIF and 21225PA.GIF images. They share not only the same color map, but also the same five formula types selected by the digits: "21225" in the file's name: Mandelbrot, Secant, Mandelbrot, Mandelbrot, and Many Mods. The features in the fractal make some use of the smooth gradations of the four colors in the color map: http://www.emarketingiseasy.com/Albrecht/21225MM_map.jpg producing some smoothly-shaded areas. See my comments about this color map in yesterday's (Dec 16, 2012) Fractint post. It almost seems like delicate gold ferns are dipping into the blue water making waves in the water. The red and gold circular frame around the blue water makes it feel like the blue water is in a small artificial pond -- surrounded by a walkway made of tiny pieces of colorful gravel. The vertically centered ball balanced on a cone is rendered in bold patterns and colors with some features having a bit of the three dimensional aspect mentioned above. The Fractint parameter set is below. The ready-to-run full parameter file for the fractal, including the multifractal_10 formula, is here: http://www.emarketingiseasy.com/Albrecht/21225LZ.par - Hal Lane ######################## # hallane(a)earthlink.net ######################## ===== Start of par file ============================== 21225lz { ;Lite_Zoom (2005) ; Different outside ; Time 1.51.37.67 reset=2004 type=formula formulafile=mfr10.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=-1.50466/1.66533e-016/4.219409/1/-90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/21225.64595767025/13234.0\ 311030602/151024.0204808192/384.32768524288/384.00482000595/256.10076830\ 01/512.1007683001/768.1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=2000LS<11>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<21>icNkeOmfP<3\ >unTwpVxqWzsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>00\ 0<11>LLLNNNPPPQQQSSSUUU<6>fffgggiiijjjlll<3>sss<25>BBB999777<2>222000012\ <11>0JQ } ==== End of par file ================================

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FOTD 16-12-12 (Five to Doomsday [No Rating])
by Jim Muth 17 Dec '12

17 Dec '12

FOTD -- December 16, 2012 (No Rating) Fractal visionaries and enthusiasts: Today's image is a result of mixing 0.01 part of Z^(-2) with Z^(2) and adding straight Z on each iteration. The parent fractal is a moth-eaten Mandelbrot set filled with debris. This debris is filled with smaller distorted M-sets and lots of mandel fragments. Today's image with its minibrot at the center is located in the East Valley area of what remains of the large minibrot on the main-stem of the moth-eaten parent. The name "Five to Doomsday" indicates that time is growing short. The calculation time of one short minute will waste little of the precious remaining time. Save time. Check the finished image at: <http://www.crosscanpuzzles.com/Archives.html> The hi-def variations are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> and the back images are at: <http://www.Nahee.com/FOTD/> Heavy clouds and a temperature of 48F +9C made today a day to be soon forgotten. The fractal cats forgot it before it began, while the humans had a rather busy day. The next FOTD will be posted in 24 hours. Until then, take care, and the problem with our society is that it has programmed itself into a dead end. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Five_to_Doomsday { ; time=0:01:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-1.554435017013601/+0.0000055252962729/\ 9470414/1/-115/0 params=1/2/0.01/-2/0/0/0/0 float=y maxiter=1400 inside=0 logmap=61 periodicity=6 colors=000HbuK`qMZmNViNReONaOJYPFTPBOP7JUBHZEGbIEg\ LDkPBpSAtV9sbNrj_qrlroksljsjitgitehubgu`gppiC64H9C\ LBJPDRTFYXHd`JldLshNzcRsZVmVZgQb`MfVHjPDmJfoNbhVZa\ bVWjRPrOJzPPvPUsPZpPcmPiiPnfPscPx`_mTibLsTD3Qy5Uz7\ Yz9azBezDizFmzGqzHkxHfwIauIXtIRsJMqJHpJCoLGgNJ`PNT\ QQMSQKUQIVQGXQFZQD_QBaQ9bQ8RD2QB6PA9O9CN8FM7ISAOXC\ TbEZgGcmIirKnwMsRH9MSJHbTCmb7wlCumHtmMrmRqmWpn`nne\ mnilnZa`PSNFIArf0ka4dX7YSBSOELJHEEL79O15RuVCp_GkcK\ fgOakSXoWTsZSh8QeGObOM`VKYbIWiOPTUJDJ_H8oKSbLkQLWN\ XHLgOKdUJb_J_eIYkIVqHTwHRxGSxFTyEUyDVyDVqBXi9Zb8`V\ 6bN4dG3eF7bFA_FEYFHVELSEOQESNEVLHZPJbTLeXNi`PldRph\ TslcoZnkLxg8mZBcRETIHJAK92MKFPUSSccUb_VaXWaUW`RX`O\ X_LY_IYXPZVV_Ta`RgaPnbNtcLzdSkhZYkeJol5rnBloGfqL`r\ QWsWQu`KveEwj9xa7yT5zK3zC1Y`96yGCuFIrFOoEUlE_iDefD\ kcCq`CSiA3q9Id7XS5_VBbXGdZMg`RibXldanffibcd_a_X_VU\ YQRWO63D822925DA8HIBLPEPX } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 15-12-12 (Six to Doomsday [No Rating])
by Jim Muth 17 Dec '12

17 Dec '12

FOTD -- December 15, 2012 (No Rating) Fractal visionaries and enthusiasts: If you're looking for a long fractal discussion, look elsewhere. For the next several days I'll be spreading my ideas about the disintegration of our culture. Today's image is a near-Julia set of the Z^(1.5)+C ground level Mandeloid. It is rotated 0.01 degree toward the Oblate direction, and is striking for the number and variety of fractal trees it holds. And like the strange mysterious rectangle, it is also one of my very early fractals. The finished image is at: <http://www.crosscanpuzzles.com/Archives.html> High-definition variations are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are at: <http://www.Nahee.com/FOTD/> When I began the countdown to doomsday, I was being frivolous. I didn't actually expect the end of time to come on December 21. Until now, all predictions of the end of the world have had one thing in common -- they have been wrong. But now, after the latest school massacre, it looks like I could be right, maybe not in six days, but not too long thereafter. With unending massacres and depressed adolescents walking about in a technological trance, texting like frustrated demons, maybe the end really is approaching, at least the end of our present way of life. Invading aliens from Alpha Centauri could hardly have done a better job of destruction than we have done and are still doing to ourselves. The human race is a part of the great spiritual reality known as nature. (Of course, rationalists will deny the spiritual part.) With all the technological gadgets, video games, mass media entertainment etc. we have basically cut ourselves off from our source and are floundering about like fish out of water. And what are we willing to do about it? Little more than purchase ever more advanced technological devices. Technology will save us . . . I guess it will, but . . . then again I'm not too sure. I see myself as one of a dying breed. When I go out on my morning walk to the nearby river, I carry no smart device with me. I enjoy the nature in which I am immersed. I see the high clouds in the sky indicating that warmer weather is on the way. I see the early sun striking the bare treetops. At the river I see that the water level has gone down a bit. It has been rather dry recently. And I hear honking. Looking up, I see geese flying overhead. Out on the water I see ducks bobbing, and an egret wading near the bank. And all this is free. Then I think of a local boy who was killed about a week ago when he was struck by a train while walking along the tracks to school. His hi-tech headset was so loud that he did not hear the train coming. Could something be wrong with our modern life style? It's no problem however. Before long, the codgers like myself who still remember the old times will be gone, and everyone will be free to enjoy the technological wonderland we are creating for ourselves. The day actually turned rather pleasant here at Fractal Central. At least the cats thought so. The temperature of 46F +8C was above normal, while the variably cloudy sky let through just enough sun to keep things cheerful. The next FOTD will be posted in about 24 hours. Until then, take care, and there are far too many people being killed with illegal guns. Why can't our congressmen get off their bottoms and pass legislation banning illegal guns? (Hey, I actually heard it on the local talk radio.) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Six_to_Doomsday { ; time=0:00:45.22 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=0.28169/0/1.2 params=89.99/89.99/90.01/0/-0.186/0/0/0/1.5/0 float=y maxiter=5000 inside=0 periodicity=6 colors=0000I40I40Ia0He0Hg0Gj0Gk0Fl0Fk0Ek0Eh0Ef0Dc0\ D`0CZ0CW0BT0AR09O08L07I06G05D04A038025012TAsO8iJ6`\ E5S93I4194Pz3Nw3Mt3Lq3Kn3Jk2Ih2He2Fc2E`2DY2CV1BS1A\ P19M17K16H05E04B038025012zyIsrGmlEgfC``AVV9PO7II5C\ C3661ceH`bGZ`FXZEVXDTUCRUYTSZUR_WP`YNa_Lb`KbYI_WHY\ UGWSFUQESODQMCNKBLIAJG8H1B0E7FC6DA5A848636424212xl\ 2h_1UO1FC0aygJVMekichfafd_dbYa`W_ZUYWSWUQTSORQMPOK\ MLIKJGIHEGFCDDABA898666444222yzqstlmnghhbbcYXYTSSO\ MMJGHEBB95547MW6KT6IR5HP5FM4EK4CI3BG39D27B26914613\ 4012Ec7C_6BX5AU59R48O47L36H35D24A2361221qCRnANk9Kf\ 8Ia7GX6ES5CO4AJ38E26914402TvCRrBPoAOlAMi9Lf8Jc8I`7\ GY6FV6DR5CO5AL49I37F36C24913611307tA3S5XKsUInRGiOF\ eMD`JBWGASD8NB6I85E5392148PQ7MN6KL6IJ5GH4EF4CD3AA2\ 88266144022pC3mB2jA2gA2d92b82_82X71U61R61P51M51J41\ G30D30B20810510200RwZMmTIcNDUH9KB4A5hoEelDciCagB_d\ BXbAV_9TX9RV8OS7MQ7KN6IK5 } frm:SliceJulibrot4 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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Albrecht Niekamp's "Wild Vision" (2012-12-16)
by Hal Lane 16 Dec '12

16 Dec '12

While Albrecht Niekamp is on vacation and away from a computer, he has asked me to put some of his images onto my server. Here is a link to Albrecht's fractal "Wild Vision" created using his multifractal_10 formula: http://www.emarketingiseasy.com/Albrecht/21225MM.GIF Click the image in your browser for its full size, 1600 x 1200 pixels, and to prevent its being resampled by your browser. Albrecht says that there was a typing error in the original parameter file that he posted 2005, so no one has seen this image yet. I tested the parameter file at the link below and it appears to work correctly. Albrecht's fractal, "Wild Vision" is very striking to me, primarily because its features almost seem carefully arranged -- and has a nice combination of bold and intricate features. The features of the fractal make good use of the smooth shading of the four colors in the color map: http://www.emarketingiseasy.com/Albrecht/21225MM_map.jpg producing smoothly-shaded areas. These smoothly- shaded areas have the further characteristic of being shaded from black to the fully-saturated color, and then back to black, creating a three dimensional effect that reminds me of many of Paul Carlson's fractals. The Fractint parameter set is below. The ready-to-run full parameter file for the fractal, including the multifractal_10 formula, is here: http://www.emarketingiseasy.com/Albrecht/21225MM.par - Hal Lane ######################## # hallane(a)earthlink.net ######################## ===== Start of par file ============================== 21225mm { ; Wild_Vision (2005) ; Time 3.23.44.07 reset=2004 type=formula formulafile=mfr10.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=-1.22699/8.32667e-017/13.33333/1/90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/21225.64595718025/23434.4\ 911030602/152048.0409608192/384.3276898304/384.00482000595/256.100768300\ 1/512.1007683001/768.1007683001 float=y maxiter=3072 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=2000KQ<6>09C08A068<2>022000211<21>icNkeOmfP<3>unTwpVxqWzsX<25>CB7\ A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<9>IIIKKKLLL<9>bbbd\ ddfffgggiiijjj<3>qqqsssqqq<24>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<1\ 7>0LS } ==== End of par file ================================

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Albrecht Niekamp's "Pandemonium " (2012-12-15)
by Hal Lane 16 Dec '12

16 Dec '12

While Albrecht Niekamp is on vacation and away from a computer, he has asked me to put some of his images onto my server. Due to sub-standard book-keeping here, it may happen that a post of one of Albrecht's fractals might be duplicated. Please try to find it in your heart to forgive me if this happens. Here is a link to Albrecht's fractal "Pandemonium" created using his multifractal_10 formula: http://www.emarketingiseasy.com/Albrecht/21225PA.GIF Click the image in your browser for its full size, 1600 x 1200 pixels, and to prevent its being resampled by your browser. Albrecht's fractal, "Pandemonium" seems very 'regal' to me, primarily because of its 'royal' colors: gold, silver, red and blue. The features in the fractal are varied and complex. The features of the fractal (with the exception of the background) do not make use of the smooth shading of the four colors in the color map: http://www.emarketingiseasy.com/Albrecht/21225PA_map.jpg I suspect that Albrecht may have posted this fractal in 2005, when it was originally created. The Fractint parameter set is below. The ready-to-run full parameter file for the fractal, including the multifractal_10 formula, is here: http://www.emarketingiseasy.com/Albrecht/21225PA.par - Hal Lane ######################## # hallane(a)earthlink.net ######################## ===== Start of par file ============================== 21225pa { ;pandemonium (2005) ; Time 0.21.15.48 ; reset=2004 type=formula formulafile=mfr10.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=-0.489028/0/0.6666667 params=-0.05825983458967864/0.3785210730307932/21225.64595718025/21235.0\ 311030602/150056.0204808192/384.32768524288/384.00482000595/256.10076830\ 01/512.1007683001/768.1007683001 float=y maxiter=3072 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=2000gt<22>09C08A068<2>022000211<21>icNkeOmfP<3>unTwpVxqWzsX<25>CB\ 7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<23>fffgggiiijjjll\ l<3>sss<25>BBB999777<2>222000012<22>0_k0am0bo0cq<4>0kz0jx0hv } ==== End of par file ================================

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FOTD 14-12-12 (Seven to Doomsday [No Rating])
by Jim Muth 15 Dec '12

15 Dec '12

FOTD -- December 14, 2012 (No Rating) Fractal visionaries and enthusiasts: Today there are only seven short days before the end of time, and we all know how quickly a day can go by. But even when we are all gone, fractals will continue forever, so who am I to give up on fractals when they will never give up on me. Today's image is a view of the mysterious Z^(2.003) rectangle as it appears when rotated 4 degrees from the Julia direction toward the oblate direction. At this angle the original rectangle appears more like a fan partly filled with debris, but in this debris a new shorter and wider rectangle has appeared. The features surrounding the rectangle have been altered to the point of unrecognizability, though a few patches of the pure Julia features still remain. And even though today's change is great, you ain't seen nothing yet! The name "Seven to Doomsday" simply tells the time remaining for each of us to exist. The calculation time of 2-1/2 minutes cuts into this brief time, but let's eat, drink and be merry today, for in seven days we . . .? Time is growing short. Before the final end arrives, check the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> And enjoy the variations in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are available at: <http://www.Nahee.com/FOTD/> Lots of sun and a temperature of 46F +8C made today quite pleasant here at Fractal Central. While the cats watched the world go by, the humans kept busy preparing for the upcoming holidays, which will be in the past in 19 days -- that is unless the day of doom arrives in only seven days, in which case the holidays will never end. The next FOTD is due to be posted in 24 hours, so check for it then. Until next time, take care, and there has been another mass shooting. Ho hum! Such mass shootings are becoming all the rage among the trendy set. It looks like everyone wants a slice of the action! But murder is wrong! Something must be done! So why don't we ban all private possession of firearms? Then when a lunatic shoots up a school and kills some kids, we'll be able to charge him with possession of an illegal and probably stolen firearm. With such a serious charge hanging over his head and possible imprisonment facing him, even the most determined lunatic would think twice before killing innocent people. My opinion -- to ban all firearms would be futile. My solution -- to change the materialistic, technologically advanced but spiritually bankrupt world view of our modern culture, which makes our existence appear meaningless and totally hopeless. (And I don't mean we should go out and try to persuade people to believe in any particular religion.) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Seven_to_Doomsady { ; time=0:02:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=1 float=y center-mag=+0.004422/0/118/0.6326/0/14.19452852516 params=86/86/90/86/-1.7435/0/0.000175/0.073883/2.0\ 03/0 maxiter=2750 inside=0 logmap=58 periodicity=6 colors=0009RA8PA7NA6M95L84K73K5BK4KU3Vd2eo1mwCitBe\ oAaj9Ye8Ua7QX6NS5JN4FJ3BE2791340a4D_3CY3BW3BV3AT3A\ R29P28O28M27K27J26H15F15D14C14A13802602501301000cw\ KUtKMqKIlKGiJFgIEeHDcGDaFC_EBYEBWDAUC9SB9QA8O97M96\ K86I75G64E54C43A4283262141020bLX`KVZJUXISWHRUGPSFO\ REMPDLNCKMBIKAHIAFG9EF8CD7BB6AA588476355243121U1Bu\ qAqn9nk9kh8he8eb7b_6_Y6XV5US5RP4OM4LJ3IH2FE2ZB1Z81\ Z50Z2sWeePVSILEZA5lk4gf4ba3YX3TS2OO2JJ1EE1Z90Z4vCx\ pAqj9kd8eZ7_TBUNZOHZIBZC5Z6XyuTrnPkhMdaIbWEWPBZJ7Z\ C3Z6BMdAKa9JZ8IW7HT7FQ6ZN5ZK4ZH3ZE3ZB2Z81Z50Z2AZT5\ ZEDzjBtc9kX7bQ5VK3MD1Z6BzKAxI9tH8pGb_`fbUjdMnfFrh8\ kfAedCZbDT`FNZHGXIAVK4UL6WN7YP8_QAaSBcTCeVEgXFiYGk\ _Hl`JkZLkXNkWPkUQkTSkRUkQWkOXkNZhL`hKbhIdhGehFghDi\ hCkhAlm9nm7pm6rm4sm3tm8tmCumGzzKzzOzzTzzXzz`zzdzzh\ zzfzzezzdzzbzzazz`zzZzzYzzXzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:SliceJulibrot4 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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Albrecht Niekamp's "The Miracle" (2012-12-14)
by Hal Lane 15 Dec '12

15 Dec '12

While Albrecht Niekamp is on vacation and away from a computer, he has asked me to put some of his images onto my server. Due to sub-standard book-keeping here, it may happen that a post of one of Albrecht's fractals might be duplicated. Please try to find it in your heart to forgive me if this happens. Here is a link to Albrecht's fractal "The Miracle" created using his multifractal_10 formula: http://www.emarketingiseasy.com/Albrecht/1536141.GIF Click the image in your browser for its full size, 1600 x 1200 pixels, and to prevent its being resampled by your browser. Albrecht's fractal, "The Miracle" has a comment in its parameter file: "There's life inside." I'm afraid that what I see is 'afterlife.' Inside the confetti-like chaos in the top half of his fractal, I see a blue 'heaven' -- and the lower half of the fractal seems to be an appropriately-colored burning Hades. There's a tense standoff in the black field between the two choices of afterlife -- between a pair of scrolls above and a triangular devil's head below. The maw to the fiery furnace awaits below. Good luck! The color map in Albrecht's fractal is here: http://www.emarketingiseasy.com/Albrecht/1536141_map.jpg -- and is a map used by Albrecht in several of his fractals. The Fractint parameter set is below. The ready-to-run full parameter file for the fractal, including the multifractal_10 formula, is here: http://www.emarketingiseasy.com/Albrecht/1536141.par - Hal Lane ######################## # hallane(a)earthlink.net ######################## ===== Start of par file ============================== 1536141 { ; The_Miracle ; Theres life inside ; Time 0.29.05 Dos Shell 1600/1200 ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=0.0206766/-0.0053525/6.831816/1/-90/3.8\ 8578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/213\ 64.64595712822/14235.4911030602/152048.0404808048/\ 384.1604894048/384.00482000595/256.1007683001/512.\ 1007683001/768.1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000000zr0zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>L\ Q8KM8KJ8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>\ qeBriAtm9vq8xu7zz5zz4zz3<4>zj4zg4zc4<3>zS5zP5zL6zI\ 6zE6wE6tD6<6>vAIv9Kv9M<3>x7Sy7Uy6Wz6Yz5_<3>f5Ma5IW\ 4E<2>_4H<3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>\ y0fz0gy0h<3>u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAA\ G7FO4KW0Qc<3>5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<\ 3>civflvinvlqvotvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa\ <3>8JP8FL8CI<3>SCCXCAaB9<3>uA2zA0xA0<12>SA1QA1NA1<\ 3>D92<6>UXAW`BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJo\ SFlWAi_5fc0ce7_jFRoNIzb0zj0 } ==== End of par file ================================

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FOTD 11-12-12 (Ten to Doomsday [No Rating])
by Jim Muth 14 Dec '12

14 Dec '12

FOTD -- December 11. 2012 (No Rating) Fractal visionaries and enthusiasts: Today's image is named "Ten to Doomsday". As everyone who watches TV knows, the world will end on December 21, 2001, ten days from today, on Friday of next week at 23:60:00 hours GMT, the single moment when the day of doom will prevail over the entire earth! In recognition of the coming end, I am beginning the countdown to destruction today and presenting ten doomsday fractals, the first of which appears as today's FOTD. I gave the image no rating. After all, what is the use of rating an image that will be swallowed up and forgotten in the mists of history in just ten days. For those who still care, the image is a scene in the area of the period-5 bud on the southwest shore line of the main bay of the Mandelbrot set. It looks nothing at all like a Mandelbrot bud because it is sliced at an unimaginable angle in four-dimensional space. To see the Mandelbrot bud in its true form, simply change the p1 and p2 parameters to 0,0 and recalculate the scene. The prominent vertical pillars are what I call bridges. They appear only in the odd planes of the Julibrot, and indicate that no matter where the points begin their wanderings, they will eventually settle into the same orbits. The calculation time of 1-1/4 minutes is mercifully brief. With so little time remaining to enjoy life, we would not want to waste a single precious minute. The mercy can be increased by viewing the finished image at: <http://www.crosscanpuzzles.com/Archives.html> And by checking the hi-def variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are available at: <http://www.Nahee.com/FOTD/> Yesterday's rain ended early this morning after dropping about 1/2 inch or 1-1/2cm of rain. A mix of left-over clouds and sun with a temperature of 45F +7C made today feel like a typical mid- December day here at Fractal Central. The humans and cats had a typical day also. The next FOTD will be posted in the proper time, whenever that is. Until the next FOTD appears, take care, and don't be fooled into believing that those so-called 'reality' shows flooding the TV channels are actually real. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Ten_to_Doomsday { ; time=0:01:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=t float=y center-mag=0.263913/-0.578499/9.105478 params=75/\ 90/0/80/-0.75/0/0/0/2/0 maxiter=5200 inside=0 logmap=5 periodicity=6 colors=000JF1MJ6PNBSQGVULYXP``UbcZegchjgknlnqqquvs\ xzprxnmwlhujbthYrfTqdOp_OoVPnQPmLQlGQkBRj5Pi6Rj7Sk\ 7Tl8Ul8Vm9WnAYoAZoB_pB`qCarCarkgSigTggUffVdfWbeXae\ Y_dYYdZXc_Vc`TcaSbbQbcOacNadL`eJ`fI_gG_hE_iDZiBZj9\ Yk8Yl6Xm4Xn1Wo3Xn4Yn5Yn7Zn8Zn9_nB_nC`nD`nFanGanHbn\ IbnKcnLcnMdnOdnPenQenSfnTfnUgnVgnXhnYhnZin`inajnbj\ ndkneknflnglnimnjmnknnmnnnonoonqpnrpnsqntqnqrmosmm\ tmjumhvmfwmgulgtkgsjgqigphhohhmghlfhkehjdihcigcifb\ idaic`jb_ja_j_ZjZYjYXkWWkVVkUVkTUkRTlQSlPRlNQlMQlL\ PmKOmINmHMmGMmELnDKnCJnBIn9Hn8Ho7Go5Fo4Eo3Dn1Eo2Do\ 3Dp4Dp5Cp6Cq7Cq8Cq9BrABrBBrCBsDAsEAsFAtGAtH9tI9uJ9\ uK9uL8vM8vN8vO8wP7wQ7wR7xS7xT6xU6yV6yW6yX5zY5zZ5zZ\ 5ya6xc7wf8vh9ukAtmBvn9soBpoDmoEkoGhoHeoJcoK`oMYoNW\ oPTpRQpSNpULpVIpXFpYDp_Ap`7pb3oe5pc6pb8p`9p_ApZCpX\ DpWFpUGpTHpSJqQKqPMqNNqMOqLQqJRqITqGUqFXtBVqEToGRm\ JPkLOhNMfQKdSIbUG`XFYZDW` } frm:SliceJulibrot4 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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FOTD 13-12-12 (Eight to Doomsday [No Rating])
by Jim Muth 14 Dec '12

14 Dec '12

FOTD -- December 13, 2012 (No Rating) Fractal visionaries and enthusiasts: Today's pre-doomsday fractal is a close-up of the edge of the curious rectangle that appeared in yesterday's image. The slow top part of the scene is the inside of the rectangle, the much faster bottom part consists of outside stuff. To me, the image appears as little more than a vast wasteland, perhaps the way our earth will appear the day after doom. The calculation starts out slow, but as the scan moves down the screen, the calculation speeds up condiderably. The total time of 3-3/4 minutes is slower than I would prefer, but still fast enough to allow time to prepare for the end. The name "Eight to Doomsday" indicates that the remaining days are dwindling fast. The finished image may be viewed at: <http://www.crosscanpuzzles.com/Archives.html> with the hi-def variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are posted at: <http://www.Nahee.com/FOTD/> Total sun and a temperature of 43F +6C made today near ideal for the middle of December here at Fractal Central. The cats and humans had an uneventful day of preparing for the holiday season. The next FOTD will be posted in 24 hours, but beware, the day of doom is steadily approaching. Until then, take care, and where will you be when time runs out? Or perhaps a better question is where will I be. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Eight_to_Doomsday { ; time=0:03:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=1 center-mag=-0.001145394/-0.003838487/2218/1/7.5/0 params=90/90/90/90/-1.74358/7.09952e-005/0.00011/\ 0.07389/2.003/0 float=y maxiter=3600 inside=0 logmap=50 periodicity=6 colors=000BRQBRPAQOAQN9PM9PL9OK8OJ8NI7NH7MG7MF6LE6\ LD5KD5KC4JB4JA4I93I83H72H62G52G41F31F20E10E0MzzJzz\ HwzFqwDlmBgd8bW6UP4NI2I5OMKIKFCIA6G51ex0cu0bs0ap0`\ n0_l0Zi0Yg0Xe0Wb0V`0UZ0TW0SU0QS0PP0ON0NL0MI0LG0KE0\ JB0I9wtzusxsrvqqtpproopnnolmmjllikjhjhhhghgehfdceb\ cdacc_cbYc`Xc_VcZUcYScXQcWPcVNcTMcSKcRJcQHcPFcOEcN\ CcLBcK9cJ7cI6cH4cG3cF1WZYTXVQVSOTPLSMIQJGOHDMEALB8\ J85H52F2UEzUEzUEzUEzUEzUEzUEzUEzUEzUEzUEzbEz`Ez_Ez\ ZEzYEzWEzVEzUEzTEzREzQEzPEzNEzMEzLEzKEzIVzHUzGSzFR\ zDQzCPzBOzANz8Mz7Kz6Jz5Iz3Hz2Gz1FzUEzUEzUEzUEzUEzU\ EzUEzUEzUEzUEzUEzUEzfEzeEzdEzbEzaEz`gz_gzZgzXmzWgz\ VgzUgzTgzRfzQezPdzObzMazL`zKZzJYzIXzGWzFUzETzDSzCQ\ zAPz9Oz8Nz7Lz6Kz4Jz3Hz2Gz1FzjYvhXtgWreWpdVnbUlaUj_\ TiZTgXSeWRcURaTQ_RPZQPXOOVNOTMNzKMzJMzHLzGKzEKzDJz\ BJzqnzqnzpmzpmzpmzpmzpmzpmzolzolzolzolzolzolznkznk\ znkznkznkznkznkzVazCSz0Gz } frm:SliceJulibrot4 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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FOTD 12-12-12 (Nine to Doomsday [No Rating])
by Jim Muth 14 Dec '12

14 Dec '12

FOTD -- December 12, 2012 (No Rating) Fractal visionaries and enthusiasts: Today's image shows the mysterious rectangle in the Julia sets corresponding to the fractured Seahorse Valley of the Z^(2.003)+C Mandelbrot set. To add excitement to the scene, I have offset the slice ever so slightly in the imag(c) direction. This slight aberration fills the rectangle with debris, breaks up the surrounding features and also rotates the rectangle a few degrees. Since no one will be around to check ratings after the world ends next Friday, I gave the image no rating. The name "Nine to Doomsday" needs no explanation. The big day is but nine days off. The image calculation time of 1-2/3 minutes is blessedly fast. After all, with the remaining time so limited, we don't want to waste a single second. So hurry! Before the end arrives, check the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> And don't forget the hi-def variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are posted online at: <http://www.Nahee.com/FOTD/> Lots of sun and a temperature of 41F +5C made today a typical average December day here at Fractal Central. Both the cats and humans did average things, mostly preparing for the holidays. We all want to be ready if doomsday fails to arrive as foretold. If the end does not arrive early, the next FOTD will be posted in a reasonable amount of time. Until then, take care, and no one will be more surprised than me if the world really does end in nine days. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Nine_to_Doomsday { ; time=0:01:40.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=1 center-mag=-0.00016692749087116/-0.000445372303409\ 87/110.94 params=90/90/90/90/-1.74358/7.09952e-005\ /0.00011/0.07389/2.003/0 float=y maxiter=3600 inside=0 logmap=50 periodicity=6 colors=000BDQBDPACOACN9BM9BL9AK8AJ89I79H78G78F67E6\ 7D56D56C45B45A449348337236225224113112001000MozJlz\ HizFcwDZmBUd8PW6GP49I245O8KI6FC4A6251Sx0Qu0Ps0Op0N\ n0Ml0Li0Kg0Je0Ib0H`0GZ0FW0EU0CS0BP0AN09L08I07G06E0\ 5B049037024012SdtRbrQapP`oO_mOZlNYjMXhLVgLUeKTdJSb\ IRaHQ_HPYGNXFMVELUEKSDJQCIPBHNAFMAEK9DJ8CH7BF7AE69\ C57B469357346234123011WLYTJVQHSOFPLEMICJGAHD8EA7B8\ 58535212pUznUzmUzlUzjUziUzhUzgUzeUzdUzcUzbZz`Yz_Xz\ ZWzYUzWTzVSzURzTQzRPzQOzPMzNLzMKzLJzKIzIHzHGzGEzFD\ zDCzCBzBAzA9z88z76z65z54z33z22z11zUUzsUzrUzqUzpUzn\ UzmUzlUzkUzjUzhUzgUzfUzeUzdUzbUzaUz`Uz_UzZUzX_zWUz\ VUzUUzTUzRTzQSzPRzOPzMOzLNzKLzJKzIJzGIzFGzEFzDEzCC\ zABz9Az89z77z66z45z33z22z11zjKvhJtgIreIpdHnbGlaGj_\ FiZFgXEeWDcUDaTC_RBZQBXOAVNATM9zK8zJ8zH7zG6zE6zD5z\ B5zq`zq`zp_zp_zp_zp_zp_zp_zoZzoZzoZzoZzoZzoZznYznY\ znYznYznYznYznYzVOzCEz02z } frm:SliceJulibrot4 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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Albrecht Niekamp's "The World inside Inside" (2012-12-13)
by Hal Lane 14 Dec '12

14 Dec '12

While Albrecht Niekamp is on vacation and away from a computer, he has asked me to put some of his images onto my server. Here is a link to Albrecht's "The World inside Inside" fractal created using his multifractal_10 formula: http://www.emarketingiseasy.com/Albrecht/1536143A.GIF Click the image in your browser for its full size, 1600 x 1200 pixels, and to prevent its being resampled by your browser. Albrecht's fractal, "The World inside Inside" is the fractal that was zoomed into to create yesterday's image. In the fractal, there's a small version of yesterday's image, and other, somewhat similar, image elements. A new feature is the attractive silver lacework at the bottom center of the image. However, a very different new feature seems to be crawling down from the top of the image -- a kind of "creeping confetti rot" is starting to eat away at the main fractal. The fractal is created by running the iterated values through *all* of the following formulas: Mandelbrot, secant, bees, phoenix and Julia A few experiments, sequentially altering the input parameters slightly might show the source of the creeping rot... The color map in Albrecht's fractal is the same as yesterday's map: http://www.emarketingiseasy.com/Albrecht/1536143B_map.jpg -- which is effectively the same map as used in his previously-posted: 1536143C "Playground" fractal. The Fractint parameter set is below. The ready-to-run full parameter file for the fractal, including the multifractal_10 formula, is here: http://www.emarketingiseasy.com/Albrecht/1536143A.par - Hal Lane ######################## # hallane(a)earthlink.net ######################## ===== Start of par file ============================== 1536143a { ; The_World_inside_Inside ; Mand-secant-bees-phoen-jul ; Time 0.23.47 DOS Shell 1600/1200 ; Fractint Version 2004 Patchlevel 11 ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=-0.71172813771936520/-0.078809827898776\ 27/266.4266/1/75.00000000000054/-6.484465742140343\ 99e-013 params=-0.05825983458967864/0.3785210730307932/213\ 64.64595712822/14235.4911030602/152048.0404808048/\ 384.1604894048/384.00482000595/256.1007683001/512.\ 1007683001/768.1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000000zr0zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>L\ Q8KM8KJ8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>\ qeBriAtm9vq8xu7zz5zz4zz3<4>zj4zg4zc4<3>zS5zP5zL6zI\ 6zE6wE6tD6<6>vAIv9Kv9M<3>x7Sy7Uy6Wz6Yz5_<3>f5Ma5IW\ 4E<2>_4H<3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>\ y0fz0gy0h<3>u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAA\ G7FO4KW0Qc<3>5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<\ 3>civflvinvlqvotvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa\ <3>8JP8FL8CI<3>SCCXCAaB9<3>uA2zA0xA0<12>SA1QA1NA1<\ 3>D92<6>UXAW`BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJo\ SFlWAi_5fc0ce7_jFRoNIzb0zj0 } ==== End of par file ================================

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Albrecht Niekamp's "Ritual Gear" (2012-12-12)
by Hal Lane 12 Dec '12

12 Dec '12

While Albrecht Niekamp is on vacation and away from a computer, he has asked me to put some of his images onto my server. Here is a link to Albrecht's "Ritual Gear" fractal created using his multifractal_10 formula: http://www.emarketingiseasy.com/Albrecht/1536143B.GIF Click the image in your browser for its full size, 1600 x 1200 pixels, and to prevent its being resampled by your browser. Albrecht's fractal, "Ritual Gear", is a zoom into his fractal: 1536143a.GIF -- which, unfortunately, has not yet had a link to it posted. Due to a quirk in the space-time continuum, it's scheduled to arrive tomorrow. In Albrecht's fractal the two cheerfully-colored arms coming down from the top right and left seem to be carrying large blue knife blades studded with colorful spikes. The spikes are menacing the almost-touching ritual gears of the center and lower areas of the fractal. And the ritual gears have only mounted a defense of a few small blue knife blades -- whose spikes are pointing the wrong way for defense! The certain-to-be-doomed ritual gears are giving their all to protect the flame in their vertically-centered tall blue cup. The bright colors in Albrecht's fractal are shown in its color map: http://www.emarketingiseasy.com/Albrecht/1536143B_map.jpg -- which is effectively the same map as used in his previously-posted: 1536143C "Playground" fractal. The Fractint parameter set is below. The ready-to-run full parameter file for the fractal, including the multifractal_10 formula, is here: http://www.emarketingiseasy.com/Albrecht/1536143B.par - Hal Lane ######################## # hallane(a)earthlink.net ######################## ===== Start of par file ============================== 1536143b { ; Ritual Gear ; Zoom into 1536143a ; Time 0.22.49 DOS Shell 1600/1200 ; mandel-secant-bees-phoenix-julia ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=-0.71016733426941010/-0.078514738672469\ 15/1091.912/1/74.9999999999988631/8.27331259056762\ 747e-013 params=-0.05825983458967864/0.3785210730307932/213\ 64.64595712822/14235.4911030602/152048.0404808048/\ 384.1604894048/384.00482000595/256.1007683001/512.\ 1007683001/768.1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000000zr0zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>L\ Q8KM8KJ8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>\ qeBriAtm9vq8xu7zz5zz4zz3<4>zj4zg4zc4<3>zS5zP5zL6zI\ 6zE6wE6tD6<6>vAIv9Kv9M<3>x7Sy7Uy6Wz6Yz5_<3>f5Ma5IW\ 4E<2>_4H<3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>\ y0fz0gy0h<3>u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAA\ G7FO4KW0Qc<3>5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<\ 3>civflvinvlqvotvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa\ <3>8JP8FL8CI<3>SCCXCAaB9<3>uA2zA0xA0<12>SA1QA1NA1<\ 3>D92<6>UXAW`BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJo\ SFlWAi_5fc0ce7_jFRoNIzb0zj0 } ==== End of par file ================================

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Albrecht Niekamp's "Playground" (2012-12-11)
by Hal Lane 11 Dec '12

11 Dec '12

While Albrecht Niekamp is on vacation and away from a computer, he has asked me to put some of his images onto my server. Here is a link to his "Playground" fractal created using his multifractal_10 formula: http://www.emarketingiseasy.com/Albrecht/1536143C.GIF Click the image in your browser for its full size, 1600 x 1200 pixels, and to prevent its being resampled by your browser. Of the many colorful shapes in Albrecht's "Playground," the one that strikes me the most is the "face" between the top two largest purple and blue areas. The face has curly black hair, blue eyes with red eye shadow, a pointed chin and an open mouth -- giving a permanently surprised look to the face. The bright colors in Albrecht's fractal are shown in its color map: http://www.emarketingiseasy.com/Albrecht/1536143C_map.jpg The Fractint parameter set is below. The full parameter file for the fractal, including the multifractal_10 formula, is here: http://www.emarketingiseasy.com/Albrecht/1536143C.par - Hal Lane ######################## # hallane(a)earthlink.net ######################## ===== Start of par file ============================== 1536143c { ; Playground ; Zoom into 1536143b ; Time 0.29.52 DOS Shell 1600/1200 ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=-0.70943787030482360/-0.078332525529522\ 47/253933/1/74.9999999995186215/5.2023735319650654\ 7e-010 params=-0.05825983458967864/0.3785210730307932/213\ 64.64595712822/14235.4911030602/152048.0404808048/\ 384.1604894048/384.00482000595/256.1007683001/512.\ 1007683001/768.1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000000zr0zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>L\ Q8KM8KJ8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>\ qeBriAtm9vq8xu7zz5zz4zz3<4>zj4zg4zc4<3>zS5zP5zL6zI\ 6zE6wE6tD6<6>vAIv9Kv9M<3>x7Sy7Uy6Wz6Yz5_<3>f5Ma5IW\ 4E<2>_4H<3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>\ y0fz0gy0h<3>u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAA\ G7FO4KW0Qc<3>5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<\ 3>civflvinvlqvotvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa\ <3>8JP8FL8CI<3>SCCXCAaB9<3>uA2zA0xA0<12>SA1QA1NA1<\ 3>D92<6>UXAW`BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJo\ SFlWAi_5fc0ce7_jFRoNIzb0zj0 } ==== End of par file ============================

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Lee Skinner kindly pointed out to me that...
by Hal Lane 11 Dec '12

11 Dec '12

Lee Skinner kindly pointed out to me that two of my links to fractals on November 29th, 2012 gave 404-Not Founds. I've fixed the problems and added an additional image. The November 29th fractals in question are all on this page: http://tinyurl.com/Jim-muths-fotd-2012-11-Nov or: http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd_2012_11_Nov.html Jim Muth's explanation as to what's going on in his unusual FOTD is interesting -- and surprisingly understandable for what he's describing: http://www.crosscanpuzzles.com/Nov12/112912.html - Hal Lane ######################## # hallane(a)earthlink.net ########################

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Albrecht Niekamp's "Multiple Directions" (2012-12-10)
by Hal Lane 11 Dec '12

11 Dec '12

While Albrecht Niekamp is on vacation and away from a computer, he has asked me to put some of his images onto my server. Here is a link to his "Multiple Directions" fractal created using his multifractal_10 formula: http://www.emarketingiseasy.com/Albrecht/1536164E.GIF Click the image in your browser for its full size, 1600 x 1200 pixels, and to prevent its being resampled by your browser. Most of the golden spirals in Albrecht's "Multiple Directions" are spiraling down to "infinity and beyond" -- although a couple of them on the vertical centerline are content to form teardrop shapes, instead of spiraling. The colors in Albrecht's fractal are shown in the fractal's color map: http://www.emarketingiseasy.com/Albrecht/1536164E_map.jpg The Fractint parameter set is below. The full parameter file for the fractal, including the multifractal_10 formula, is here: http://www.emarketingiseasy.com/Albrecht/1536164E.par - Hal Lane ######################## # hallane(a)earthlink.net ######################## ===== Start of par file ============================== 1536164e { ; Multiple Directions ; jul-sec-bees-phoen-mand ; time 24.52 1600/1200 ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=+1.33193274819753900/-0.000000000005385\ 46/9.345637e+008/1/90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/413\ 62.64595712822/14235.4911030602/152048.0404808048/\ 384.1604894048/384.00482000595/256.1007683001/512.\ 1007683001/768.1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000zzizzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8KJ8<2>I\ 88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriAtm9vq8\ xu7zz5zz4zz3<4>zj4zg4zc4<3>zS5zP5zL6zI6zE6wE6tD6<6\ >vAIv9Kv9M<3>x7Sy7Uy6Wz6Yz5_<3>f5Ma5IW4E<2>_4H<3>P\ 3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0gy0h<3>\ u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4KW0Qc<3\ >5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<3>civflvinvl\ qvotvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI\ <3>SCCXCAaB9<3>uA2zA0xA0<12>SA1QA1NA1<3>D92<6>UXAW\ `BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJoSFlWAi_5fc0c\ e7_jFRoNIzb0zj0000zr0zz1zzCzzT } ==== End of par file ============================

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FOTD 09-12-12 (Broken Hyperspiral [5])
by Jim Muth 10 Dec '12

10 Dec '12

FOTD -- December 09, 2012 (Rating 5) Fractal visionaries and enthusiasts: Today's image of a strange spiral is located in the Scepter Valley area of the Z^2+C Julibrot. It is sliced in a direction halfway between the Oblate and the Rectangular, and has been stretched and skewed to a rather large extent to bring it to a recognizable shape. The name "Broken Hyperspiral" refers to the infinitely divided nature of the features in the image. This unlimited division, known as 'Cantor Dust', is typical of the Julia sets of points outside the Mandelbrot set, but as today's image shows, it also exists in the odd planes and angles. The image consists totally of points, with no two points being connected. A zoom into one of the sub-spirals will reveal a never-ending chain of similar broken spirals, and this series continues all the way to infinity, which is not an end point or a very large number, but an abstract idea that can never be reached. The rating of a 5 is pretty pathetic by FOTD standards, but it's all I could give the image, which has little more than a bit of pop-math interest going for it. More effort on the coloring might have raised the rating a point or two. The calculation time of 1-3/4 minutes is about average, but perhaps a bit slow for an image with so little reward. The situation is resolved on the web sites. The completed image is posted for instant viewing at: <http://www.crosscanpuzzles.com/Archives.html> with high-definition variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are online at: <http://www.Nahee.com/FOTD/> Clouds ruled the sky today here at Fractal Central, while the temperature of 45F +7C kept things feeling seasonal. The forecasted rain held off until sunset however. Both the cats and humans had a typical uninteresting day. The next FOTD will be posted when it is ready. Until whenever, take care, and if humans ever populate the galaxy, how will they agree on a universal galactic time? (IMO, we will never populate anything but planet earth, so there is no problem.) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Broken_Hyperspiral { ; time=0:01:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=1 center-mag=+0.03264445237728411/+0.172536526663781\ 00/8438.382/0.1402/79.9353442340639617/73.17794208\ 35490413 params=45/90/0/90/-1.25/0/0/0/2/0 float=y maxiter=2200 inside=255 logmap=-126 periodicity=6 colors=000knUknUloUloTmpTmpSmqSmqRmrRmrRmsQmsQmtPm\ tPmuOmuOmuNmvMmvLkvKiwKhwJfwIdxHcxGaxG_yFZyEXyDVzC\ ayIcyMeyQgyUiyYky`mydoyhqylpykoyjmygjxdhxafxZcwWaw\ T_vQXuN`sT_qSZoRYmQWkQViPUgOTdNSbMQ`MPYLOWKNUJMRIK\ PIJMHIKGHIFGFEEDEGBDI8CK6BM3AO8HQ7MS6RU5WW4`Y3eZ2j\ Z4kZ6kZ8kZAkZCk_EkaGlbIncKodMqfOseQsdSrcUqbWq`Xp_Y\ oZYoYYnWZmVZmUZlTZkSZkQ_jP_iO_iN_hL`gK`gJ`fI`eH`eF\ adEacDacCabAba9ba8b`7b_5cZAbaBcaDdaEdaGeaHfaJgaKga\ MhaNiaOiaQjaRkaTlaUl`Wm`Xn`Zo`_o``p`bq`cq`er`fs`ht\ `it`ku`lv`nw_nw_mw`mw`lwalwakwbjwbjwczzczzdzzdzzez\ zezzfzzfzzgzzgzzhzzhzzizzizzjzzjzzkzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:SliceJulibrot4 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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Albrecht Niekamp's "Inside View" (2012-12-09)
by Hal Lane 09 Dec '12

09 Dec '12

While Albrecht Niekamp is on vacation and away from a computer, he has asked me to put some of his images onto my server. Here is a link to his "Inside View" fractal created using his multifractal_10 formula: http://www.emarketingiseasy.com/Albrecht/1536704E.GIF Click the image in your browser for its full size: 1600 x 1200 pixels, and to prevent its being resampled by your browser. Albrecht's "Inside View" has muted and darker tones predominating. The dark intricate patterns on the light background make me think of back-lit suspended metal filigree. The somber colors in Albrecht's fractal are created by this color map: The more colorful hues are essentially not used at all by his fractal. http://tinyurl.com/1536704E-map or: http://www.emarketingiseasy.com/Albrecht/1536704E_map.jpg The Fractint parameter set is below. The full parameter file for the fractal, including the multifractal_10 formula, is here: http://www.emarketingiseasy.com/Albrecht/1536704E.par - Hal Lane ######################## # hallane(a)earthlink.net ######################## ===== Start of par file ============================== 1536704e { ; Inside_View ; secant-mmods-bees-phoen-newt ; time 0.33.55 XP Dos shell ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=mfr.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=-1.50145147245682100/+0.100169185289958\ 60/843407.3/1/74.9999999981563263/2.46247487678541\ 432e-009 params=-0.05825983458967864/0.3785210730307932/153\ 67.64595767025/14235.4911030602/152048.0404808048/\ 384.1604894048/384.00482000595/256.1007683001/512.\ 1007683001/768.1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000<3>000000304<8>X0a_0dc0h<3>p0w<4>_0dX0aU\ 0Y<2>K0NH0JG0NE1R<3>7UX6`Z4h_2oa0wc<11>2TG2RE3OC<3\ >4D3<17>kkammcpoe<3>zwm<6>cYO`UKYQG<3>KA0000<43>00\ 0<4>000330<11>110110110<3>000KA4<7>gcOjgRmjT<3>zzc\ <9>UOFRKDOGA<3>A00<9>f0Ci0Dl0F<3>z0K<6>Z0EV0DR0C<3\ >A08004000<26>000 } ==== End of par file ============================

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I had forgotten to post this "investigation"
by Hal Lane 09 Dec '12

09 Dec '12

I had forgotten to post this "investigation" into Jim Muth's FOTD for November 10th. It had been marked on my web page as "soon..." The fractal is up there now, and a direct link to it is below. It's not especially artistic, but rather interesting. It's a spike that has another, apparently independent, spike embedded within it. Interestingly, the internal spike wanders from one side to the other within the containing spike, but doesn't seem to leave it -- at least at the magnifications I used. It seemed to stay inside at 4k x 3k also. Anti-aliased. Click the image to prevent resampling by your browser, and to see its actual size:(1200x900). http://www.emarketingiseasy.com/TESTS/FOTD/F121110V.jpg - Hal Lane ######################## # hallane(a)earthlink.net ########################

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Albrecht Niekamp's "The Big Ball" (2012-12-08)
by Hal Lane 09 Dec '12

09 Dec '12

While Albrecht Niekamp is on vacation and away from a computer, he has asked me to put some of his images onto my server. Here is a link to his "The Big Ball" fractal created using his multifractal_10 formula: http://www.emarketingiseasy.com/Albrecht/1536705D.GIF Click the image in your browser for its full size: 1600 x 1200 pixels. "The Big Ball" is a very "busy" fractal containing a great variety of sunny features -- including (at the very center of the ball) a sort of smiling clown face wearing green goggles. The cheery colors in Albrecht's fractal are created by this color map: http://tinyurl.com/1536705D-map or: http://www.emarketingiseasy.com/Albrecht/1536705D_map.jpg The Fractint parameter set is below. The full parameter file for the fractal, including the multifractal_10 formula, is here: http://www.emarketingiseasy.com/Albrecht/1536705D.par - Hal Lane ######################## # hallane(a)earthlink.net ######################## ===== Start of par file ============================== 1536705d { ; The_Big_Ball ; secant-mmods-bees-phoen-newt ; time 0.02.44 XP Dos shell ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=mfr.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=-0.0231296/0.0288228/0.5500051/1/92.499\ 9999999409539/2.09411585294638769e-011 params=-0.05825983458967864/0.3785210730307932/153\ 67.64595767025/14235.4911030602/152048.0404808048/\ 384.1604894048/384.00482000595/256.1007683001/512.\ 1007683001/768.1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000000oNIzb0<2>zz1zzC<2>zzz<3>jqdfo_blU<3>M\ b8<3>LQ8KM8KJ8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBiOD\ jQF<3>qeBriAtm9vq8xu7zz5zz4zz3<8>zY4zV5zS5<3>zE6wE\ 6tD6<10>w8Px8Rx7S<3>z5_<3>f5Ma5IW4E<2>_4H<3>P3DN2C\ K2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0gy0h<3>u1mt1\ ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4KW0Qc<3>5Xc6\ Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<3>civflvinvlqvotv\ sww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI<4>XC\ AaB9fB7<3>zA0<13>SA1QA1NA1<3>D92<6>UXAW`BYcC<3>hrI\ <3>UnXRm_NlcJkgFfpAaz<6>_5fc0ce7_jFR } ==== End of par file ============================

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still inside the orbit ..?
by MARSON Guy 08 Dec '12

08 Dec '12

Dear All, .. or slightly out of the orbit of our fractals? Click start an move the bar (l/r)..: http://static.flabber.net/files/scale-of-the-universe-2.swf Cheers, Guy ##################################################################################### Scanned by MailMarshal - Marshal's comprehensive email content security solution. #####################################################################################

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Albrecht Niekamp's "Beauty Contest" (2012-12-07)
by Hal Lane 07 Dec '12

07 Dec '12

While Albrecht Niekamp is on vacation and away from a computer, he has asked me to put some of his images onto my server. Here is a link to his "Beauty Contest" fractal created using his multifractal_10 formula: http://www.emarketingiseasy.com/Albrecht/1536706E.GIF Click the image in your browser for its full size: 1600 x 1200 pixels. The rainbows pierced by the prickly spikes in Albrecht's fractal are created by this color map -- that appears to have its rainbow sequence repeated twice: http://tinyurl.com/1536706E-map or: http://www.emarketingiseasy.com/Albrecht/1536706E_map.jpg The Fractint parameter set is below. The full parameter file for the fractal, including the multifractal_10 formula, is here: http://www.emarketingiseasy.com/Albrecht/1536706E.par - Hal Lane ######################## # hallane(a)earthlink.net ######################## ===== Start of par file ============================== 1536706e { ; Beauty_Contest ; Secant-mmods-bees-phoen-newt ; Time 0.35.31 XP Dos Shell ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=multifra.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=-1.44852915023346500/+0.004606349313312\ 62/4400.041/1/-65.000000000068539/2.73531544636718\ 138e-011 params=-0.05825983458967864/0.3785210730307932/153\ 67.64595767025/14235.4911030602/152048.0404808048/\ 384.1604894048/384.00482000595/256.1007683001/512.\ 1007683001/768.1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000<9>000000000<3>000<9>bbbfffjjj<3>zzz<4>I\ zz9zz0zz<7>0Rz0Nz0Iz<3>00z<5>V0z_0zd0z<3>z0z<3>z0e\ z0`z0V<3>z0Bz06z00<5>zV0z_0zd0<3>zz0<3>ez0`z0Vz0<3\ >Bz06z00z0<5>0zV0z_0zd<3>0zz<3>0ez0`z0Vz<3>0Bz06z0\ 0z<9>00O00K00G<3>000<9>00b00f00j<3>00z<9>b0zf0zj0z\ <3>z0z<9>z0Oz0Kz0G<3>z00<9>zb0zf0zj0<3>zz0<9>Oz0Kz\ 0Gz0<3>0z0<9>0zb0zf0zj<3>0zz<9>0Oz0Kz0Gz<3>00zzE0z\ D0 } ==== End of par file ============================

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FOTD 06-12-12 (Seeing Double [7])
by Jim Muth 07 Dec '12

07 Dec '12

FOTD -- December 06, 2012 (Rating 7) Fractal visionaries and enthusiasts: Not another 7-rated image? Yes, another 7-rated image. This one lies in the parent fractal that results when 0.1 part of Z^(2) is subtracted from 0.2 part of Z^(1.5) and straight C is added on each iteration. This parent is an oversized thing resembling a Mandelbrot set rotated 180 degrees so that its west parts face east. Both the west and east parts of this parent are split into two, and today's scene lies in a valley of a sub-bud of the southern main bud. The name "Seeing Double" does not refer to someone with eye problems. It refers to the doubling of many of the elements in the image. The calculation time of 4-1/2 minutes is more than the image is worth. But thanks to the web sites, the image may be seen without the need of calculating it. The completed image is posted at: <http://www.crosscanpuzzles.com/Archives.html> High-definition variations are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are online at: <http://www.Nahee.com/FOTD/> Total sun prevailed here at Fractal Central today, though the high temperature of only 41F +5C kept a mild chill in the air. Both the cats and humans had an uneventful day. (It's boring but true.) The next FOTD will be posted when it is ready, most likely about 24 hours from now. Until whenever, take care, and in the quantum world, not only is it (apparently) possible to receive information from the future, it is also (apparently) possible to change the past. Of course, the qualifier 'apparently' must be added to these two demonstra- ted facts because in our common-sense world they are impossible. This means that, when we try to describe quantum things, we are doing little more than mental gymnastics. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Seeing_Double { ; time=0:04:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+20.38865970233759/-1.853988362389582/\ 2.089299e+009/1/177.5/0 params=0.2/1.5/-0.1/2/0/\ 1000/0/0 float=y maxiter=1800 inside=0 logmap=358 periodicity=6 mathtolerance=0.05/1 colors=000KERIHRGKRDMQBPQ9SQ7VQ5XQ9ZOC`NFbMIdLMfJP\ gISiHVkGZmEaoDdpCgrBkt9nv8qx7ty6su6sq6rm6rj6qf6qb6\ pZ6pW6oS6oO6oL6mJ7lI7jH8iG8gE9fD9eC9cBAbAAc8Be7Bg6\ Ci5Ck4CmBGoIKqOOsVSu`Wtg_xmcurgxzjssinphjjgedf`XeX\ PdSMcOJbKGbGDaCAa87`45`84ZC4XF4VJ3TM3RQ3PT3NS4MR5L\ Q5KP6JO7IO7HN8GM8FL9EKADKACnWKh_KbbKXfKRjKMmKPdJRX\ ITPHVGGX8FZ0FNVPCxZXhjRilMjmHkoCipKblVXidSfkMopJpw\ FrtKvqWHa`DMe9FVH8LO1BVDCTPDS`EQkFPgDUcBZ`9bX7gdTR\ dXQc`OccNdXZeQifKthPqjUnlZknchphermbtr_vwXekRQ`MAQ\ H7WN5`T3fZ1kc5gf9ciC_lGWoJSrNOuQKwLNwGczBhz6mz1zz4\ mz6hz8czASgCQcEP_GNWIMSMOPQQMUSJYUGaWDdYAeZAe_Ae`A\ faAfbAfbAgcAgdAgeAhfAhgApnoomnommomlomkomjomjnminl\ hnlgnlfnlfnlenldMBRJBBICAHC9GD8GD8IHAKKBMNDOQEQcGS\ cHUcJWcKYcM_cNajPbmQbmQcmPclOczNdzMdzLdzLezKzzkzzg\ zzdzz`zzYzzVzzZzzbzzfzzjzznzzazzQzzEzzKzzQzzWzzazz\ gzzmzzszzmzzgzzazzWzzQzzK } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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Albrecht Niekamp's "Platinum Riddle" (2012-12-06)
by Hal Lane 07 Dec '12

07 Dec '12

While Albrecht Niekamp is on vacation and away from a computer, he has asked me to put some of his images onto my server. Here is a link to his: "Platinum Riddle" fractal created using his multifractal_10 formula: http://www.emarketingiseasy.com/Albrecht/16731A.GIF Click the image in your browser for its full size: 1600 x 1200 pixels. A copy of the color map that creates the gold and silver colors is here: http://tinyurl.com/16731A-map or: http://www.emarketingiseasy.com/Albrecht/16731A_map.jpg The fractal appears to be intricate gold and silver filigree executed by a master jeweler -- in a somewhat forceful overall design. The Fractint parameter set is below. The full parameter file for the fractal, including the multifractal_10 formula, is here: http://www.emarketingiseasy.com/Albrecht/16731A.par - Hal Lane ######################## # hallane(a)earthlink.net ######################## ===== Start of par file ============================== 16731a { ; Platinum_Riddle ; Time 0.05.37 1600/1200 ; sec-phoen-newt-bees-sec reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=-0.516993/-0.00123494/0.7928157/1.1324/\ -90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/167\ 31.32595752213/25234.0311099861/151024.0204808192/\ 384.32768524288/384.00482000595/128.2007683001/256\ .2007683001/384.8007683001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=000<21>000000000<2>000111333<27>oooqqqsss<2\ >xxxzzzyyy<25>CCCAAA888<2>222000000<56>000000000<2\ >000111332<23>ldTnfUpgV<3>xn_<27>A8687565444322200\ 0<30>000 } ==== End of par file ============================

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FOTD 06-12-12 (Wheel of Destiny [7])
by Jim Muth 06 Dec '12

06 Dec '12

FOTD -- December 04, 2012 (Rating 7) Fractal visionaries and enthusiasts: Today's image lies in the same parent fractal as yesterday's, but at a far different location. It is located in the valley of a mandel-bud some distance south of the large minibrot that held yesterday's image. I named the image "Wheel of Destiny". The reason for the 'wheel' part of the name is made clear enough in the 'spinning' minibrot at the center of the image. It is up to the individual viewer to interpret the 'destiny' part. The rating of a 7 is once again merely average. Average and below-average images are easy to create, which is why we see so many of them. Finding the above average ones is the challenge. The calculation time of 1-1/4 minutes is a fair price for an average fractal. The time will pass quickly enough once the image gets a good start. The pre-calculated image is posted and available for free on the FOTD web sites. Avoid calculation by viewing the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> High-definition variations of the image are online at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The entire FOTD library is available at: <http://www.Nahee.com/FOTD/> Light rain fell overnight here at Fractal Central. The day dawned with fog that hung around for a while, but things improved markedly at mid-morning, when the sun broke through. The sunny afternoon temperature reached a very spring-like high of 64F 18C. The fractal cats enjoyed the sun coming in the southwest window, while the humans enjoyed a day with nothing major going wrong. Most likely, the next FOTD will be posted soon. Until whenever, take care, and fortune tellers claim to be able to see into the future. At first hearing, this claim seems preposterous, but some rational scientists now claim that at the sub-atomic level, information can actually travel backward in time. I guess it's another of those curious but supposedly meaningless quantum coincidences, and rationalists can still consider fortune tellers to be charlatans. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Wheel_of_Destiny { ; time=0:01:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip center-mag=+1.039956082615642/-0.6873303266486848/\ 4.176185e+010/1/35/0 params=-9/-1.9/-1/-9.1/0/0/0/0 float=y maxiter=1800 inside=0 logmap=150 periodicity=6 mathtolerance=0.05/1 colors=0002002002002002002012022032042052062072082\ 08208208208207204204304405505626746856987A77BBFBA8\ BFJBD9EITAG9GN_AJMHVjAMhAWmAOCAQb9WBAY`AUDAVD5Sh6U\ yAUcAUaAU_AUyAVWAVUAVSAgyAVOAWMAWKApyAWGAxyAxyAxyi\ xyhzzewlkvlauZ_sYYqWWoVUmUSkTQiROgQLePJcOIbMHaLH`K\ G_JGZHFYGFXF7bl8ay8al9`y9`lA`yA_lB_SBZQBZPCZOCYMDY\ LDXKEXJEXHFWGFWFDgDEeDEdDEbDEaDF_DFZDFXDKW3JW5IW6H\ W8HW9GWBFWCdg9aeA_dAXcBVbBSaBQ_CMZCKYDHXD8hF9gD9fD\ AeDAeDAdDBcDBcDBbDCaDCaDD`DD_DD_DEZDEYDEYDFXDFWDTo\ pQkiOhcLeXJaRHZKkYbgX_cXX`XUXXRUWPQWMMWJIWGzUnxVlv\ VjtVirVgpVenVdlVbjVahV_fVYdVXaWV_WUYWSWWQUWPSWNQWM\ OWKLWIJWHHWFvf8se9pd9mc9kcAhbAeaAcaB``BY_BW_CTZCQY\ COYDKXDHWDz4Jx6Ju8JrAToBTlDTiFTfGbcIb`KbYLbVNlSPlP\ QlLSlIVlsblqaloalm`lk`li`lg_le_yc_yaZy_ZyYZyWYyUYy\ SYyQXyOXyLXyJWyHWyUEySHyQJyOMyLOyJRyHUyGZyFYyFYyFY\ yFYyFYyFYyFYyFXyFXyFXyXRy } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 05-12-12 (Star Light Star Bright [7])
by Jim Muth 06 Dec '12

06 Dec '12

FOTD -- December 05, 2012 (Rating 7) Fractal visionaries and enthusiasts: The string of perfectly average 7-rated images continues today, with a scene in the parent fractal that results when the formula Z^(2.05)+C is iterated 11 levels down the hyperladder with no function applied. This parent resembles a distorted Mandelbrot set rotated so that its west end faces east. A mysterious axeman appears to have taken a slice out of its main bud. Today's scene is located where the axe appears to have sliced through Seahorse Valley. The name "Star Light Star Bright" refers to the star-shaped pattern of elements surrounding the central minibrot. It is also the first line of a well-known children's poem. The rating of a 7 is a fair appraisement of the image, which takes a mere 1-3/4 minutes to finish on one of today's speed demons. And as always, all the hassle of setting up and running the parameter file may be avoided by checking the FOTD web sites. The finished image is online at: <http://www.crosscanpuzzles.com/Archives.html> Variations are available at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Thousands of back images are posted at: <http://www.Nahee.com/FOTD/> A mix of sun and clouds with a brisk northwest wind and a temperature of 48F +9C made today seem more seasonal here at Fractal Central. The fractal cats would have preferred more sun and less clouds, or at least steadier sun. The humans made it through the day with ease. Preparing the next FOTD will mean less ease however, and if all goes well, it will be posted in a day or so. Until whenever, take care, and the confirmation of Bell's Theorem (that there can be no hidden variables in quantum mechanics and information must get around faster than the velocity of light) is the only time in the history of science when a brilliant theorist made a prediction, brilliant experimentalists pushed the boundaries of their art to test it, the theory was resoundingly confirmed, and every rational thinker was miserable. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= StarLiteStarBright { ; time=0:01:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident center-mag=+0.735201305568/+0.032356486996/2.2e+07\ /1/40/0 params=2.05/0/-11/0 float=y maxiter=2000 inside=0 logmap=221 periodicity=6 colors=000FAKC8G96C6483245cT4WN3OH2GB185EtwBhk8Y_5\ MO2BCZunSicLYUENK7BA9hV6UK3FA3GV2CN18F047iGtWGwQDm\ LAcG8UA5K52AE4b9CN2BH5LO7UV9caBlhDuoGnjJgeM``PUWRO\ RiGZbDUWBPB3FQ9KJ6FD4A625NL9HF6BA45526f75`64W53Q43\ L32G21A1050nXBgS9aO8VK6PG5JC4C82641ydwdRcKDKtw2jm1\ ac1SU1JK09A0zd7zZ6hU5zP4cK3zF2hA1c50qR_TNVPKRLGMHD\ ICAD869434XatSWkNRcILWEGO9AG458BPRp3Mh2I`2FU1CM19F\ 06703aIoPCYC6Hbw5Wm4Qc3JU2DK16A0xbLmWHcQEUJAKD7A63\ 1qE0cA0R70D3pfsbWeQLSDAExAIWpkPeaJVSCLJ6A9xYSmSNcM\ IUHEKB9A54JUpFPgCKZ9FQ6AH3584Gi3Ec3CY2AS28N16H14B0\ 252Zw1Nc0BKs3Oe2IS1CE06fjHLN8hbU3Ku2Hl2Ed1BX18O05G\ 028sgSeYdVPULHKA8ABrr7__3IIihfLtQGhKCYF8MA4B5HrfEk\ `CdWAYQ8RL6KGUDAU65UllU8jU6bU5VUANUKFUK7UKscKecKSc\ KEcYhcU`cUUcUMcUFmU7mU5mU2miOzbczWczQczJczDcz6czCm\ zAmz8mz6mz4mz2mz0zzbzzJzzFzzCzzAzz8zz6zz4zz2zz5zz4\ zz3zz2zz2zz1zz0zzGzzEzzCz } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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Albrecht Niekamp's "From Outer Space" (2012-12-05)
by Hal Lane 05 Dec '12

05 Dec '12

While Albrecht Niekamp is on vacation and away from a computer, he has asked me to put some of his images onto my server. Here is a link to his: "From Outer Space" fractal created using his multifractal_10 formula: http://www.emarketingiseasy.com/Albrecht/21705B.GIF Click the image in your browser for its full size: 1600 x 1200 pixels. When I initially saw Albrecht's "From Outer Space" I thought that it had 5-fold symmetry for a minute. However, there are six arms on the central figure -- and more clearly -- a center hexagon of blue circles with glowing yellow hazes on a small circular blue background. The six orange and yellow "hazes" at the ends of each of the arms remind me of glowing stellar atmospheres. A copy of the color map that creates the glowing hazes (and blue background) is here: http://tinyurl.com/21705B-map or: http://www.emarketingiseasy.com/Albrecht/21705B_map.jpg The Fractint parameter set is below. The full parameter file for the fractal, including the multifractal_10 formula, is here: http://www.emarketingiseasy.com/Albrecht/21705B.par - Hal Lane ######################## # hallane(a)earthlink.net ######################## ===== Start of par file ============================== 21705b { ; From_Outer_Space ; Time 0.34.07 1600/1200 ; man-sec-newt-zer-mmods reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=cos/exp/exp/sin passes=t center-mag=-1.08278931330657500/+0.000679771447793\ 55/30.94201/1.1324/-90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/217\ 05.03564960102/25234.2207090221/151024.0204808192/\ 384.32768524288/384.00482000595/128.1007683001/256\ .1007683001/256.2007683001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=n0B00z<78>vv4ww3ww2<2>zz0zz0zy0<77>z40z30z2\ 0z20z10z00<9>s07r08q08<3>n0Cm0Dl0E<59>50u40v30w<3>\ 00z000 } ==== End of par file ============================

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Albrecht Niekamp's "The Twain Shall Meet" (2012-12-04)
by Hal Lane 05 Dec '12

05 Dec '12

While Albrecht Niekamp is on vacation and away from a computer, he has asked me to put some of his images onto my server. Here is a link to his: "The Twain Shall Meet" fractal created using his multifractal_10 formula: http://www.emarketingiseasy.com/Albrecht/51765AZ8.GIF Click the image in your browser for its full size: 1600 x 1200 pixels. The mixing of more than one fractal type in Albrecht's multifractal_10 formula can create fractal shapes fractalists might not usually run across. This fractal combines the fractal types: many-mods, secant, Newton, phoenix and many-mods a second time. The Fractint parameter set is below. The full parameter file for the fractal, including the multifractal_10 formula, is here: http://www.emarketingiseasy.com/Albrecht/51765AZ8.par - Hal Lane ######################## # hallane(a)earthlink.net ######################## ===== Start of par file ============================== 51765AZ8 { ; The_Twain_Shall_Meet ; Time 0.49.45 1600/1200 ; mmods-sec-newt-phoen-mmods reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=sqr/exp/exp/sin passes=t center-mag=+0.53209050020148800/+0.307041785398280\ 10/283.836/1/59.9999999999993463/6.364977989115061\ 52e-013 params=-0.05825983458967864/0.3785210730307932/517\ 65.03595750222/14235.4911030602/152048.0404808048/\ 384.1604894048/384.00482000595/128.1007683001/256.\ 1007683001/512.1007683001 float=y maxiter=3072 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000LOr<3>_5fc0ce7_jFRoNIzb0zj0000zr0zz1zzC<\ 2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8KJ8<2>I88H44G00<3>\ TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriAtm9vq8xu7zz5zz4zz\ 3<4>zj4zg4zc4<3>zS5zP5zL6zI6zE6wE6tD6<6>vAIv9Kv9M<\ 3>x7Sy7Uy6Wz6Yz5_<3>f5Ma5IW4E<2>_4H<3>P3DN2CK2A<3>\ 805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0gy0h<3>u1mt1ns1or2\ q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4KW0Qc<3>5Xc6Zc7`c7\ aa7c_7eY<3>FcgHciJbl<3>S_v<3>civflvinvlqvotvsww<2>\ zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI<3>SCCXCAaB\ 9<3>uA2zA0xA0<12>SA1QA1NA1<3>D92<6>UXAW`BYcC<3>hrI\ <3>UnXRm_NlcJkgFfpAazEXwITu } ==== End of par file ============================

3 2

FOTD 03-12-12 (At the Breaking Point [7])
by Jim Muth 04 Dec '12

04 Dec '12

FOTD -- December 03, 2012 (Rating 7) Fractal visionaries and enthusiasts: Today's image is a harmless scene in the parent fractal that results when 9 negative parts of Z^(-1.9) are combined with one negative part of Z^(-9.1) and (1/C) is added on each iteration. This parent vaguely resembles a three-leaf clover inside a 5-sided area of chaos inside an outer 7-sided figure. A small minibrot lies on the eastern edge of the field of chaos. Today's scene lies in a valley of this minibrot. The name "At the Breaking Point" implies less stress than it might imply. It is a phrase that came to mind when I shut off my thinking apparatus. The rating of a 7 is right at FOTD average, while the calcula- tion time of 3-1/4 minutes means that little effort will be expended when the parameter file is calculated. Be free of all calculation effort! Check the finished image online at: <http://www.crosscanpuzzles.com/Archives.html> And check the hi-def variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images may be accessed at: <http://www.Nahee.com/FOTD/> The day began with heavy fog here at Fractal Central, but the fog cleared off during the morning, leading to a sunny afternoon with a temperature of 59F 15C. The fractal cats enjoyed an afternoon in the sun. The humans made it through the day with nothing happening that was worth telling. The next FOTD will be posted when it is ready. Until whenever, take care, and mystics tell that the physical world we observe with our senses is the mere surface of a far greater incomprehensible multi-dimensional ocean of non-material spiritual reality. Physicists tell that the physical world we observe with our senses is a mere subset of a far greater incom- prehensible multi-dimensional quantum reality, which curiously is also non-material. Of course, it's all an unlikely coinci- dence, into which I'm putting far too much significance. Or is it? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= AtTheBreakingPoint { ; time=0:03:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip center-mag=+0.8766875323567763/-0.0239258828535604\ 1/1.06232e+012/1/-152.5/0 params=-9/-1.9/-1/-9.1/0\ /0/0/0 float=y maxiter=1500 inside=0 periodicity=6 mathtolerance=0.05/1 colors=000LTSKSRKSQJRPIQPIPOHONGNMGMLFLKFLKEKJDJID\ IHCHGBKFBKFAKEAKD9UC8UB8UA7UA6U96U85c75c64c53c53m4\ 2m3zm2zm1zm0zz9zz7zz6zz4zz36z1zzmxzkvzitzhrzfpzenz\ clzbjz`hz_fzYezXczVazU_zSYzRWzPUzOSzMQzLOzJ04BL6GJ\ 6FH5D74CD4AK39JAO72C51h31c10Sx`UtYSpWQlUOhRMdPKaNI\ YKGURFQGDMDBJB9KRDB65743321ARKaOAXL9RH75RMGA4B7353\ 13PT2QO2PN2OM2NQ2MK2LK2KJ2JO2IH2IG1HF1GK1FE1ED1DC1\ CH1BA1AA19919F08707606505C044033022B9b0004G50T10VZ\ 0Q00P00N0BFF0L00J00I0BDEACAAC99B99BC9A88A889779B78\ 6676676010565565454454443343333232222121111010000R\ `cQZaPY`OXZNVYMUXLTVKSUJQSIPRHOQGMOFLNEKMDJKDHJCGH\ BFGAEF9CD8BC7AB689578466355234122011Kr1Hk0Fe0D_0BU\ 08O06I04C0260idreanbZj_WgXUcUR_ROXOLTLJPIGMFDICAE9\ 8B657323h`f_TYRMPIEH978N4IL3HK3GJ3FI3EH3DG2CE2BD2A\ C29B29A18917816615514403302201100UecTdbScaSb`Ra_Q`\ ZQ_ZPZYPZXOYWNXVNWUMVULUT } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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Albrecht Niekamp's "Inner Secret" (2012-12-03)
by Hal Lane 03 Dec '12

03 Dec '12

While Albrecht Niekamp is on vacation and away from a computer, he has asked me to put some of his images onto my server. Here is a link to his "Inner Secret" fractal created using his multifractal_10 formula: http://www.emarketingiseasy.com/Albrecht/56715AB3.GIF Click the image in your browser for its full size: 1600 x 1200 pixels. Albrecht's fractal gives me the feeling that I want to look closer (zoom in) and see what secrets are hidden in the central figure. The Fractint parameter set is below. The full parameter file for the fractal, including the multifractal_10 formula, is here: http://www.emarketingiseasy.com/Albrecht/56715AB3.par - Hal Lane ######################## # hallane(a)earthlink.net ######################## ===== Start of par file ============================== 56715ab3 { ; Inner_Secret ; Time 0.27.18 1600/1200 ; mmods-phoen-newt-sec-spid reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=asin/exp/exp/sin passes=t center-mag=+0.00082010874916853/+1.264362085302365\ 00/57.86304/1/180 params=-0.05825983458967864/0.3785210730307932/567\ 15.06595750222/14235.4911030602/152048.0404808048/\ 384.1604894048/384.00482000595/128.1007683001/256.\ 1007683001/512.1007683001 float=y maxiter=3072 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000LOr<3>_5fc0ce7_jFRoNIzb0zj0000zr0zz1zzC<\ 2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8KJ8<2>I88H44G00<3>\ TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriAtm9vq8xu7zz5zz4zz\ 3<4>zj4zg4zc4<3>zS5zP5zL6zI6zE6wE6tD6<6>vAIv9Kv9M<\ 3>x7Sy7Uy6Wz6Yz5_<3>f5Ma5IW4E<2>_4H<3>P3DN2CK2A<3>\ 805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0gy0h<3>u1mt1ns1or2\ q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4KW0Qc<3>5Xc6Zc7`c7\ aa7c_7eY<3>FcgHciJbl<3>S_v<3>civflvinvlqvotvsww<2>\ zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI<3>SCCXCAaB\ 9<3>uA2zA0xA0<12>SA1QA1NA1<3>D92<6>UXAW`BYcC<3>hrI\ <3>UnXRm_NlcJkgFfpAazEXwITu } ==== End of par file ============================

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FOTD 02-12-12 (On the Odd Side [6])
by Jim Muth 02 Dec '12

02 Dec '12

FOTD -- December 02, 2012 (Rating 6) Fractal visionaries and enthusiasts: Today's quickie image shows an under-resolved minibrot in the parent fractal that comes about when 8 parts of Z^(-0.1) are combined with 0.8 part of straight Z before (1/C) is added on each iteration. This parent appears as a small lima bean. When enlarged, this lima bean becomes an oval-shaped open area with a smooth perimeter except on the eastern edge, where a small stretch of mandel buds lies. Today's image lies in this small area of mandel stuff. Perhaps the most striking feature in the scene is the wildly discontinuous iteration bands, which in places appear as angular patches rather than the expected smoothly curved bands. A higher maxiter would have fully resolved the central minibrot, but would also have changed the colors. The rating of an everyday 6 indicates that I find nothing exceptional in the image or its colors. The name "On the Odd Side" has little to do with the image except to express my feelings toward it. The calculation time of 9 minutes is more than the image is worth. Save time by visiting the FOTD web sites. Avoid calculation by viewing the finished image online at: <http://www.crosscanpuzzles.com/Archives.html> And check the hi-def variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are posted at: <http://www.Nahee.com/FOTD/> Increasing clouds through the day led to light rain beginning around sunset. The temperature of 50F 10C felt pretty much normal for the start of December. The fractal cats, Nico and Callie, passed the day doing what cats do best. The humans passed the day doing nothing. The next FOTD will be posted in the proper time. Until whenever, take care, and mystics tell us it's impossible for the puny human mind to grasp what's going on up there, while quantum theorists tell us it's impossible for the puny human mind to grasp what's going on down there. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= On_the_Odd_Side { ; time=0:09:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-0.1223958572564503/-0.0168408862844925\ /2.2e+09/1/70/0 params=8/-0.1/0.8/1/0/0/0/0 float=y maxiter=2750 inside=0 logmap=678 periodicity=6 colors=000E9PFAQGBRHCSIDTJEUKFVLGWMHXNIYOJZNK_ML`M\ MaLNbKMcKKdJIeIGeIEfHDgGBhG9hF7iE5jE4jH8kKBkNElQHl\ SKmVNmYQn`UncXoe_ohbpkepnhqpkqlimigjffgbdd_baXaZU_\ WQYTNXQKVNHUKJVJLVJNVIPWIRWHTWHVXGXXGZXF`XFbVIdULe\ SOgRQhPTjOWkMYmL`oKcpIerHhsFkuEmvCpxBsyAumLqbVnSdk\ HnhFmeEmbCm_BmYAmV8lS7lP6lN4lK3lH2lF6hJAdND`RHXVLT\ YOPaSLeWHiZDl_Em_Fm_Gm_Hm_Im_Jm`Kn`Ln`Mn`Nn`On`Pn`\ QnbUhcYcdaYeeTghNhlIipCjt7kw2gv4cu5_u6Wt7St8Os9KrA\ GrBCqC8qD4pE1pF2mH2jI2hJ3eK3bL3`M4YN4VP4TQ5QR5NS5L\ T6IU6FV6DW9GVBJUELUGOTJQTLTSOVSQYRT`QVbQYeP_gPbjOd\ lOchNbdMb`LaXKaTKcSOdSReSUgSXhR_iRbkRelRhmQkoQnpQq\ qQteD`V1IquZjqedmkYirSexOYkLQZHIMEA9ECAEDBEECEGDEH\ EEIEEJFELGEMHENIEOIDLGDJFCGECECCCBB9AB78A47A26A058\ 05704603503402301201100dXI`UGXRETODQLBMI9IF8EC6B94\ 763331tmmrkkqjjpiinhhmgglffjddicchbbfaae``d__bYYaX\ X`WWZVVYUUXTTVRRUQQTPPROO } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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Albrecht Niekamp's "Phoenix on Fire" (2012-12-02)
by Hal Lane 02 Dec '12

02 Dec '12

While Albrecht Niekamp is on vacation and away from a computer, he has asked me to put some of his images onto my server. Here is a link to his "Phoenix on Fire" created using his multifractal_10 formula: http://www.emarketingiseasy.com/Albrecht/252341.GIF Click the image in your browser for its full size: 1600 x 1200 pixels. Albrecht's image has a quite strong 3D effect due to the different depth of focus in our eyes of the dominant red and blue elements in his image. The delicate blue lacework seems to be imprisoned by the blood-red, sharp-edged bands. The par set is below. The full parameter file for the fractal, including the multifractal_10 formula, is here: http://www.emarketingiseasy.com/Albrecht/252341.par - Hal Lane ######################## # hallane(a)earthlink.net ######################## ===== Start of par file ============================== 252341 { ; Phoenix on Fire ; Spider, phoenix ; Time 0.17.32 ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=cos/exp/exp/sin passes=t center-mag=0.017473/0.00308737/1.279389/0.8004/80.114682\ 5257964537/-5.86499452750839545 params=-0.05825983458967864/0.3785210730307932/80006.325\ 64900001/25234.2207090221/151024.0204808192/384.32768524\ 288/384.00482000595/128.1007683001/256.1007683001/128.10\ 07683001 float=y maxiter=3072 inside=maxiter logmap=5 periodicity=0 rseed=-2436 colors=200654<2>000400<23>o00q00s00<3>z00<25>C00A00800<3\ >000<7>FFFHHHJJJ<9>___aaaccc<3>iiijjjlll<3>sss<25>BBB999\ 777<2>222000012<24>0bo0cq0es<3>0kz<25>09C08A068<2>022000\ 211<21>icNkeOmfP<3>unTwpVxqWzsX<27>875 } ==== End of par file ============================

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Albrecht Niekamp's "Ornaments" (2012-12-01)
by Hal Lane 02 Dec '12

02 Dec '12

While Albrecht Niekamp is on vacation and away from a computer, he has asked me to put some of his images onto my server. Here is a link to his "Ornaments" created using his multifractal_10 formula: http://www.emarketingiseasy.com/Albrecht/1536143D.GIF Click the image in your browser for its full size: 1600 x 1200 pixels. Albrecht's image has a great variety of shapes and colors -- all floating on an inky sea. The variety is the result of combining more than one fractal type at the same time. For this fractal, Albrecht used the mandel, secant, bees, phoenix and julia types. The par set is below. The full parameter file for the fractal, including the multifractal_10 formula, is here: http://www.emarketingiseasy.com/Albrecht/1536143D.par - Hal Lane ######################## # hallane(a)earthlink.net ######################## ===== Start of par file ============================== 1536143d { ; Ornaments ; Zoom into 1536143b ; Time 0.25.37 DOS Shell 1600/1200 ; mandel-secant-bees-phoenix-julia ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=-0.71012896882282740/-0.078504458682040\ 03/21838.24/1/75.0000000000001847/-1.0075613954274\ 5871e-011 params=-0.05825983458967864/0.3785210730307932/213\ 64.64595712822/14235.4911030602/152048.0404808048/\ 384.1604894048/384.00482000595/256.1007683001/512.\ 1007683001/768.1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000000zr0zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>L\ Q8KM8KJ8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>\ qeBriAtm9vq8xu7zz5zz4zz3<4>zj4zg4zc4<3>zS5zP5zL6zI\ 6zE6wE6tD6<6>vAIv9Kv9M<3>x7Sy7Uy6Wz6Yz5_<3>f5Ma5IW\ 4E<2>_4H<3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>\ y0fz0gy0h<3>u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAA\ G7FO4KW0Qc<3>5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<\ 3>civflvinvlqvotvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa\ <3>8JP8FL8CI<3>SCCXCAaB9<3>uA2zA0xA0<12>SA1QA1NA1<\ 3>D92<6>UXAW`BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJo\ SFlWAi_5fc0ce7_jFRoNIzb0zj0 } ==== End of par file ============================

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FOTD 30-11-12 (Art-Deco Breakup [7])
by Jim Muth 30 Nov '12

30 Nov '12

FOTD -- November 30, 2012 (Rating 7) Fractal visionaries and enthusiasts: Early in their fractal explorations, beginning fractalists discover that the higher dimensional fractals hold little of interest. To put it bluntly, the images all look the same. But to disprove a point, I present today's image, which lies in the very narrow ring of interest at the western edge of the Z^(100)+C Mandeloid. The unexpected action was created by calculating the image with the 'exp' function applied to initial C. This slight addition changed the entire nature of the image. Instead of a screen filled with similar minibrots, we have an interesting assortment of effects, including a vertical range of resolution, from near perfect at the top to total breakdown at the bottom. Curiously, though the large scale breakup is quite obvious, the small-scale edges of the breaks are well resolved. The lower half of the image in particular has an art-deco feeling about it. The name "Art-Deco Breakup" refers to this resemblance. The rating of a 7 is FOTD average. The calculation time of 1-1/3 minutes is also near average. The finished image is online at: <http://www.crosscanpuzzles.com/Archives.html> High-def variations are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images may be accessed at: <http://www.Nahee.com/FOTD/> A mix of sun and clouds with a temperature of 43F +6C made today the latest in a string of similar days here at Fractal Central. The fractal cats passed the day watching the outside conditions as well as each other. The humans did a lot less watching and notably more working. The next FOTD fractal will be posted around December 2. Until whenever, take care, and pseudoscientific occultists claim there are higher-dimensional realities they call astral planes. Totally scientific physicists claim there are higher dimensional realities they call parallel alternate universes. As for me, I'm waiting to see some kind of solid proof that any of these invisible worlds actually exist. (Of course, by definition they are invisible, so how can anyone find solid proof?) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Art-Deco_Breakup { ; time=0:01:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotFNC function=exp passes=t center-mag=-34.2/0/0.3267943/1/90/0 params=100/0/0\ /0/-1.007026054383232/0 logmap=9 maxiter=1800 inside=0 float=y periodicity=0 mathtolerance=0.05/1 colors=000B8s9Br8Er6Hq5Kp4NpDQnKWlVdjcohYigTdfOZeJ\ UdEOc9JcKMdUPdRqNWrO_sOdtOhtOmuOqvOuvOzsTzqYzobzmg\ zj`zgVzdPzbIz_CzX6zV0zS1zP2zM3tK3qO9lSFgWLa_RUbXTa\ TTaQSaMSaJR`FR`CQ`8Q`5NXDLUKIRRGOYEKeBHl9Es7Bz8Hv8\ Mr8Rn8Xj8af8fb8kZBgWDdUGaRIZPLWMNTKJPQGMWDJ`AFf7Ck\ 49q16v7AsDDpJGmPJjVMg`PebOddOdfNchNcjMclMbnLboLbgT\ _``YUhVNpTpvomc_jLLh26e9GcFPaLY_SfYYoWcx__ocWfgSYk\ OPoKGrH8nFEkEKhDQeCWbBa_AgX9m_EdaJXdOOfSG`eCWr8YsE\ _tKauQcuWevagwgiwlgugetbcsYarT_pOYoJWnEVm9akIgiQng\ Ztefzcnxajv_ftYbsXZqVVoTRnSOUeCAs1SWBi9KYm5`gAcaFe\ WJhROjLSmFXoA`iLacVaeBmUPpJarLcdNeSPgERi1Vk3Zm4bo6\ ep7VqKLrXAsi0sv4pp7nkAlfEi`HgWKeRNcMTUNZKNdAOi0ObU\ PXvQ`vSdwUhwXmxZqxauycyyeZh5_g9`fD`eHadLadPbcTbbWc\ a_cacd`gd_keZoeZrUYKSXLQWLOWMNVMLUMJUNITNGTOESODRO\ BRP9QP8QP7UL6YH6aE5eA4i64m3omytqzxuzrnwmguh`rcVpZO\ mOG2RA3hVT`X`TZgL`nEbuCYt } frm:MandelbrotFNC {; Jim Muth b=p1, z=p2, c=p3+fn1(pixel): z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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Albrecht Niekamp's "Mandel Invasion" (2012-11-30)
by Hal Lane 30 Nov '12

30 Nov '12

While Albrecht Niekamp is on vacation and away from a computer, he has asked me to put some of his images onto my server. Here is a link to his "Mandel Invasion" created using his multifractal_10 formula: http://www.emarketingiseasy.com/Albrecht/2022201.GIF Click the image in your browser for its full size: 1600 x 1200 pixels. The "marching Mandeloids," crackling with electricity, seem to be colliding in the center. The red, blue, silver and gold color map appears to be similar to the one used in yesterday's fractal. The par set is below. The full parameter file for the fractal, including the multifractal_10 formula, is here: http://www.emarketingiseasy.com/Albrecht/2022201.par - Hal Lane ######################## # hallane(a)earthlink.net ######################## ===== Start of par file ============================== 2022201 { ; Mandel_Invasion ; Time 0.02.37 1600/1200 ; 4*mandel reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=exp/exp/exp/sin passes=t center-mag=-0.491807/5.55112e-016/0.9752988 params=-0.05825983458967864/0.3785210730307932/202\ 22.32595710666/25234.4911020602/151024.0204808192/\ 384.32768524288/384.00482000595/128.1007680001/512\ .10076800005/768.10076800002 float=y maxiter=1024 inside=maxiter logmap=4 periodicity=0 rseed=-2436 colors=200A85<17>icNkeOmfP<3>unTwpVxqWzsX<25>CB7A9\ 6875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>00\ 0<23>fffgggiiijjjlll<3>sss<25>BBB999777<2>22200001\ 2<24>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<2>86\ 4 } ==== End of par file ============================

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FOTD 29-11-12 (Kinky Corner [?])
by Jim Muth 29 Nov '12

29 Nov '12

FOTD -- November 29, 2012 (Rating ?) Fractal visionaries and enthusiasts: The FOTD is currently being posted every other day. This is due to an unusually busy spell here at FC. After the holidays, the FOTD will return to its almost-every-day schedule. Today's image shows what a person would see surrounding him if he stationed himself at the center of a Julia spiral. (In this case, the spiral is one of those associated with Seahorse Valley of the Mandelbrot set.) As he looked around, he would see a wall of rings in all directions. If his view were unwrapped and projected onto a flat screen, it would appear as today's image, which is part of a periodic larger image. This larger image is periodic because the 'exp' function shows what he would see if he continued rotating his view indefinitely. Don't shuffle the kids away. The name "Kinky Corner" refers to the small kink in the lower left corner. The image has been stretched about three times in the vertical direction to make the straightened-out spiral arms more apparent. Since the interest is purely mathematical, I could not give the image a rating. The question mark indicates the uncertainty. Unfortunately for those with limited time, the image is a slow one, taking 11 minutes to finish. The good news is that the web sites are there to make fractal life easier. The image may be viewed without the need to calculate it by visiting the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> Variations are posted in high-definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are at: <http://www.Nahee.com/FOTD/> Cloudy periods alternated with sunny periods here at Fractal Central today, while the temperature of 43F +6C was close to normal. The fractal cats had an average day of it, as did the humans. The next FOTD will be posted in a day or two. Until whenever, take care, and which is more likely to be in two different places at the same time, a Christian saint in a state of bilocation or an electron in its wave aspect? (Both things are apparently impossible, yet both are claimed to be true.) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Kinky_Corner { ; time=0:11:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=slices.frm formulaname=JuliaFNZ function=exp passes=1 center-mag=-5.62965/12.738/0.5560629/0.3862/-95/0 params=2/0/-0.5010419796557/0.0152933866127/-0.751\ 85195471/0.030619434187 float=y maxiter=2450 inside=0 logmap=-777 periodicity=0 colors=0000Xd0Ye0Zf0_g0`h0ai1bj2ck3dl4em5fn6go7hp8\ iq9jr9iq9iq9hp9ho9go9fnAfmAemAelAdlAckAcjAbjBbiBah\ B`hB`gB_fB_fBZeBYeCYdCXcCXcCWbCVaCVaCU`DU_DT_DSZDS\ ZDRYDRXDQXDPWEPVEOVEOUENTEMTEMSELSFLRFKQFJQFJPFIOF\ IOFHNDILEHMFHMFHNGHNGHOHHOIHPIHPJHQJHQKHRKHRLHRMHS\ MHSNHTNHTOHUPHUPHVQHVQHWRHWRHWSHXTHXTHYUHYUHZVHZWH\ _WH_XH`XH`YHaYHaZGa_Gb_Gb`Gc`GcaGdbGdbGecGecGfdGfd\ GfeGgfGgfGhgGhgGihGiiGjiGjjGkjGkkGlkGllGlmGmmGmnGn\ nGnoGopGopGpqGpqGqrGqvDxtEusFsrGqqHopImnJkmKhlLfkM\ djNbhO`gPZfQXeRUdSSbTQaUO`VM_WKZXHXYFWZDV_BU`9Ta7T\ c4Sb5Sb5Rb5Rb5Ra5Qa6Qa6Qa6P`6P`6P`6O`7O`7O_7N_7N_7\ M_8MZ8MZ8LZ8LZ8LZ8KY9KY9KY9JY9JX9JX9IXAIXAIXAHWAHW\ AGWBGWBGVBFVBFVBFVBEUCEUCEUCDUCDUCDTCCTDCTDBTDBSDB\ SDASEASEASE9RE9RE9RE8RF8QF8QF7QF7QF3TG5SF6RF7QF8QF\ 9PFBOECOEDNEEMEFMEHLEIKDJKDKJDLIDNIDOHDPGCQFCRFCTE\ CUDCVDCWCBXBBZBB_AB`9Ba9B } frm:JuliaFNZ {; Jim Muth b=p1, z=p2+fn1(pixel), c=p3: z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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While Albrecht Niekamp is on vacation (2012-11-29)...
by Hal Lane 29 Nov '12

29 Nov '12

While Albrecht Niekamp is on vacation and away from a computer, he has asked me to put some of his images onto my server. Here is a link to his "Mother of Pearls" created using his multifractal_10 formula: http://www.emarketingiseasy.com/Albrecht/3518702.GIF Click the image in your browser for its full size: 1600 x 1200 pixels. I like the image's Paul Carlson-esque color map. The image's unusual features also seem to be suited to the red, blue, silver and gold color map. You can see the gradual changes in the colors of the map that make the .gif image almost appear like a full color image here: http://www.emarketingiseasy.com/Albrecht/3518702_c.jpg The full parameter file for the fractal, including the multifractal_10 formula is here: http://www.emarketingiseasy.com/Albrecht/3518702.par - Hal Lane ######################## # hallane(a)earthlink.net ######################## ===== Start of par file ============================== 3518702 { ; Mother_of_Pearls ; Time 0.09.83 1600/1200 ; bees-mmods-sec-spid-newt reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=-0.0962826/1.11022e-016/4.901961/1/90/3\ .88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/351\ 87.64595767025/14235.4911030602/152048.0404808048/\ 384.1604894048/384.00482000595/256.1007683001/512.\ 1007683001/768.1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=200777<2>222000012<22>0_k0am0bo0cq<3>0jx0kz\ 0jx<24>09C08A068<2>022000211<21>icNkeOmfP<3>unTwpV\ xqWzsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25\ >C00A00800<3>000<11>LLLNNNPPPQQQSSSUUU<6>fffgggiii\ jjjlll<3>sss<26>999 } ==== End of par file ============================

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Re: [Fractint] This fractal reminds me of an interstate highway interchange.
by Hal Lane 28 Nov '12

28 Nov '12

Mike, > This fractal reminds me of an interstate > highway interchange. That's a nice image. I remember once getting caught up in a highway interchange that felt like that. The exit I wanted was always one loop away. - Hal Lane ######################## # hallane(a)earthlink.net ######################## Author: Mike Frazier Date: 2012-11-25 20:18 -500 To: Fractint and General Fractals Discussion Subject: [Fractint] Interchange This fractal reminds me of an interstate highway interchange. I will be working on some user interface enhancements for Fracton so I probably won't post many fractals until it is done. Here is a link to an image: http://dl.dropbox.com/u/33642054/image/interchange_1200_5.jpg The Fractint compatible PAR file for the image is: Interchange { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20121125_1809 passes=1 float=y center-mag=-3.25645846439087/-3.814661194115161e-0\ 7/21845.33374956558/1/0/0 params=-1/-1/0/4/-1/0/1/0/0/0 maxiter=2000 inside=0 periodicity=6 colors=bbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooop\ ppqqqrrrssstttuuuvvvwwwxxxyyyzzzrrrsssqqqooommmkkk\ iiigggeeecccaaa___YYYWWWUUUSSSQQQOOOMMMKKKIIIGGGEE\ ECCEAAE88E66E44E22E00F00G00I00K00M00O00P00R00T00V0\ 0X00Z00`00b00c00e00g00i00k00m00o00q00r00t00v00x00z\ 01z13z25z37z39z4Bz5Dz6Fz7Hz8Jz9Lz9NzAPzBRzCTzDUzEW\ zFYzF_zGazHczIezJgzKizLkzLmzMozNqzOszPuzOtyNsxNqwM\ pvLntKmsKkrJjqIhpHgoHenGdmFbkEajE_iDZhCXgBWfBUeATd\ 9Rb8Qa8O`7N_6LZ5KY5IX4HW3FU2ET2CS1BR09P19Q3AR4BT6C\ U7DW9EXAFZCG_DG`FHbGIcIJeJKfLLhMMiONkQPkSSlVUmXXn_\ Zoaapdcqffrhhskktmmuppvrrwuuxwwyzzzzwxzsuzoszkpzgn\ zckz_izWfzSdzOazK_zGXzCVz8Sz4Qz0Nw1Mt1Mp2Lm2Kj2Jh3\ Ie4Hb4G_5GX5FU6ER6DP7DM8CJ8BG9AD99AA97A84B75D86FA7\ IB8KD9ME000111222333444555666777888999AAABBBCCCDDD\ EEEFFFGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPQQQRRRSSSTTTUU\ UVVVWWWXXXYYYZZZ___```aaa } frm:F_20121125_1809 { ; Similar to the parallel resistance formula a=real(p1),b=real(p2),d=imag(p1),f=imag(p2), z=0,c1=pixel-p3,c2=pixel-p4: z=1/(1/(a*z*(cosh(z)-1)+c1)+1/(d*z*z*sinh(z)+c2)), |z|<100 } -- Mike Frazier www.fracton.org -----

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FOTD 27-11-12 (Broken Arches [7])
by Jim Muth 27 Nov '12

27 Nov '12

FOTD -- November 27, 2012 (Rating 7) Fractal visionaries and enthusiasts: Today's image takes us to a tiny minibrot far out on the main spike of the Mandelbrot set, to the region of -1.9999.... As has been the case recently, the minibrot has been enlarged to millions of times its normal size by calculating the scene with exp(C) instead of straight C. The name "Broken Arches" does not refer to a foot problem. It refers to the resolution breakdown in the upper part of the image, and indicates that there is no tricky way to gain extra magnitude other than with more math precision. The rating of a 7 is what I think the image is worth. And it is certainly worth a trip to the FOTD web sites. Gain total worth by viewing the finished image at: <http://www.crosscanpuzzles.com/Archives.html> Feel better by viewing the hi-def variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Feel best of all by checking thousands of back images at: <http://www.Nahee.com/FOTD/> The day began with snow here at Fractal Central. The snow fell at a moderate rate all morning before slacking off and ending just after noon. The 'official' FC measurement was 3-1/2 inches or 9mm. When the snow ended, the afternoon temperature rose to 37F +3C, which melted about half the ice. The fractal cats spent the morning watching the big sloppy flakes fall, and the afternoon sleeping. I spent a half hour in the afternoon clearing slush from the walkway, while FL took charge of the hot coffee. The next FOTD will be posted when I think it's ready. Until whenever, take care, and if the same single thing is seen to exist in two separate places at the same time, is it a demonstrated fact of quantum physics or a bilocation miracle claimed by the church? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Broken_Arches { ; time=0:05:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotFNC function=exp float=y center-mag=-29.3728/0.0981905/0.1252939/1.952/-90/0 params=2/0/0/0/-1.999911750271786/4.64e-12 inside=0 maxiter=30000 periodicity=0 mathtolerance=0.05/1 colors=000Whaah`gh_riYlhZfh_`h`Vh`PhaJhbDhc0oM7hcF\ cwEbuDbtDbrCaqCaoBanB`lA`kA`jCciEehGggIjfJleLndNqc\ PsbRuaSw`SpWSiRScMSXHSQCSK8XHF`ELdBSi8Ym5dq2jo8enD\ alIYkNTiSPhXLfaGefCck8bp4al7ahA`dD``G_XI_TLZPOZLRX\ LVZIT`GSaERcBQe9Pf7Oh4Nj2Mk0Ll3Kl5Jm7Im9HnBGnEGoGF\ oIEpKDpKCpKCpJCsIBrGCrEDqCEqAFpBGpBGoCHoCIoCJnDKnD\ KmELmEMlFNlFOnCNlFOkHOjJPiLPhOQgQQfSReTRcURbWSaYS`\ _T_aTZcUYcUacVXcUScQOcMRcOUbPWaQZ`R``Sc_TeZUhYVkXW\ mXUpWSrVQuUOqUMmUKhUIcUGZUEUUCPUAKT8IQ6FN6CL5AJ39I\ 5BK7HR9KWBN`DReFVjHYoJatLrzKdxMzvOctPbrRbpSaoU`mW`\ kX_iZ_g_Zea`jeZdbYZ`XTZUJYWNXXRWZUV_YUa`UbdTdhSekR\ goQnqShrQcrOZsMTsKOtIHuCJtGKsKMrONqSPpWQo_SncWreTn\ fRkfPhfNefLbfJ_fGWfETfCQfANf8Kf18o6HfAPYFYPHhGJeHL\ cHN`HPZIRXITUIVSJXPJZNJeOF`LJXINTFROCVK9ZB6ZG7aL7c\ Q7eV7g_8jd8li8nn8pr8rp9oo9lm9il9gjAdiAagAZfAXeBUcB\ RbBO`BMAkc9je8igEheKhdQhc } frm:MandelbrotFNC {; Jim Muth b=p1, z=p2, c=p3+fn1(pixel): z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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Interchange
by Mike Frazier 26 Nov '12

26 Nov '12

This fractal reminds me of an interstate highway interchange. I will be working on some user interface enhancements for Fracton so I probably won't post many fractals until it is done. Here is a link to an image: http://dl.dropbox.com/u/33642054/image/interchange_1200_5.jpg The Fractint compatible PAR file for the image is: Interchange { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20121125_1809 passes=1 float=y center-mag=-3.25645846439087/-3.814661194115161e-0\ 7/21845.33374956558/1/0/0 params=-1/-1/0/4/-1/0/1/0/0/0 maxiter=2000 inside=0 periodicity=6 colors=bbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooop\ ppqqqrrrssstttuuuvvvwwwxxxyyyzzzrrrsssqqqooommmkkk\ iiigggeeecccaaa___YYYWWWUUUSSSQQQOOOMMMKKKIIIGGGEE\ ECCEAAE88E66E44E22E00F00G00I00K00M00O00P00R00T00V0\ 0X00Z00`00b00c00e00g00i00k00m00o00q00r00t00v00x00z\ 01z13z25z37z39z4Bz5Dz6Fz7Hz8Jz9Lz9NzAPzBRzCTzDUzEW\ zFYzF_zGazHczIezJgzKizLkzLmzMozNqzOszPuzOtyNsxNqwM\ pvLntKmsKkrJjqIhpHgoHenGdmFbkEajE_iDZhCXgBWfBUeATd\ 9Rb8Qa8O`7N_6LZ5KY5IX4HW3FU2ET2CS1BR09P19Q3AR4BT6C\ U7DW9EXAFZCG_DG`FHbGIcIJeJKfLLhMMiONkQPkSSlVUmXXn_\ Zoaapdcqffrhhskktmmuppvrrwuuxwwyzzzzwxzsuzoszkpzgn\ zckz_izWfzSdzOazK_zGXzCVz8Sz4Qz0Nw1Mt1Mp2Lm2Kj2Jh3\ Ie4Hb4G_5GX5FU6ER6DP7DM8CJ8BG9AD99AA97A84B75D86FA7\ IB8KD9ME000111222333444555666777888999AAABBBCCCDDD\ EEEFFFGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPQQQRRRSSSTTTUU\ UVVVWWWXXXYYYZZZ___```aaa } frm:F_20121125_1809 { ; Similar to the parallel resistance formula a=real(p1),b=real(p2),d=imag(p1),f=imag(p2), z=0,c1=pixel-p3,c2=pixel-p4: z=1/(1/(a*z*(cosh(z)-1)+c1)+1/(d*z*z*sinh(z)+c2)), |z|<100 } -- Mike Frazier www.fracton.org

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FOTD 25-11-12 (Multiplication of the Rectangles [7])
by Jim Muth 25 Nov '12

25 Nov '12

FOTD -- November 25, 2012 (Rating 7) Fractal visionaries and enthusiasts: NEW FORMULA ALERT. This is the first time I have posted an image created with today's JuliaFNZ formula, which is simply the Julia version of the MandelbrotFNC formula. The name "Multiplication of the Rectangles" refers to the brilliant blue arch-shaped features in the image. These blue areas are actually close-up views of the mysterious rectangle in the Z^(2.003)+C Julia set, which have been distorted beyond recognition. The rating of a 7 is a continued improvement, though far from the lofty heights reached by some FOTD images. The calculation time of 2-1/2 minutes will pass quickly. Gratification may be achieved faster on the FOTD web sites. Avoid calculation altogether by viewing the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> And enjoy the hi-def variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are available at: <http://www.Nahee.com/FOTD/> Heavy scudding clouds, blustery winds and a temperature of 36F +2C made today feel like midwinter here at Fractal Central. The fractal cats made it through the day peacefully, while the humans did the same. The next FOTD will be posted in a day or two. Until whenever, take care, and nothing is more frustrating than people out demanding that we adopt their solutions to problems they don't comprehend. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Mult_of_the_Rects { ; time=0:02:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=slices.frm formulaname=JuliaFNZ function=exp passes=1 center-mag=-8.53244/1.57069/0.2026689/1/-90/0 params=2.003/0/0/0.074253572/-1.74315/0 float=y maxiter=1500 inside=fmod proximity=0.045 logmap=28 periodicity=0 mathtolerance=0.05/1 colors=0005Pz6Uz6Zz7cz7hz8rz9zz_gUZeTYdSXbRVaQU`PT\ ZOSYNRWMPVMOTLNSKMRJLPIJOHIMGHLFGJEFIDAGBCHCEHDGIE\ IIEKJFMJGOKGQKHSLIULIWLJYMK_MLaNLcNMeONgONiPOkPPlP\ PjOQiNRhNRgMSfMTeLTdLUcKVbJVaJW`IX_IXZHYYHYWGZVF_U\ F_TE`SEaRDaQDbPCcJBbHBbCAbAAaKAaIA_DA_A9ZC7ZA5Y84X\ D5U45T26RA6Q97O07N08L08K08J29I49H6AG8AFABECBDEBDGC\ CICCKDBMDBOEAQEASE9UF9WF9XGAYGAZHA_HA`HAZIEYJJWKMV\ LPRJQUMRWOSZRS`TTbVTeYUg_UjbVldVnfWqiWskXumXtkWtjW\ tiWshVsgVsfVseVrcUrbUraUq`Tq_TqZTqYTpWSpVSpUSoTRoS\ RoRRoQRpRTpSUpSVqTXqTYqUZqU_rVarVbrWcrWdsXfsYgsYht\ ZjtZkt_lt_mu`ou`puaqybvwatuars`qq`op_nn_llZkjZihYh\ gYfeYdcXcaXa_W`ZWZXVYVVWTUVRUTQUSRVTSVUSVUTVVUVVUV\ WVVWWVXWVXXVYYVYYWZZWZ_W__W_`W`aW`aWabWacWbcWbdWcV\ ckdWcfShjQbmPXqNR7TLtMMsKOsJQsISsHUsGWsFYsE_uCbsDa\ rE`qF_pG_oHZmIYlJYkKXjLWiMWgNVfOUePUdQTcRSaSR`TR_U\ QZVPYWPWXOVYNUZNT_MS`LScJ } frm:JuliaFNZ {; Jim Muth b=p1, z=p2+fn1(pixel), c=p3: z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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Orbicular
by Mike Frazier 24 Nov '12

24 Nov '12

This fractal has circles, ovals, rounded rectangles, diamonds, and a square. Here is a link to an image: http://dl.dropbox.com/u/33642054/image/orbicular_1200_5.jpg The Fractint compatible PAR file for the image is: Orbicular { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20121123_2022 passes=1 float=y center-mag=-3.953281687312188/-5.224562695854533e-\ 15/888888900000/1/0/0 params=-1/1/0/4/-1/0/1/0/0/0 maxiter=2000 inside=0 periodicity=6 colors=000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O\ 40C10000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40\ C10000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C1\ 0000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C100\ 00C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000\ C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C1\ 0O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O\ 40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40\ ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA\ 0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0h\ I0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0\ oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS\ 0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0u\ a0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0ua0\ ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0ua0ym\ 0zy0ym0ua0oS0hI0ZA0O40C10 } frm:F_20121123_2022 { ; Similar to the parallel resistance formula a=real(p1),b=real(p2),d=imag(p1),f=imag(p2), z=0,c1=pixel-p3,c2=pixel-p4: z=1/(1/(a*z*(cos(z)-1)*sin(z)+c1)+1/(d*(z^f)+c2)), |z|<100 } -- Mike Frazier www.fracton.org

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The broken parameter files
by Jim Muth 24 Nov '12

24 Nov '12

Fractal fans: The broken parameter files are what happens when formula names are changed after the images are created. Hopefully, it will not happen again . . . but there is no guarantee. JIM

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Corrected -- FOTD 23-11-12 (Total Absurdity [6])
by Jim Muth 24 Nov '12

24 Nov '12

FOTD -- November 23, 2012 (Rating 6) Fractal visionaries and enthusiasts: Today's image places the emphasis on the large minibrot on the main stem of the Mandelbrot set. Yes, that is the large minibrot itself, appearing as the two large bays at the top of today's image. The M-set is the half-squashed thing at the bottom right of the frame. The name "Total Absurdity" refers to the ridiculous distortion of today's image, and also to a comment I heard on the lunch- time news show. The image rates a 6, a point above the most recent Mandelbrot distortion, yet well below FOTD average. The calculation time of 1-1/4 minutes is mercifully brief. The image is also avaliable on the web sites. See the finished image online at: <http://www.crosscanpuzzles.com/Archives.html> Check the hi-def variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And return to the past where the back images are posted at: <http://www.Nahee.com/FOTD/> Morning sun gave way to afternoon clouds here at Fractal Central today. The temperature of 54F 12C was mild enough, but a cold front is drawing close, and by Saturday we'll be lucky to see a high of 41F +5C. The fractal cats spent the day taking it easy, while the humans tended to human chores. The next FOTD will be posted when the time is right. Until whenever, take care, and believe it or not, on the lunch- time news show today, a so-called 'scientist', (I wonder if he really was a scientist.), was asked what we might do about global warming. He ignored the question and replied 'put the electric wires underground'. If this were economically possible, which at a cost of several million dollars per mile, it is not, it would certainly improve the appearance of our surroundings, but it didn't seem to prevent a massive outage in Manhattan when they were flooded, and I'm not sure how it would fight global warming. The question of what the 'scientist' thought we might do about global warming, remained unanswered. BTW, my solution to the problem of power outages is to return to the instruction book and trim *all* the trees that might fall on power lines in a wind or ice storm. My solution to global warming is to stop debating whether it exists, (it does), and to spend our money preparing for it instead of wasting energy trying to pass futile laws to slow or stop it. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Total_Absurdity { ; time=0:01:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotFNC function=exp center-mag=-4.32344/-1.39951/0.1838365/2.1609/-90/0 params=2/0/0/0/-1.768651397/0.001551282 float=y maxiter=7500 inside=0 logmap=yes periodicity=0 colors=000iaQibQhcRheRgfSggTfiTfjUekUemVdnVdoWcqXc\ rXbsYbuYavZcyYawZ`vZ_uZYsZXr_Wq_Up_Tn_Sm`Ql`Pj`Oi`\ MhaLgaKeaJdaHcbGbbF`bD_bCZcBXc9Wc8Vc7Ud5Sd4Rd3Qd2P\ d5Qc7Rc9SbBTbDUaFVaIWaKX`MX`OY_QZ_S_ZU`ZXaZZbY`cYb\ dXddXfeWifWkgWmhVoiVqjUskUukUsjWriYqh_pgaofcneemdg\ ldikckjbmiaoh`qg_sfZugYweZvcZvbZu`Zu__tY_tX_sV_sU_\ rS`rR`qP`qN`qM`pKapJaoHaoGanEanDbmBbmAbl8bl6ck7bl7\ bl7bl7bm8bm8bm8bm8bn8bn9bn9bo9bo9boAboAbpAbpAbp9`t\ AbpAdmAfiAgfAicBk_BmXBnTBpQBrNCtJCuGCwCCy9Cz6Hs8Ll\ 9QfAU_BZTDbNEgGFk9Gq2Eo3Hn4Jm5Ll6Nk7Pi8Sh9UgAWfBYe\ C_cDbbEdaFf`Gh_HjYHmZIlZIl_Il_Ik_Ik`Ik`Ij`IjaIjaIj\ bIibIibIicIhcIhcIhdIgdIgeIgeIgeIffIffIffIegIegIegI\ edKbbM_`OXZQUXSRVUOTWMRYJP_GNaDLcAJe7Fk6Hg5Ic5J_4L\ W4MT3NP3PL2QH2RE2YAWd6x`AsYEnVHiSLdPP_MSVJWQGZLEXN\ DWPCVRAUT9TV8RX6QZ5P`4Ob3Nc5Oa6P`7Q_8QZ9RYASXBTVCT\ UDUTEVSFWRGWQHXPJYNKZMLZL } frm:MandelbrotFNC {; Jim Muth b=p1, z=p2, c=p3+fn1(pixel): z=z^(b)+c, |z| <= 16 } END PARAMETER FILE========================================= > > >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint >

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Corrected -- FOTD 21-11-12 (Re-Arranged Mandy [5])
by Jim Muth 24 Nov '12

24 Nov '12

FOTD -- November 21, 2012 (Rating 5) Fractal visionaries and enthusiasts: Today's quick image shows a Mandelbrot set with its parts re- arranged beyond recognition. The largest bay in the image is actually the period-2 bud of the M-set. The bay on the left side of the image is the second bud along the negative X-axis of the M-set. The true main bay of the M-set is the little dimple hanging from the largest bay in the image. East valley lies at the bottom of the dimple. The most prominent valley in the image is actually Scepter Valley. Seahorse Valley lies at the bottom of the large bay in the image, where the little dimple is hanging. The spike shooting downward from the bay on the left of the image is the main spike of the M-set. The name "Re-Arranged Mandy" needs no explanation. The rating of a 5 reflects my opinion of the image. The calculation time of one minute is fast enough to keep boredom at bay. Avoid calculation. View the finished image at: <http://www.crosscanpuzzles.com/Archives.html> Hi-def variations are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are at: <http://www.Nahee.com/FOTD/> The morning fog cleared by 9am here at Fractal Central, leading to a sunny day with a temperature of 52F 11C. The fractal cats enjoyed the near perfect conditions. The humans, busy as always, enjoyed things also. The next FOTD will be posted in a couple days. Until this glorious moment arrives, take care, and pick the doomsday of your choice. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Re-Arranged_Mandy { ; time=0:01:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotFNC function=exp center-mag=-3.71379/-1.27343/0.2237866/1.7473/-90/\ -1.23373533611470521e-014 params=2/0/0/0/-1.25/0.02 float=y maxiter=10000 inside=0 logmap=yes symmetry=none periodicity=6 sound=off mathtolerance=0.05/1 colors=000hGweIwcKv`MvZOvWQvURvRTvPVvMXvKZuH`uFauC\ cuAeuAguDiuGkuIluMirOgpQenSckUaiX_g_YdbWbeU`hSZjQW\ mOUoMSqKPsINuGLwDIwEJwEJwEJwEJwEJwEJwEJwFJwFJwFJwF\ JvFKvFKvFKvGKvGKvGKvGKvGKvGKvGKvGKvHLvHLvHLvHLvHLv\ HLvHLwILwILwILwILwIMwIMwIMwJMwJMwJMwJMwJMwJMwJMyHK\ xILwJMwKNvLOuLPuMQtNRsOSsOTrPUrQVqRWpRXpSYoTZnU_nU\ `mVamWblXckYdkYejZfi_gi`hh`igajgbkfclfcmedndeodfpc\ fqbgrbhsaitaiuXjuTkuOluKmuElxGmuHmsJnpKnnLokNoiOpg\ PpdRqbSq_UrYVrWWrTYsRZsO_tMatJbuHduFevCfvAhw7iw5nz\ 4jw3gt3dq3ao3Zl3Wi3Tg3Qd3Ma2J_2GX2DU2AS27P24M21K23\ L34L36L37L49L4AL4BL4DL5EL5GL5HL6IL6KL6LL6NL7OL7QL7\ RL7SL8UL8VL8XL9YL9ZL9`L9aLAcLAdLAfLBgLBhLBjLBkLCmL\ CnLCoLCpMDpNEpOFpPGpQHpRIpRJpSKpTLpUMpVNpWOpXPpXQp\ YRpZRp_Sp`TpaUpbVpbWpcXpdYpeZpf_pg`phaphbpicpjdpke\ plepmfpngpnhpoippjpqkprlpsmptnptopuppvqpwrpxspytpy\ tqtjrp`skRvdEtfGsgHrhIpiJ } frm:MandelbrotFNC {; Jim Muth b=p1, z=p2, c=p3+fn1(pixel): z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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FOTD 23-11-12 (Total Absurdity [6])
by Jim Muth 24 Nov '12

24 Nov '12

FOTD -- November 23, 2012 (Rating 6) Fractal visionaries and enthusiasts: Today's image places the emphasis on the large minibrot on the main stem of the Mandelbrot set. Yes, that is the large minibrot itself, appearing as the two large bays at the top of today's image. The M-set is the half-squashed thing at the bottom right of the frame. The name "Total Absurdity" refers to the ridiculous distortion of today's image, and also to a comment I heard on the lunch- time news show. The image rates a 6, a point above the most recent Mandelbrot distortion, yet well below FOTD average. The calculation time of 1-1/4 minutes is mercifully brief. The image is also avaliable on the web sites. See the finished image online at: <http://www.crosscanpuzzles.com/Archives.html> Check the hi-def variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And return to the past where the back images are posted at: <http://www.Nahee.com/FOTD/> Morning sun gave way to afternoon clouds here at Fractal Central today. The temperature of 54F 12C was mild enough, but a cold front is drawing close, and by Saturday we'll be lucky to see a high of 41F +5C. The fractal cats spent the day taking it easy, while the humans tended to human chores. The next FOTD will be posted when the time is right. Until whenever, take care, and believe it or not, on the lunch- time news show today, a so-called 'scientist', (I wonder if he really was a scientist.), was asked what we might do about global warming. He ignored the question and replied 'put the electric wires underground'. If this were economically possible, which at a cost of several million dollars per mile, it is not, it would certainly improve the appearance of our surroundings, but it didn't seem to prevent a massive outage in Manhattan when they were flooded, and I'm not sure how it would fight global warming. The question of what the 'scientist' thought we might do about global warming, remained unanswered. BTW, my solution to the problem of power outages is to return to the instruction book and trim *all* the trees that might fall on power lines in a wind or ice storm. My solution to global warming is to stop debating whether it exists, (it does), and to spend our money preparing for it instead of wasting energy trying to pass futile laws to slow or stop it. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Total_Absurdity { ; time=0:01:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotFN function=exp center-mag=-4.32344/-1.39951/0.1838365/2.1609/-90/0 params=2/0/0/0/-1.768651397/0.001551282 float=y maxiter=7500 inside=0 logmap=yes periodicity=0 colors=000iaQibQhcRheRgfSggTfiTfjUekUemVdnVdoWcqXc\ rXbsYbuYavZcyYawZ`vZ_uZYsZXr_Wq_Up_Tn_Sm`Ql`Pj`Oi`\ MhaLgaKeaJdaHcbGbbF`bD_bCZcBXc9Wc8Vc7Ud5Sd4Rd3Qd2P\ d5Qc7Rc9SbBTbDUaFVaIWaKX`MX`OY_QZ_S_ZU`ZXaZZbY`cYb\ dXddXfeWifWkgWmhVoiVqjUskUukUsjWriYqh_pgaofcneemdg\ ldikckjbmiaoh`qg_sfZugYweZvcZvbZu`Zu__tY_tX_sV_sU_\ rS`rR`qP`qN`qM`pKapJaoHaoGanEanDbmBbmAbl8bl6ck7bl7\ bl7bl7bm8bm8bm8bm8bn8bn9bn9bo9bo9boAboAbpAbpAbp9`t\ AbpAdmAfiAgfAicBk_BmXBnTBpQBrNCtJCuGCwCCy9Cz6Hs8Ll\ 9QfAU_BZTDbNEgGFk9Gq2Eo3Hn4Jm5Ll6Nk7Pi8Sh9UgAWfBYe\ C_cDbbEdaFf`Gh_HjYHmZIlZIl_Il_Ik_Ik`Ik`Ij`IjaIjaIj\ bIibIibIicIhcIhcIhdIgdIgeIgeIgeIffIffIffIegIegIegI\ edKbbM_`OXZQUXSRVUOTWMRYJP_GNaDLcAJe7Fk6Hg5Ic5J_4L\ W4MT3NP3PL2QH2RE2YAWd6x`AsYEnVHiSLdPP_MSVJWQGZLEXN\ DWPCVRAUT9TV8RX6QZ5P`4Ob3Nc5Oa6P`7Q_8QZ9RYASXBTVCT\ UDUTEVSFWRGWQHXPJYNKZMLZL } frm:MandelbrotFNC {; Jim Muth b=p1, z=p2, c=p3+fn1(pixel): z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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Smiling Face
by Mike Frazier 23 Nov '12

23 Nov '12

When there is two way symmetry in fractal images it is not uncommon to see faces. I can't remember seeing a face with a smile before though. Here is a link to an image: http://dl.dropbox.com/u/33642054/image/smiling_face_640_5.jpg The Fractint compatible PAR file for the image is: Smiling_Face { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20121123_1148 passes=1 float=y center-mag=-0.5350693519219983/4.443105269772777e-\ 14/74074075000/1/-90/0 params=-1/1/0/100/-1/0/1/0/0/0 maxiter=2000 inside=0 periodicity=6 colors=000QepQgpRipSkoSmoTooTqoUsoVunWsmYplZmk`jja\ gicdhdbgf_fhXeiUdkRclObnMaoJ`qG_rDZtAYv7Xu7Xs8Yr9Y\ pAZoAZmB_lC`jD`iEagEafFbdGccHcaHd`IdZJeYKfWLfVLgTM\ gSNhQOiPOiNPjMQjKRkISlZm3Zh6ZcAZZDYTHYOKYJOYERX8VW\ 8WU8YS8ZR8`P8aN8cL8dK7fI7gG7iE7jD7lB7m97o76q86o96m\ B6jC6hD5eF5cG5`H5ZJ4WL9UNFSPLPRRNTXLVbIXhGZnEatBar\ BapB`nB`lB_jB_hBZfBZdBYbBY`BXZBXXBWVBWTBWRBVPBVNBU\ LBUJBTHBTFBSDBSBBR9BR7BQ5BQ3BP1CQ2CR4CS6BT8BUAAWCA\ XD9YF9ZH8_J8aL8bN7cP7dQ6eS6fU5hW5iY4j_4ka4lb3nd3of\ 2ph2qj1rl1tn0tl2tj5th8tfBtdEtbHu`KuZNuXQuVSuTVuRYv\ P`vNcvLfvJivHlvFowDrvEqtForGmpHkoIimJgkKeiLchMafN_\ dOYbPWaQU_RSYSQWTOUVMWTMYRM`PNbMNdKOgIOiFPlDPnBQp8\ Qs6Ru4Rx1Sv6StBRqHQoMPlSOjXNgbMegLbmK`rJYxIYxJXxKW\ xMVxNUwOUwQTwRSwTRwUQvVPvXPvYOv_Nu`MuaLucKudKufJtg\ IthHtjGtkFsmKmlPfkU_i_ThdMgiFen8dt1bq2bn3bj5bg6bd9\ c`DeXJgTOiQSkOVmOZoPaqPdp } frm:F_20121123_1148 { ; Similar to the parallel resistance formula a=real(p1),b=real(p2),d=imag(p1),f=imag(p2), z=0,c1=pixel-p3,c2=pixel-p4: z=1/(1/(a*z*(cos(z)-1)+c1)+1/(d*(z^f)+c2)), |z|<100 } -- Mike Frazier www.fracton.org

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Multilake:12d
by Albrecht 23 Nov '12

23 Nov '12

Hi, I will be on a trip for several weeks and Hal is taking over. Therefore I present an image I love. It?s an older one and again it is more a painting then a fractal. This is not on Hal?s server as it is a special one, you will have to wait until it?s finished, but maybe it?s worth it. Albrecht ---------------------start-par--------------------------------------------- multilake_12d { ; mother and child ; Version 2002 Patchlevel 4 reset=2002 type=formula formulafile=multlke.frm formulaname=Multi_lake12 ismand=n passes=t center-mag=0/0/0.6666667 params=-1/-0.75/512/40/0.3/300 float=y maxiter=1094 inside=maxiter outside=tdis periodicity=0 colors=000WPE<3>gcOjgRmjT<3>zzc<9>UOFRKDOGA<3>A00<9>f0Ci0Dl0F<3>z0K<6>Z0\ EV0DR0C<3>A08004000<26>000<4>000<9>X0a_0dc0h<3>p0w<4>_0dX0aU0Y<2>K0NH0JG\ 0NE1R<3>7UX6`Z4h_2oa0wc<11>2TG2RE3OC<3>4D3<17>kkammcpoe<3>zwm<6>cYO`UKYQ\ G<3>KA0000<43>000<4>000330<11>110110110<3>000KA4<2>TLB } frm:Multi_lake12 { ; ; p1: Julia seed ; real part of p2: bailout value ; imag part of p2: water level in % of the screen height ; real part of p3: amplitude of the wave (try 0.2) ; imag part of p3: frequency (try 300) bailout = real(p2) if (imag(p2) > 0 && imag(p2) <= 100) level = imag(p2) / 100 ; water level ampl = real(p3) ; amplitude of the wave freq = imag(p3) ; frequency angle = real(rotskew * pi / 180) exp_irot = exp(-flip(angle)) h = 1 / real(magxmag) w = h / 0.75 * imag(magxmag) tanskew = tan(imag(rotskew * pi / 180)) u = 2 * w * exp_irot v = 2 * h * (tanskew + flip(1)) * exp_irot z3rd = center + (-w-h*tanskew - flip(h)) * exp_irot z = pixel - z3rd b = imag(conj(u)*z) / imag(conj(u)*v) if (b <= level) dy = level - b z = z + 2*dy * (1+ampl*sin(freq*dy^0.2)) * v endif z = z + z3rd else z = pixel endif if (ismand) c = z else c = p1 endif x=0 y=0 : ; multifrac7 variation y2 = y*y x2 = x*x x = x2-y2-real(c) y = 2*x*y-imag(c) z =(z*x)^(z*y) |z| <=bailout } ------------------------------------------end--------------------------

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Mike, If I read the parameter set correctly, you have z*100 in it!
by Hal Lane 23 Nov '12

23 Nov '12

Mike, > I was experimenting with formulas to see what would happen when mixing > large exponents of z with trigonometric functions. The changes weren't > really that different from smaller exponents. I did notice a small area > that looked totally different than the rest of the fractal and I zoomed in > there to find this. > Here is a link to an image: > http://dl.dropbox.com/u/33642054/image/funneled_1200_5.jpg Mike, If I read the parameter set correctly, you have z*100 in it! An interesting idea, and an interesting image. Thanks for posting it. - Hal Lane ######################## # hallane(a)earthlink.net ########################

2 1

World_Inside
by Albrecht 22 Nov '12

22 Nov '12

Hi, reading the title you will know what it?s all about, but this version is completely new, even for me. The image is available for immediate viewing on Hal?s server in FULL HD 1600/1200: http://www.emarketingiseasy.com/Albrecht/61537A1.GIF Albrecht --------------------------start-par----------------- 61537A1 { ; World_Inside ; Time 0.47.52 1600/1200 ; phoen-sec-mmods-bees-newt reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=-3.33188088650739500/+0.000597524951209\ 18/32.45382/1/-90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/615\ 37.07595712021/14235.4911030602/152048.0404808048/\ 384.1604894048/384.00482000595/256.1007683001/512.\ 1007683001/768.1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000000zr0zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>L\ Q8KM8KJ8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>\ qeBriAtm9vq8xu7zz5zz4zz3<4>zj4zg4zc4<3>zS5zP5zL6zI\ 6zE6wE6tD6<6>vAIv9Kv9M<3>x7Sy7Uy6Wz6Yz5_<3>f5Ma5IW\ 4E<2>_4H<3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>\ y0fz0gy0h<3>u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAA\ G7FO4KW0Qc<3>5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<\ 3>civflvinvlqvotvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa\ <3>8JP8FL8CI<3>SCCXCAaB9<3>uA2zA0xA0<12>SA1QA1NA1<\ 3>D92<6>UXAW`BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJo\ SFlWAi_5fc0ce7_jFRoNIzb0zj0 } frm:multifractal_10 { ; Albrecht Niekamp Jan2005 ;RP2 Left: 5 Digits_Channel:1_main 2_outside 3_inside1 4_inside2 5_inside3 ; Frms: 0_off 1_Sec 2_Mand(2) 3_Bees 4_Jul 5_Mmod 6_Phoen 7_Newt 8_Spid ; Right: 2 Digits_MMods_Number of sides 2 Dig_Phoenix 2 Dig_Spider ; 1 Dig_TransReset_main :0_no 1_dblmand 2_Iter-res 3_both +5_warp ; 4 Dig_TransReset_Ch2-5:0_no 1_z-reset 2_Iter-res 3_both +5_warp ;IP2 Left: 5 Digits_Bailout Number for Channels 1 to 5 ; Right: Variab: 4 Digits_Mand/Jul(2 var) 2 Digits_Secant 4 Digits_Bees ;RP3 Left: 2 Digits_Newtonvariable 4 Digits_Colour1 ; Right: 5 Digits_Colour2 5 Digits_Colour3 ;IP3 Left: Main: 5 Digits_Warp-factor (fn1 is used) ; Right: 5 Digits_Colour4 6 Digits_Colour5 ;RP4 Left: Outside: 5 Digits_Warp-factor (fn2 is used) ; Right: Outside: 4 Dig+1 fractaldig_bord-out 4 Dig+1 fractaldig_bord-in ;IP4 Left: Inside1_Maxiter ; Right: Inside1_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn2 used) 4 Dig+1 fractaldig_border1 ;RP5 Left: Inside2_Maxiter ; Right: Inside2_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn3 used) 4 Dig+1 fractaldig_border2 ;IP5 Left: Inside3_Maxiter ; Right: Inside3_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn4 used) 4 Dig+1 fractaldig_border3 ; Altnat: Left: 1_Lake effect enabled (Inside3 disabled) ; Right: 2 Digit_Frequency 2 Digit_Waterlevel 2 Digit_Amplitude ; le=0 z=pixel da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+11111 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==4)+(d==5)+(d==8)+(d==9) d4=d3==0 vb=d>5 sc=d==2 mo=d==6 px=d==7 ab=px+(d==3)+(d==5)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>1 sc1=d==2 mo1=d==6 px1=d==7 v1m=mo1+px1 v1j=d>7 dd1=v1j+(d==4)+(d==5) ab1=px1+(d==3)+(d==5)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=d>1 sc2=d==2 mo2=d==6 px2=d==7 v2m=mo2+px2 v2j=d>7 dd2=v2j+(d==4)+(d==5) ab2=px2+(d==3)+(d==5)+(d==9) d=trunc(dd/10) ex3=d>1 sc3=d==2 mo3=d==6 px3=d==7 v3m=mo3+px3 v3j=d>7 dd3=v3j+(d==4)+(d==5) ab3=px3+(d==3)+(d==5)+(d==9) d=dd-d*10 ba=imag(p5) mi3=trunc(ba) dd=(d>1)+(mi3>1) ex4=dd==2 sc4=d==2 mo4=d==6 px4=d==7 v4m=mo4+px4 v4j=d>7 dd4=v4j+(d==4)+(d==5) ab4=px4+(d==3)+(d==5)+(d==9) ; mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 dm=(d==2)+(d==4) ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex1+ex0+ex2+ex3+ex4 ; d=real(p3) dd=trunc(d) da=(d-dd)*10000000000 pp=trunc(dd/10000) ba1=dd-10000*pp ba2=trunc(da/100000) ba3=da-100000*ba2 ; d=imag(p3) sfac=trunc(d) da=(d-sfac)*100000000000 ba4=trunc(da/1000000) ba5=da-ba4*1000000 ; d=real(p4) ofac=trunc(d) da=(d-ofac)*10000000000 bh=trunc(da/100000)/10 bl=(da-bh*1000000)/10 bs=bl/2 ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) da=round((d-dd)*10000000000) d=trunc(dd/10000) dd=dd-d*10000 bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/1000) dd=dd-d*1000 bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/100) dd=dd-d*100 bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/10) dd=dd-d*10 bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=round(dd) bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) ; d=da p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 dp=p6+p0/100 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=d==3 fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 ; d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=d==3 fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 ; if (mi3==1) d=(ba-mi3)*1000000 fr=round((trunc(d/10000))*10) ;lake effect by S.Gallet d=d-fr*1000 lv=(trunc(d/100))/100 d=d-lv*10000 am=d/100 u=real(rotskew*pi/180) t=exp(-flip(u)) bo=1/real(magxmag) q=bo/0.75*imag(magxmag) dd=tan(imag(rotskew*pi/180)) da=2*q*t rs=2*bo*(dd+flip(1))*t zz=center+(-q-bo*dd-flip(bo))*t z=z-zz d=imag(conj(da)*z)/imag(conj(da)*rs) le=d<=lv if (le) dd=lv-d z=z+2*dd*(1+am*sin(fr*dd^0.2))*rs endif z=z+zz else da=(ba-mi3)*100000000000 d=trunc(da/10000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=d==3 fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 endif ; if (vb) if (d3) if (ab) z=z*le+pixel*(le==0) ;Spider c=p1 else z=z*le+pixel*(le==0) c=p1 ;newton endif elseif (ab) c=z ;Phoenix z=z*le+pixel*(le==0) else c=0.4*log(sqr(z^mm)) ;many mods z=0 endif elseif (d3) if (ab) c=p1 ;Julia z=z*le+pixel*(le==0) else ;bees c=p1 z=z*le+pixel*(le==0) endif elseif (ab) c=z ;Mandel z=0 else c=z ;Secant z=z*le+pixel*(le==0) endif t=0 bo=|z| p=pp z0=p7 zold=(0.0,0.0) cb=p9 ba=bb0 : if (tt) t=t+1 if (ex0) ex0=t<mi1 if (bo>bs) u=2*(fn1(t/sfac)) ex0=0 if (ir0) t=0 endif if (d4) z=z*u if (mo) c=0.4*log(sqr(z^mm)) else c=pixel endif else z=z*le+pixel*(le==0) cb=p9*u c=p1*u p=pp*u endif tt=tt-1+ex0 endif elseif ((ex1)&&bo>bl) if (bo<bh) d3=dd1 ba=bb1 ab=ab1 ex1=0 tt=tt-1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif if (ir1) t=0 endif if (d3) vb=v1j if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif else vb=v1m if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo1) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) ab=ab2 d3=dd2 ba=bb2 ex2=0 tt=tt-1 if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif if (ir2) t=0 endif if (d3) vb=v2j if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v2m if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo2) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) ab=ab3 d3=dd3 ba=bb3 ex3=0 tt=tt-1 if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif if (ir3) t=0 endif if (d3) vb=v3j if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v3m if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) ab=ab4 d3=dd4 ba=bb4 ex4=0 tt=0 if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (d3) vb=v4j if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v4m if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo4) c=0.4*log(sqr(z^mm)) endif endif endif endif endif if (vb) if (d3) if (ab) z=z*z+c ;Spiderjul John Horner c=c*sp+z else z1=z^p-1 ;Quasinewton Puskas Istvan z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+0.56+ph/100-0.5*zold ;Phoenix Mike Wareman zold=z z=z1 else z2=fn1(z)+c ;Many_mods Linda Allison z1=cos(z2) z=c*(1-z1)/(1+z1) endif elseif (d3) if (ab) z2=z*z ;Julia Puskas Istvan z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb ;Bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) if (dm) z=z*z+c+c*c-dp ;Double Mandel else z2=z*z ;Mandel Puskas Istvan z=z2*z2+p6*z2+c-p0 endif else z3=z ;Secant Mike Wareman z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<ba } --------------------------------end-------------------------------------

1 0

Funneled
by Mike Frazier 22 Nov '12

22 Nov '12

I was experimenting with formulas to see what would happen when mixing large exponents of z with trigonometric functions. The changes weren't really that different from smaller exponents. I did notice a small area that looked totally different than the rest of the fractal and I zoomed in there to find this. Here is a link to an image: http://dl.dropbox.com/u/33642054/image/funneled_1200_5.jpg The Fractint compatible PAR file for the image is: Funneled { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20121122_0942 passes=1 float=y center-mag=-0.5347914944581987/9.38169058092517e-1\ 3/4938271666666.666/1/0/0 params=-1/1/0/100/-1/0/1/0/0/0 maxiter=2000 inside=0 logmap=20 periodicity=6 colors=bbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooop\ ppqqqrrrssstttuuuvvvwwwxxxyyyzzzrrrsssqqqooommmkkk\ iiigggeeecccaaa___YYYWWWUUUSSSQQQOOOMMMKKKIIIGGGEE\ ECCEAAE88E66E44E22E00F00G00I00K00M00O00P00R00T00V0\ 0X00Z00`00b00c00e00g00i00k00m00o00q00r00t00v00x00z\ 01z13z25z37z39z4Bz5Dz6Fz7Hz8Jz9Lz9NzAPzBRzCTzDUzEW\ zFYzF_zGazHczIezJgzKizLkzLmzMozNqzOszPuzOtyNsxNqwM\ pvLntKmsKkrJjqIhpHgoHenGdmFbkEajE_iDZhCXgBWfBUeATd\ 9Rb8Qa8O`7N_6LZ5KY5IX4HW3FU2ET2CS1BR09P19Q3AR4BT6C\ U7DW9EXAFZCG_DG`FHbGIcIJeJKfLLhMMiONkQPkSSlVUmXXn_\ Zoaapdcqffrhhskktmmuppvrrwuuxwwyzzzzwxzsuzoszkpzgn\ zckz_izWfzSdzOazK_zGXzCVz8Sz4Qz0Nw1Mt1Mp2Lm2Kj2Jh3\ Ie4Hb4G_5GX5FU6ER6DP7DM8CJ8BG9AD99AA97A84B75D86FA7\ IB8KD9ME000111222333444555666777888999AAABBBCCCDDD\ EEEFFFGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPQQQRRRSSSTTTUU\ UVVVWWWXXXYYYZZZ___```aaa } frm:F_20121122_0942 { ; Similar to the parallel resistance formula a=real(p1),b=real(p2),d=imag(p1),f=imag(p2), z=0,c1=pixel-p3,c2=pixel-p4: z=1/(1/(a*z*(cos(z)-1)+c1)+1/(d*(z^f)+c2)), |z|<100 } -- Mike Frazier www.fracton.org

1 0

FOTD 21-11-12 (Re-Arranged Mandy [5])
by Jim Muth 22 Nov '12

22 Nov '12

FOTD -- November 21, 2012 (Rating 5) Fractal visionaries and enthusiasts: Today's quick image shows a Mandelbrot set with its parts re- arranged beyond recognition. The largest bay in the image is actually the period-2 bud of the M-set. The bay on the left side of the image is the second bud along the negative X-axis of the M-set. The true main bay of the M-set is the little dimple hanging from the largest bay in the image. East valley lies at the bottom of the dimple. The most prominent valley in the image is actually Scepter Valley. Seahorse Valley lies at the bottom of the large bay in the image, where the little dimple is hanging. The spike shooting downward from the bay on the left of the image is the main spike of the M-set. The name "Re-Arranged Mandy" needs no explanation. The rating of a 5 reflects my opinion of the image. The calculation time of one minute is fast enough to keep boredom at bay. Avoid calculation. View the finished image at: <http://www.crosscanpuzzles.com/Archives.html> Hi-def variations are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are at: <http://www.Nahee.com/FOTD/> The morning fog cleared by 9am here at Fractal Central, leading to a sunny day with a temperature of 52F 11C. The fractal cats enjoyed the near perfect conditions. The humans, busy as always, enjoyed things also. The next FOTD will be posted in a couple days. Until this glorious moment arrives, take care, and pick the doomsday of your choice. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Re-Arranged_Mandy { ; time=0:01:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotFN function=exp center-mag=-3.71379/-1.27343/0.2237866/1.7473/-90/\ -1.23373533611470521e-014 params=2/0/0/0/-1.25/0.02 float=y maxiter=10000 inside=0 logmap=yes symmetry=none periodicity=6 sound=off mathtolerance=0.05/1 colors=000hGweIwcKv`MvZOvWQvURvRTvPVvMXvKZuH`uFauC\ cuAeuAguDiuGkuIluMirOgpQenSckUaiX_g_YdbWbeU`hSZjQW\ mOUoMSqKPsINuGLwDIwEJwEJwEJwEJwEJwEJwEJwFJwFJwFJwF\ JvFKvFKvFKvGKvGKvGKvGKvGKvGKvGKvGKvHLvHLvHLvHLvHLv\ HLvHLwILwILwILwILwIMwIMwIMwJMwJMwJMwJMwJMwJMwJMyHK\ xILwJMwKNvLOuLPuMQtNRsOSsOTrPUrQVqRWpRXpSYoTZnU_nU\ `mVamWblXckYdkYejZfi_gi`hh`igajgbkfclfcmedndeodfpc\ fqbgrbhsaitaiuXjuTkuOluKmuElxGmuHmsJnpKnnLokNoiOpg\ PpdRqbSq_UrYVrWWrTYsRZsO_tMatJbuHduFevCfvAhw7iw5nz\ 4jw3gt3dq3ao3Zl3Wi3Tg3Qd3Ma2J_2GX2DU2AS27P24M21K23\ L34L36L37L49L4AL4BL4DL5EL5GL5HL6IL6KL6LL6NL7OL7QL7\ RL7SL8UL8VL8XL9YL9ZL9`L9aLAcLAdLAfLBgLBhLBjLBkLCmL\ CnLCoLCpMDpNEpOFpPGpQHpRIpRJpSKpTLpUMpVNpWOpXPpXQp\ YRpZRp_Sp`TpaUpbVpbWpcXpdYpeZpf_pg`phaphbpicpjdpke\ plepmfpngpnhpoippjpqkprlpsmptnptopuppvqpwrpxspytpy\ tqtjrp`skRvdEtfGsgHrhIpiJ } frm:MandelbrotFNC {; Jim Muth b=p1, z=p2, c=p3+fn1(pixel): z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

1 0

Alternating Seas
by Mike Frazier 21 Nov '12

21 Nov '12

I made the alternating blue areas by zooming in on left, right, left, and then right side minibrots. Here is a link to an image: http://dl.dropbox.com/u/33642054/image/alternating_seas_1200_5.jpg The Fractint compatible PAR file for the image is: Alternating_Seas { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20121121_1433 passes=1 float=y center-mag=-0.6476413187257524/-1.455197400109031e\ -09/9523809.642857142/1/0/0 params=1/1/4/4/-1/0/1/0/0/0 maxiter=2000 inside=0 periodicity=6 colors=CCCNakK_lGYmHZlI_jI_iJ`hKafLbeLbdMcbNdaOe_Q\ e_Se_Vf_Xf`Zg``g`ch`eh`gi`iialjanjaqdXsZSvTNrQLoMJ\ kJGgFEcCC`8AX57T15S48R8AQBDPEFOIIOLLNONMSQLVSKYVJa\ XId_Ha`FZaEWbDUbBRcAOd9Le8If6Fg5Dg4Ah27i14j46j78iA\ AiDDhGFhJHgMJgPLfSNfVPeYSe`UdcWdfYcj`bk`ala_mbYncW\ odUpeSqfQrgPshNtiLujJvkHwlFxmDynBymBylAyjAyi9yg9yf\ 8yd8yc7ya6y`6yZ5yY5yW4yV4yT3xWOjbYXifJppdm5en8fnCg\ oFgoIhpMiqPjqSkrVlsZlsamtdnthouklnghhceaZbVVZORWIN\ SBIP4ET6CW7B_99bB8fC6iE5mG3pH2tJ0rL2pM5mO7kPAiRCgT\ EeUHbWJ`XMZZOX`QVaTScVQdYOf_Pe`RdbSbcTadV`fW_gXYhZ\ Xj_WkaUmbTndRpdSocTmcUkbVjaWhaXf`Yd_Zb__`Z`_YaYYbW\ XcU`fKcWRgMXjBcm0ia1ZP2OQ6PQBPRFQRJRSNRSSSTWTU_TUd\ UVhUVlVWpWWuWXyXap`ghcl_gqRjqQgpOepNboQXnTRnWMmZGl\ aAhdDefFaiIYlKVnNRqPNtSKvUGyXGsbGmhHkiIikJflKdmLbo\ M`pNZqOWrPUtQSupqCppBppBpoApoApn9pn9pm8pm8pl7pl7pk\ 6pk6pj5pj5pi4ph3qe6qb9r_C } frm:F_20121121_1433 { ; Similar to the parallel resistance formula a=real(p1),b=real(p2)-1,d=imag(p1),f=imag(p2)-1, z=0,c1=pixel-p3,c2=pixel-p4: z=1/(1/(a*(z^b)*sinh(z)+c1)+1/(d*(z^f)*tanh(z)+c2)), |z|<100 } -- Mike Frazier www.fracton.org

1 0

Painting School
by Albrecht 21 Nov '12

21 Nov '12

Hi, An impossible image, 5 times secant, and impossible colours. It?s a fractal, but doesnt look like one. Hal called it a "Strange Beast". Here?s the FULL HD link on his server: http://www.emarketingiseasy.com/Albrecht/11111D.GIF Albrecht -----------------------start-par------------------ 11111D { ; Painting_School ; Time 0.25.30 1600/12 ; 5 times secant reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=sin/sqr/sin/sqr passes=t center-mag=-1.21009211910711000/+0.360885141158024\ 80/172.9903/1/117.500000000000369/-5.9755672632277\ 8786e-013 params=-0.05825983458967864/0.3785210730307932/111\ 11.64595705001/14235.4911030602/152048.0404808048/\ 384.1604894048/384.00482000595/128.1007683001/194.\ 1007683001/256.1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000PJo<2>_5fc0ce7_jFRoNIzb0zj0000zr0zz1zzC<\ 2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8KJ8<2>I88H44G00<3>\ TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriAtm9vq8xu7zz5zz4zz\ 3<4>zj4zg4zc4<3>zS5zP5zL6zI6zE6wE6tD6<6>vAIv9Kv9M<\ 3>x7Sy7Uy6Wz6Yz5_<3>f5Ma5IW4E<2>_4H<3>P3DN2CK2A<3>\ 805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0gy0h<3>u1mt1ns1or2\ q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4KW0Qc<3>5Xc6Zc7`c7\ aa7c_7eY<3>FcgHciJbl<3>S_v<3>civflvinvlqvotvsww<2>\ zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI<3>SCCXCAaB\ 9<3>uA2zA0xA0<12>SA1QA1NA1<3>D92<6>UXAW`BYcC<3>hrI\ <3>UnXRm_NlcJkgFfpAaz<2>LOr } frm:multifractal_10 { ; Albrecht Niekamp Jan2005 ;RP2 Left: 5 Digits_Channel:1_main 2_outside 3_inside1 4_inside2 5_inside3 ; Frms: 0_off 1_Sec 2_Mand(2) 3_Bees 4_Jul 5_Mmod 6_Phoen 7_Newt 8_Spid ; Right: 2 Digits_MMods_Number of sides 2 Dig_Phoenix 2 Dig_Spider ; 1 Dig_TransReset_main :0_no 1_dblmand 2_Iter-res 3_both +5_warp ; 4 Dig_TransReset_Ch2-5:0_no 1_z-reset 2_Iter-res 3_both +5_warp ;IP2 Left: 5 Digits_Bailout Number for Channels 1 to 5 ; Right: Variab: 4 Digits_Mand/Jul(2 var) 2 Digits_Secant 4 Digits_Bees ;RP3 Left: 2 Digits_Newtonvariable 4 Digits_Colour1 ; Right: 5 Digits_Colour2 5 Digits_Colour3 ;IP3 Left: Main: 5 Digits_Warp-factor (fn1 is used) ; Right: 5 Digits_Colour4 6 Digits_Colour5 ;RP4 Left: Outside: 5 Digits_Warp-factor (fn2 is used) ; Right: Outside: 4 Dig+1 fractaldig_bord-out 4 Dig+1 fractaldig_bord-in ;IP4 Left: Inside1_Maxiter ; Right: Inside1_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn2 used) 4 Dig+1 fractaldig_border1 ;RP5 Left: Inside2_Maxiter ; Right: Inside2_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn3 used) 4 Dig+1 fractaldig_border2 ;IP5 Left: Inside3_Maxiter ; Right: Inside3_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn4 used) 4 Dig+1 fractaldig_border3 ; Altnat: Left: 1_Lake effect enabled (Inside3 disabled) ; Right: 2 Digit_Frequency 2 Digit_Waterlevel 2 Digit_Amplitude ; le=0 z=pixel da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+11111 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==4)+(d==5)+(d==8)+(d==9) d4=d3==0 vb=d>5 sc=d==2 mo=d==6 px=d==7 ab=px+(d==3)+(d==5)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>1 sc1=d==2 mo1=d==6 px1=d==7 v1m=mo1+px1 v1j=d>7 dd1=v1j+(d==4)+(d==5) ab1=px1+(d==3)+(d==5)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=d>1 sc2=d==2 mo2=d==6 px2=d==7 v2m=mo2+px2 v2j=d>7 dd2=v2j+(d==4)+(d==5) ab2=px2+(d==3)+(d==5)+(d==9) d=trunc(dd/10) ex3=d>1 sc3=d==2 mo3=d==6 px3=d==7 v3m=mo3+px3 v3j=d>7 dd3=v3j+(d==4)+(d==5) ab3=px3+(d==3)+(d==5)+(d==9) d=dd-d*10 ba=imag(p5) mi3=trunc(ba) dd=(d>1)+(mi3>1) ex4=dd==2 sc4=d==2 mo4=d==6 px4=d==7 v4m=mo4+px4 v4j=d>7 dd4=v4j+(d==4)+(d==5) ab4=px4+(d==3)+(d==5)+(d==9) ; mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 dm=(d==2)+(d==4) ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex1+ex0+ex2+ex3+ex4 ; d=real(p3) dd=trunc(d) da=(d-dd)*10000000000 pp=trunc(dd/10000) ba1=dd-10000*pp ba2=trunc(da/100000) ba3=da-100000*ba2 ; d=imag(p3) sfac=trunc(d) da=(d-sfac)*100000000000 ba4=trunc(da/1000000) ba5=da-ba4*1000000 ; d=real(p4) ofac=trunc(d) da=(d-ofac)*10000000000 bh=trunc(da/100000)/10 bl=(da-bh*1000000)/10 bs=bl/2 ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) da=round((d-dd)*10000000000) d=trunc(dd/10000) dd=dd-d*10000 bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/1000) dd=dd-d*1000 bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/100) dd=dd-d*100 bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/10) dd=dd-d*10 bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=round(dd) bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) ; d=da p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 dp=p6+p0/100 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=d==3 fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 ; d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=d==3 fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 ; if (mi3==1) d=(ba-mi3)*1000000 fr=round((trunc(d/10000))*10) ;lake effect by S.Gallet d=d-fr*1000 lv=(trunc(d/100))/100 d=d-lv*10000 am=d/100 u=real(rotskew*pi/180) t=exp(-flip(u)) bo=1/real(magxmag) q=bo/0.75*imag(magxmag) dd=tan(imag(rotskew*pi/180)) da=2*q*t rs=2*bo*(dd+flip(1))*t zz=center+(-q-bo*dd-flip(bo))*t z=z-zz d=imag(conj(da)*z)/imag(conj(da)*rs) le=d<=lv if (le) dd=lv-d z=z+2*dd*(1+am*sin(fr*dd^0.2))*rs endif z=z+zz else da=(ba-mi3)*100000000000 d=trunc(da/10000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=d==3 fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 endif ; if (vb) if (d3) if (ab) z=z*le+pixel*(le==0) ;Spider c=p1 else z=z*le+pixel*(le==0) c=p1 ;newton endif elseif (ab) c=z ;Phoenix z=z*le+pixel*(le==0) else c=0.4*log(sqr(z^mm)) ;many mods z=0 endif elseif (d3) if (ab) c=p1 ;Julia z=z*le+pixel*(le==0) else ;bees c=p1 z=z*le+pixel*(le==0) endif elseif (ab) c=z ;Mandel z=0 else c=z ;Secant z=z*le+pixel*(le==0) endif t=0 bo=|z| p=pp z0=p7 zold=(0.0,0.0) cb=p9 ba=bb0 : if (tt) t=t+1 if (ex0) ex0=t<mi1 if (bo>bs) u=2*(fn1(t/sfac)) ex0=0 if (ir0) t=0 endif if (d4) z=z*u if (mo) c=0.4*log(sqr(z^mm)) else c=pixel endif else z=z*le+pixel*(le==0) cb=p9*u c=p1*u p=pp*u endif tt=tt-1+ex0 endif elseif ((ex1)&&bo>bl) if (bo<bh) d3=dd1 ba=bb1 ab=ab1 ex1=0 tt=tt-1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif if (ir1) t=0 endif if (d3) vb=v1j if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif else vb=v1m if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo1) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) ab=ab2 d3=dd2 ba=bb2 ex2=0 tt=tt-1 if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif if (ir2) t=0 endif if (d3) vb=v2j if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v2m if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo2) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) ab=ab3 d3=dd3 ba=bb3 ex3=0 tt=tt-1 if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif if (ir3) t=0 endif if (d3) vb=v3j if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v3m if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) ab=ab4 d3=dd4 ba=bb4 ex4=0 tt=0 if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (d3) vb=v4j if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v4m if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo4) c=0.4*log(sqr(z^mm)) endif endif endif endif endif if (vb) if (d3) if (ab) z=z*z+c ;Spiderjul John Horner c=c*sp+z else z1=z^p-1 ;Quasinewton Puskas Istvan z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+0.56+ph/100-0.5*zold ;Phoenix Mike Wareman zold=z z=z1 else z2=fn1(z)+c ;Many_mods Linda Allison z1=cos(z2) z=c*(1-z1)/(1+z1) endif elseif (d3) if (ab) z2=z*z ;Julia Puskas Istvan z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb ;Bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) if (dm) z=z*z+c+c*c-dp ;Double Mandel else z2=z*z ;Mandel Puskas Istvan z=z2*z2+p6*z2+c-p0 endif else z3=z ;Secant Mike Wareman z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<ba } --------------------------------------------end-------------------

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FOTD 20-11-12 (Elephant Caterpillar [?])
by Jim Muth 21 Nov '12

21 Nov '12

FOTD -- November 20, 2012 (Rating ?) Fractal visionaries and enthusiasts: The FOTD's have been coming few and far apart recently, and perhaps they have not quite been up to FOTD standards. The reason is simple -- there have been too many things to do here at FC and too little time to do them. Today's image is another distorted version of the Mandelbrot set. (As usual, the main bud is the shrunken thing on the west side of the main bay.) I named the image "Elephant Caterpillar" because the location is deep in the north shore line of Elephant (aka East) Valley, and the string of buds does rather resemble a caterpillar. This string of buds is actually the northern period-37 radical. It appears to lie on the eastern edge of the main bay, while in fact it lies much deeper on the northern shore of East Valley. The unusual proportions of the entire image were necessary to cut off the infinite string of similarly distorted M-sets that lie above and below the frame. Even then I needed to stretch the image slightly in the vertical direction. The absence of a rating indicates that I cannot decide how to rate the image. The calculation time of 2 minutes is about what the scene is worth. A better value may be found on the web sites however. The finished image is online at: <http://www.crosscanpuzzles.com/Archives.html> High-definition variations are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are at: <http://www.Nahee.com/FOTD/> A mix of sun and clouds prevailed here at Fractal Central today, while the temperature of 48F +9C kept things feeling seasonal. The humans had a typical busy day. The next FOTD will be posted when the time is right. Until whenever, take care, and reality is all in the mind, so don't take life too seriously. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= ElephantCaterpilar { ; time=0:02:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotFNC function=exp center-mag=-6.90665/15.6094/0.2944193/0.561/180 params=2/0/0/0/0.2571014/0.0010475 float=y maxiter=7200 inside=0 logmap=yes periodicity=0 viewwindows=1/0.5/yes/0/0 mathtolerance=0.05/1 colors=000x6nw7lv8iu9gtBdsCarD_qEXpFVoHSoJPoLNpLKq\ NIrOMsRQuTTxVXzW_tW`qVamUaiTbeSbaRcYRcTSdPTdLUeLVe\ JWfJXfQXeVXdaVdfTciRciT_iUXhVThWQhXMgYJgZFg_Cf`8fa\ 5fb2ed6ee9egDdhGdjJdkNcmQcnUcpXbq_bscbtfbuim_skatj\ ctidthftfgteitdjtcltZmtUihPecKaZJYUIUPHQKJOFLKANG7\ PC498YC5ZE7_G9`JBaLDaNFbQIcSKdUMdXOeZQf`SgbUgZXaV_\ XRbRNeMJhGFjBLcGRXLYQRcJWiC`gIbfOceUed_fcegadb`cZZ\ cUYbQWbLVaHUaDTYASU8RR6QN4PJ2OG0KD09A3HB0eiVdjWdkX\ dkYdlZcm_cm`cnacobcocbpdbpebqfbrgbrhasiatjatkaulau\ lbtjbshbrfcqdcpbcp`coZdnXdmWdlUekSekQejOeiMfhKfgIf\ fGffFZZLRRQJKVBC_35d45c55c65b75b85a95aA5`B5`B5`F4_\ I4_L4_P3_S3_V3_Y3_a2Zd2Zg2Zj2Zn1Zq1Zt1Zw1Zu3_t5_s7\ _r9_qB_oD_nF_mH_lJ_kL_jN_hP_gR_fT_eV_dX_cY_aZZ_ZZZ\ ZYXZYVZXUZXSZXQ_WP_WN_VL_VK_UI_UH_UGZWFZYFZZEZ`DZb\ DYcCYeBYgBYhAYj9Xl9Xm8Xo7Xq7Xr8Xq8Xp9Xo9XnAXmAXlBX\ kBXjCXiCXhDXgDXfEXeEXdFXc } frm:MandelbrotFNC {; Jim Muth b=p1, z=p2, c=p3+fn1(pixel): z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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Mike, Thanks for posting your recent images!
by Hal Lane 20 Nov '12

20 Nov '12

Mike, Thanks for posting your recent images! http://dl.dropbox.com/u/33642054/image/trapped_cosine_1200_5.jpg http://dl.dropbox.com/u/33642054/image/web_opposition_1200_5.jpg http://dl.dropbox.com/u/33642054/image/web_rings_1200_5.jpg > ...add the rings by zooming out. To perform the technique, you > repeatedly zoom in on ever smaller self similar structures. I remember your description of this process from when you described it before. It really gives nice results! In your Web Rings image, I thought it was interesting that the fractal had the usual symmetry of features of the webbing in powers of two -- but had three-fold symmetry for its Mandeloid. - Hal Lane ######################## # hallane(a)earthlink.net ########################

1 0

(Fractint] Tentacles
by Albrecht 20 Nov '12

20 Nov '12

Hi, this is a breathtaking deeper zoom into The_Big_bang image Only slightly coloured. The image is available on Hal?s Server: in full HD 1600/1200 http://www.emarketingiseasy.com/Albrecht/63718J.GIF Albrecht ------------------start-par-------------------------- 63718J { ; Tentacles ; Time 0.05.45 1600/1200 ; phoen-bees-newt-sec-spid reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=-96.7077/152.318/0.08362108/1/140/1.310\ 75705844807544e-014 params=-0.05825983458967864/0.3785210730307932/637\ 18.64595777025/14235.4911030602/152048.0404808048/\ 384.1604894048/384.00482000595/256.1007683001/512.\ 1007683001/768.1007683001 float=y maxiter=200 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000120<5>010010000010<2>000JA4<7>fcOigRljT<\ 3>yzc<9>TOFQKDNGA<3>900<9>e0Ch0Dk0F<3>y0K<6>Y0EU0D\ Q0C<3>908004000<26>000<4>000204<6>P0UT0YW0aZ0db0he\ 0l<2>o0w<4>Z0dW0aT0Y<2>J0NG0JF0ND1R<3>6UX5`Z3h_1oa\ 0wc<10>1WI1TG1RE<3>3G53D35F5<16>jkalmcooe<3>ywm<3>\ lhZidVeaS<3>UMCQI8NE4JA0000<43>000<4>000230<4>120 } frm:multifractal_10 { ; Albrecht Niekamp Jan2005 ;RP2 Left: 5 Digits_Channel:1_main 2_outside 3_inside1 4_inside2 5_inside3 ; Frms: 0_off 1_Sec 2_Mand(2) 3_Bees 4_Jul 5_Mmod 6_Phoen 7_Newt 8_Spid ; Right: 2 Digits_MMods_Number of sides 2 Dig_Phoenix 2 Dig_Spider ; 1 Dig_TransReset_main :0_no 1_dblmand 2_Iter-res 3_both +5_warp ; 4 Dig_TransReset_Ch2-5:0_no 1_z-reset 2_Iter-res 3_both +5_warp ;IP2 Left: 5 Digits_Bailout Number for Channels 1 to 5 ; Right: Variab: 4 Digits_Mand/Jul(2 var) 2 Digits_Secant 4 Digits_Bees ;RP3 Left: 2 Digits_Newtonvariable 4 Digits_Colour1 ; Right: 5 Digits_Colour2 5 Digits_Colour3 ;IP3 Left: Main: 5 Digits_Warp-factor (fn1 is used) ; Right: 5 Digits_Colour4 6 Digits_Colour5 ;RP4 Left: Outside: 5 Digits_Warp-factor (fn2 is used) ; Right: Outside: 4 Dig+1 fractaldig_bord-out 4 Dig+1 fractaldig_bord-in ;IP4 Left: Inside1_Maxiter ; Right: Inside1_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn2 used) 4 Dig+1 fractaldig_border1 ;RP5 Left: Inside2_Maxiter ; Right: Inside2_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn3 used) 4 Dig+1 fractaldig_border2 ;IP5 Left: Inside3_Maxiter ; Right: Inside3_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn4 used) 4 Dig+1 fractaldig_border3 ; Altnat: Left: 1_Lake effect enabled (Inside3 disabled) ; Right: 2 Digit_Frequency 2 Digit_Waterlevel 2 Digit_Amplitude ; le=0 z=pixel da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+11111 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==4)+(d==5)+(d==8)+(d==9) d4=d3==0 vb=d>5 sc=d==2 mo=d==6 px=d==7 ab=px+(d==3)+(d==5)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>1 sc1=d==2 mo1=d==6 px1=d==7 v1m=mo1+px1 v1j=d>7 dd1=v1j+(d==4)+(d==5) ab1=px1+(d==3)+(d==5)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=d>1 sc2=d==2 mo2=d==6 px2=d==7 v2m=mo2+px2 v2j=d>7 dd2=v2j+(d==4)+(d==5) ab2=px2+(d==3)+(d==5)+(d==9) d=trunc(dd/10) ex3=d>1 sc3=d==2 mo3=d==6 px3=d==7 v3m=mo3+px3 v3j=d>7 dd3=v3j+(d==4)+(d==5) ab3=px3+(d==3)+(d==5)+(d==9) d=dd-d*10 ba=imag(p5) mi3=trunc(ba) dd=(d>1)+(mi3>1) ex4=dd==2 sc4=d==2 mo4=d==6 px4=d==7 v4m=mo4+px4 v4j=d>7 dd4=v4j+(d==4)+(d==5) ab4=px4+(d==3)+(d==5)+(d==9) ; mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 dm=(d==2)+(d==4) ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex1+ex0+ex2+ex3+ex4 ; d=real(p3) dd=trunc(d) da=(d-dd)*10000000000 pp=trunc(dd/10000) ba1=dd-10000*pp ba2=trunc(da/100000) ba3=da-100000*ba2 ; d=imag(p3) sfac=trunc(d) da=(d-sfac)*100000000000 ba4=trunc(da/1000000) ba5=da-ba4*1000000 ; d=real(p4) ofac=trunc(d) da=(d-ofac)*10000000000 bh=trunc(da/100000)/10 bl=(da-bh*1000000)/10 bs=bl/2 ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) da=round((d-dd)*10000000000) d=trunc(dd/10000) dd=dd-d*10000 bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/1000) dd=dd-d*1000 bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/100) dd=dd-d*100 bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/10) dd=dd-d*10 bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=round(dd) bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) ; d=da p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 dp=p6+p0/100 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=d==3 fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 ; d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=d==3 fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 ; if (mi3==1) d=(ba-mi3)*1000000 fr=round((trunc(d/10000))*10) ;lake effect by S.Gallet d=d-fr*1000 lv=(trunc(d/100))/100 d=d-lv*10000 am=d/100 u=real(rotskew*pi/180) t=exp(-flip(u)) bo=1/real(magxmag) q=bo/0.75*imag(magxmag) dd=tan(imag(rotskew*pi/180)) da=2*q*t rs=2*bo*(dd+flip(1))*t zz=center+(-q-bo*dd-flip(bo))*t z=z-zz d=imag(conj(da)*z)/imag(conj(da)*rs) le=d<=lv if (le) dd=lv-d z=z+2*dd*(1+am*sin(fr*dd^0.2))*rs endif z=z+zz else da=(ba-mi3)*100000000000 d=trunc(da/10000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=d==3 fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 endif ; if (vb) if (d3) if (ab) z=z*le+pixel*(le==0) ;Spider c=p1 else z=z*le+pixel*(le==0) c=p1 ;newton endif elseif (ab) c=z ;Phoenix z=z*le+pixel*(le==0) else c=0.4*log(sqr(z^mm)) ;many mods z=0 endif elseif (d3) if (ab) c=p1 ;Julia z=z*le+pixel*(le==0) else ;bees c=p1 z=z*le+pixel*(le==0) endif elseif (ab) c=z ;Mandel z=0 else c=z ;Secant z=z*le+pixel*(le==0) endif t=0 bo=|z| p=pp z0=p7 zold=(0.0,0.0) cb=p9 ba=bb0 : if (tt) t=t+1 if (ex0) ex0=t<mi1 if (bo>bs) u=2*(fn1(t/sfac)) ex0=0 if (ir0) t=0 endif if (d4) z=z*u if (mo) c=0.4*log(sqr(z^mm)) else c=pixel endif else z=z*le+pixel*(le==0) cb=p9*u c=p1*u p=pp*u endif tt=tt-1+ex0 endif elseif ((ex1)&&bo>bl) if (bo<bh) d3=dd1 ba=bb1 ab=ab1 ex1=0 tt=tt-1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif if (ir1) t=0 endif if (d3) vb=v1j if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif else vb=v1m if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo1) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) ab=ab2 d3=dd2 ba=bb2 ex2=0 tt=tt-1 if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif if (ir2) t=0 endif if (d3) vb=v2j if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v2m if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo2) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) ab=ab3 d3=dd3 ba=bb3 ex3=0 tt=tt-1 if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif if (ir3) t=0 endif if (d3) vb=v3j if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v3m if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) ab=ab4 d3=dd4 ba=bb4 ex4=0 tt=0 if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (d3) vb=v4j if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v4m if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo4) c=0.4*log(sqr(z^mm)) endif endif endif endif endif if (vb) if (d3) if (ab) z=z*z+c ;Spiderjul John Horner c=c*sp+z else z1=z^p-1 ;Quasinewton Puskas Istvan z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+0.56+ph/100-0.5*zold ;Phoenix Mike Wareman zold=z z=z1 else z2=fn1(z)+c ;Many_mods Linda Allison z1=cos(z2) z=c*(1-z1)/(1+z1) endif elseif (d3) if (ab) z2=z*z ;Julia Puskas Istvan z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb ;Bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) if (dm) z=z*z+c+c*c-dp ;Double Mandel else z2=z*z ;Mandel Puskas Istvan z=z2*z2+p6*z2+c-p0 endif else z3=z ;Secant Mike Wareman z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<ba } -----------------------------------------end---------------------

1 0

A Bit of Exp
by Mike Frazier 20 Nov '12

20 Nov '12

This fractal uses an exponential in the parallel resistor formula. Here is a link to an image: http://dl.dropbox.com/u/33642054/image/a_bit_of_exp_1200_5.jpg The Fractint compatible PAR file for the image is: A_Bit_of_Exp { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20121120_0848 passes=1 float=y center-mag=2.643259796049618/7.461063436411377e-15\ /533333340000/1/-90/0 params=-1/-1/5/5/-1/0/1/0/0/0 maxiter=2000 inside=0 logmap=7 periodicity=6 colors=000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O\ 40C10000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40\ C10000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C1\ 0000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C100\ 00C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000\ C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C1\ 0O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O\ 40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40\ ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA\ 0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0h\ I0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0\ oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS\ 0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0u\ a0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0ua0\ ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0ua0ym\ 0zy0ym0ua0oS0hI0ZA0O40C10 } frm:F_20121120_0848 { ; Similar to the parallel resistance formula a=real(p1),b=real(p2)-1,d=imag(p1),f=imag(p2), z=0,c1=pixel-p3,c2=pixel-p4: z=1/(1/(a*(z^b)*(exp(z)-1)+c1)+1/(d*(z^f)+c2)), |z|<100 } -- Mike Frazier www.fracton.org

1 0

The Big Bang
by Albrecht 19 Nov '12

19 Nov '12

Hi, here is another "wild" one, using the same colours. A new original, no one has seen this kind of image before. Also a zoom, cant tell which is the better one. The images are available on Hal?s Server in full HD: http://www.emarketingiseasy.com/Albrecht/63718D.GIF http://www.emarketingiseasy.com/Albrecht/63718E.GIF This Hal?s link to yesterday?s image "Crosswise" http://www.emarketingiseasy.com/Albrecht/1536709A.GIF . Albrecht -------------------------start-par-------------------- 61735d { ; The_Big_Bang ; Time 0.04.34 1600/1200 ; phoen-bees-newt-sec-spid reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=2.63236/-1.24841/0.004181054/1/90/-1.23\ 373533611470521e-014 params=-0.05825983458967864/0.3785210730307932/637\ 18.64595777025/14235.4911030602/152048.0404808048/\ 384.1604894048/384.00482000595/256.1007683001/512.\ 1007683001/768.1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000120<5>010010000010<2>000JA4<7>fcOigRljT<\ 3>yzc<9>TOFQKDNGA<3>900<9>e0Ch0Dk0F<3>y0K<6>Y0EU0D\ Q0C<3>908004000<26>000<4>000204<6>P0UT0YW0aZ0db0he\ 0l<2>o0w<4>Z0dW0aT0Y<2>J0NG0JF0ND1R<3>6UX5`Z3h_1oa\ 0wc<10>1WI1TG1RE<3>3G53D35F5<16>jkalmcooe<3>ywm<3>\ lhZidVeaS<3>UMCQI8NE4JA0000<43>000<4>000230<4>120 } 61735e { ; The_Big_Bang_zoom ; Time 0.09.46 1600/1200 ; phoen-bees-newt-sec-spid reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=103.842/-104.03/0.02155183/1/137.5/1.31\ 075705844807544e-014 params=-0.05825983458967864/0.3785210730307932/637\ 18.64595777025/14235.4911030602/152048.0404808048/\ 384.1604894048/384.00482000595/256.1007683001/512.\ 1007683001/768.1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000120<5>010010000010<2>000JA4<7>fcOigRljT<\ 3>yzc<9>TOFQKDNGA<3>900<9>e0Ch0Dk0F<3>y0K<6>Y0EU0D\ Q0C<3>908004000<26>000<4>000204<6>P0UT0YW0aZ0db0he\ 0l<2>o0w<4>Z0dW0aT0Y<2>J0NG0JF0ND1R<3>6UX5`Z3h_1oa\ 0wc<10>1WI1TG1RE<3>3G53D35F5<16>jkalmcooe<3>ywm<3>\ lhZidVeaS<3>UMCQI8NE4JA0000<43>000<4>000230<4>120 } frm:multifractal_10 { ; Albrecht Niekamp Jan2005 ;RP2 Left: 5 Digits_Channel:1_main 2_outside 3_inside1 4_inside2 5_inside3 ; Frms: 0_off 1_Sec 2_Mand(2) 3_Bees 4_Jul 5_Mmod 6_Phoen 7_Newt 8_Spid ; Right: 2 Digits_MMods_Number of sides 2 Dig_Phoenix 2 Dig_Spider ; 1 Dig_TransReset_main :0_no 1_dblmand 2_Iter-res 3_both +5_warp ; 4 Dig_TransReset_Ch2-5:0_no 1_z-reset 2_Iter-res 3_both +5_warp ;IP2 Left: 5 Digits_Bailout Number for Channels 1 to 5 ; Right: Variab: 4 Digits_Mand/Jul(2 var) 2 Digits_Secant 4 Digits_Bees ;RP3 Left: 2 Digits_Newtonvariable 4 Digits_Colour1 ; Right: 5 Digits_Colour2 5 Digits_Colour3 ;IP3 Left: Main: 5 Digits_Warp-factor (fn1 is used) ; Right: 5 Digits_Colour4 6 Digits_Colour5 ;RP4 Left: Outside: 5 Digits_Warp-factor (fn2 is used) ; Right: Outside: 4 Dig+1 fractaldig_bord-out 4 Dig+1 fractaldig_bord-in ;IP4 Left: Inside1_Maxiter ; Right: Inside1_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn2 used) 4 Dig+1 fractaldig_border1 ;RP5 Left: Inside2_Maxiter ; Right: Inside2_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn3 used) 4 Dig+1 fractaldig_border2 ;IP5 Left: Inside3_Maxiter ; Right: Inside3_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn4 used) 4 Dig+1 fractaldig_border3 ; Altnat: Left: 1_Lake effect enabled (Inside3 disabled) ; Right: 2 Digit_Frequency 2 Digit_Waterlevel 2 Digit_Amplitude ; le=0 z=pixel da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+11111 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==4)+(d==5)+(d==8)+(d==9) d4=d3==0 vb=d>5 sc=d==2 mo=d==6 px=d==7 ab=px+(d==3)+(d==5)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>1 sc1=d==2 mo1=d==6 px1=d==7 v1m=mo1+px1 v1j=d>7 dd1=v1j+(d==4)+(d==5) ab1=px1+(d==3)+(d==5)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=d>1 sc2=d==2 mo2=d==6 px2=d==7 v2m=mo2+px2 v2j=d>7 dd2=v2j+(d==4)+(d==5) ab2=px2+(d==3)+(d==5)+(d==9) d=trunc(dd/10) ex3=d>1 sc3=d==2 mo3=d==6 px3=d==7 v3m=mo3+px3 v3j=d>7 dd3=v3j+(d==4)+(d==5) ab3=px3+(d==3)+(d==5)+(d==9) d=dd-d*10 ba=imag(p5) mi3=trunc(ba) dd=(d>1)+(mi3>1) ex4=dd==2 sc4=d==2 mo4=d==6 px4=d==7 v4m=mo4+px4 v4j=d>7 dd4=v4j+(d==4)+(d==5) ab4=px4+(d==3)+(d==5)+(d==9) ; mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 dm=(d==2)+(d==4) ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex1+ex0+ex2+ex3+ex4 ; d=real(p3) dd=trunc(d) da=(d-dd)*10000000000 pp=trunc(dd/10000) ba1=dd-10000*pp ba2=trunc(da/100000) ba3=da-100000*ba2 ; d=imag(p3) sfac=trunc(d) da=(d-sfac)*100000000000 ba4=trunc(da/1000000) ba5=da-ba4*1000000 ; d=real(p4) ofac=trunc(d) da=(d-ofac)*10000000000 bh=trunc(da/100000)/10 bl=(da-bh*1000000)/10 bs=bl/2 ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) da=round((d-dd)*10000000000) d=trunc(dd/10000) dd=dd-d*10000 bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/1000) dd=dd-d*1000 bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/100) dd=dd-d*100 bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/10) dd=dd-d*10 bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=round(dd) bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) ; d=da p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 dp=p6+p0/100 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=d==3 fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 ; d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=d==3 fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 ; if (mi3==1) d=(ba-mi3)*1000000 fr=round((trunc(d/10000))*10) ;lake effect by S.Gallet d=d-fr*1000 lv=(trunc(d/100))/100 d=d-lv*10000 am=d/100 u=real(rotskew*pi/180) t=exp(-flip(u)) bo=1/real(magxmag) q=bo/0.75*imag(magxmag) dd=tan(imag(rotskew*pi/180)) da=2*q*t rs=2*bo*(dd+flip(1))*t zz=center+(-q-bo*dd-flip(bo))*t z=z-zz d=imag(conj(da)*z)/imag(conj(da)*rs) le=d<=lv if (le) dd=lv-d z=z+2*dd*(1+am*sin(fr*dd^0.2))*rs endif z=z+zz else da=(ba-mi3)*100000000000 d=trunc(da/10000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=d==3 fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 endif ; if (vb) if (d3) if (ab) z=z*le+pixel*(le==0) ;Spider c=p1 else z=z*le+pixel*(le==0) c=p1 ;newton endif elseif (ab) c=z ;Phoenix z=z*le+pixel*(le==0) else c=0.4*log(sqr(z^mm)) ;many mods z=0 endif elseif (d3) if (ab) c=p1 ;Julia z=z*le+pixel*(le==0) else ;bees c=p1 z=z*le+pixel*(le==0) endif elseif (ab) c=z ;Mandel z=0 else c=z ;Secant z=z*le+pixel*(le==0) endif t=0 bo=|z| p=pp z0=p7 zold=(0.0,0.0) cb=p9 ba=bb0 : if (tt) t=t+1 if (ex0) ex0=t<mi1 if (bo>bs) u=2*(fn1(t/sfac)) ex0=0 if (ir0) t=0 endif if (d4) z=z*u if (mo) c=0.4*log(sqr(z^mm)) else c=pixel endif else z=z*le+pixel*(le==0) cb=p9*u c=p1*u p=pp*u endif tt=tt-1+ex0 endif elseif ((ex1)&&bo>bl) if (bo<bh) d3=dd1 ba=bb1 ab=ab1 ex1=0 tt=tt-1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif if (ir1) t=0 endif if (d3) vb=v1j if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif else vb=v1m if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo1) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) ab=ab2 d3=dd2 ba=bb2 ex2=0 tt=tt-1 if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif if (ir2) t=0 endif if (d3) vb=v2j if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v2m if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo2) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) ab=ab3 d3=dd3 ba=bb3 ex3=0 tt=tt-1 if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif if (ir3) t=0 endif if (d3) vb=v3j if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v3m if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) ab=ab4 d3=dd4 ba=bb4 ex4=0 tt=0 if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (d3) vb=v4j if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v4m if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo4) c=0.4*log(sqr(z^mm)) endif endif endif endif endif if (vb) if (d3) if (ab) z=z*z+c ;Spiderjul John Horner c=c*sp+z else z1=z^p-1 ;Quasinewton Puskas Istvan z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+0.56+ph/100-0.5*zold ;Phoenix Mike Wareman zold=z z=z1 else z2=fn1(z)+c ;Many_mods Linda Allison z1=cos(z2) z=c*(1-z1)/(1+z1) endif elseif (d3) if (ab) z2=z*z ;Julia Puskas Istvan z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb ;Bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) if (dm) z=z*z+c+c*c-dp ;Double Mandel else z2=z*z ;Mandel Puskas Istvan z=z2*z2+p6*z2+c-p0 endif else z3=z ;Secant Mike Wareman z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<ba } ----------------------------------end-----------------------------

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Four Pictures
by Brian Prentice 19 Nov '12

19 Nov '12

Here are four pictures that were drawn by Jim's new formula MandelbrotFNC: http://bprentice.webenet.net/Fractal%20Images/Set%2017/BP_17_96a.png http://bprentice.webenet.net/Fractal%20Images/Set%2017/BP_17_96b.png http://bprentice.webenet.net/Fractal%20Images/Set%2017/BP_17_97a.png http://bprentice.webenet.net/Fractal%20Images/Set%2017/BP_17_97b.png Brian Prentice

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Crosswise
by Albrecht 19 Nov '12

19 Nov '12

Hi, just want to inform you that yesterday?s image "Crosswise" is available in full HD on Hal?s server http://www.emarketingiseasy.com/Albrecht/1536709A.GIF Albrecht

1 0

Crosswise
by Albrecht 19 Nov '12

19 Nov '12

Hi, today?s image in fact is more an image then a fractal. But you?re going to like it. It?s a very fast one for a change, although not the fastest by far. Albrecht --------------------start-par------------------------ 1536709A { ; Crosswise ; Time 0.01.35 1600/1200 ; sec-mmods-bees-phoen-spid reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=-1.46373607365559400/-0.000000044867182\ 47/154931/1/90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/153\ 67.64595767025/14235.4911030602/152048.0404808048/\ 384.1604894048/384.00482000595/256.1007683001/512.\ 1007683001/768.1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000t2tv2u<3>c5eZ6`U6X<2>F9LAAG7FO4KW0Qc<3>5\ Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<3>civflvinvlqv\ otvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI<4\ >XCAaB9fB7<3>zA0<13>SA1QA1NA1<3>D92<6>UXAW`BYcC<3>\ hrI<3>UnXRm_NlcJkgFfpAaz<3>PJoSFlWAi_5fc0ce7_jFR00\ 0oNIzb0<2>zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8K\ J8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriA\ tm9vq8xu7zz5zz4zz3<8>zY4zV5zS5<3>zE6wE6tD6<10>w8Px\ 8Rx7S<3>z5_<3>f5Ma5IW4E<2>_4H<3>P3DN2CK2A<3>805G0B\ O0G<3>g0Ul0Xq0`v0d<2>y0fz0gy0h<5>s1or2qs2r } frm:multifractal_10 { ; Albrecht Niekamp Jan2005 ;RP2 Left: 5 Digits_Channel:1_main 2_outside 3_inside1 4_inside2 5_inside3 ; Frms: 0_off 1_Sec 2_Mand(2) 3_Bees 4_Jul 5_Mmod 6_Phoen 7_Newt 8_Spid ; Right: 2 Digits_MMods_Number of sides 2 Dig_Phoenix 2 Dig_Spider ; 1 Dig_TransReset_main :0_no 1_dblmand 2_Iter-res 3_both +5_warp ; 4 Dig_TransReset_Ch2-5:0_no 1_z-reset 2_Iter-res 3_both +5_warp ;IP2 Left: 5 Digits_Bailout Number for Channels 1 to 5 ; Right: Variab: 4 Digits_Mand/Jul(2 var) 2 Digits_Secant 4 Digits_Bees ;RP3 Left: 2 Digits_Newtonvariable 4 Digits_Colour1 ; Right: 5 Digits_Colour2 5 Digits_Colour3 ;IP3 Left: Main: 5 Digits_Warp-factor (fn1 is used) ; Right: 5 Digits_Colour4 6 Digits_Colour5 ;RP4 Left: Outside: 5 Digits_Warp-factor (fn2 is used) ; Right: Outside: 4 Dig+1 fractaldig_bord-out 4 Dig+1 fractaldig_bord-in ;IP4 Left: Inside1_Maxiter ; Right: Inside1_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn2 used) 4 Dig+1 fractaldig_border1 ;RP5 Left: Inside2_Maxiter ; Right: Inside2_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn3 used) 4 Dig+1 fractaldig_border2 ;IP5 Left: Inside3_Maxiter ; Right: Inside3_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn4 used) 4 Dig+1 fractaldig_border3 ; Altnat: Left: 1_Lake effect enabled (Inside3 disabled) ; Right: 2 Digit_Frequency 2 Digit_Waterlevel 2 Digit_Amplitude ; le=0 z=pixel da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+11111 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==4)+(d==5)+(d==8)+(d==9) d4=d3==0 vb=d>5 sc=d==2 mo=d==6 px=d==7 ab=px+(d==3)+(d==5)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>1 sc1=d==2 mo1=d==6 px1=d==7 v1m=mo1+px1 v1j=d>7 dd1=v1j+(d==4)+(d==5) ab1=px1+(d==3)+(d==5)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=d>1 sc2=d==2 mo2=d==6 px2=d==7 v2m=mo2+px2 v2j=d>7 dd2=v2j+(d==4)+(d==5) ab2=px2+(d==3)+(d==5)+(d==9) d=trunc(dd/10) ex3=d>1 sc3=d==2 mo3=d==6 px3=d==7 v3m=mo3+px3 v3j=d>7 dd3=v3j+(d==4)+(d==5) ab3=px3+(d==3)+(d==5)+(d==9) d=dd-d*10 ba=imag(p5) mi3=trunc(ba) dd=(d>1)+(mi3>1) ex4=dd==2 sc4=d==2 mo4=d==6 px4=d==7 v4m=mo4+px4 v4j=d>7 dd4=v4j+(d==4)+(d==5) ab4=px4+(d==3)+(d==5)+(d==9) ; mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 dm=(d==2)+(d==4) ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex1+ex0+ex2+ex3+ex4 ; d=real(p3) dd=trunc(d) da=(d-dd)*10000000000 pp=trunc(dd/10000) ba1=dd-10000*pp ba2=trunc(da/100000) ba3=da-100000*ba2 ; d=imag(p3) sfac=trunc(d) da=(d-sfac)*100000000000 ba4=trunc(da/1000000) ba5=da-ba4*1000000 ; d=real(p4) ofac=trunc(d) da=(d-ofac)*10000000000 bh=trunc(da/100000)/10 bl=(da-bh*1000000)/10 bs=bl/2 ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) da=round((d-dd)*10000000000) d=trunc(dd/10000) dd=dd-d*10000 bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/1000) dd=dd-d*1000 bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/100) dd=dd-d*100 bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/10) dd=dd-d*10 bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=round(dd) bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) ; d=da p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 dp=p6+p0/100 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=d==3 fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 ; d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=d==3 fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 ; if (mi3==1) d=(ba-mi3)*1000000 fr=round((trunc(d/10000))*10) ;lake effect by S.Gallet d=d-fr*1000 lv=(trunc(d/100))/100 d=d-lv*10000 am=d/100 u=real(rotskew*pi/180) t=exp(-flip(u)) bo=1/real(magxmag) q=bo/0.75*imag(magxmag) dd=tan(imag(rotskew*pi/180)) da=2*q*t rs=2*bo*(dd+flip(1))*t zz=center+(-q-bo*dd-flip(bo))*t z=z-zz d=imag(conj(da)*z)/imag(conj(da)*rs) le=d<=lv if (le) dd=lv-d z=z+2*dd*(1+am*sin(fr*dd^0.2))*rs endif z=z+zz else da=(ba-mi3)*100000000000 d=trunc(da/10000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=d==3 fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 endif ; if (vb) if (d3) if (ab) z=z*le+pixel*(le==0) ;Spider c=p1 else z=z*le+pixel*(le==0) c=p1 ;newton endif elseif (ab) c=z ;Phoenix z=z*le+pixel*(le==0) else c=0.4*log(sqr(z^mm)) ;many mods z=0 endif elseif (d3) if (ab) c=p1 ;Julia z=z*le+pixel*(le==0) else ;bees c=p1 z=z*le+pixel*(le==0) endif elseif (ab) c=z ;Mandel z=0 else c=z ;Secant z=z*le+pixel*(le==0) endif t=0 bo=|z| p=pp z0=p7 zold=(0.0,0.0) cb=p9 ba=bb0 : if (tt) t=t+1 if (ex0) ex0=t<mi1 if (bo>bs) u=2*(fn1(t/sfac)) ex0=0 if (ir0) t=0 endif if (d4) z=z*u if (mo) c=0.4*log(sqr(z^mm)) else c=pixel endif else z=z*le+pixel*(le==0) cb=p9*u c=p1*u p=pp*u endif tt=tt-1+ex0 endif elseif ((ex1)&&bo>bl) if (bo<bh) d3=dd1 ba=bb1 ab=ab1 ex1=0 tt=tt-1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif if (ir1) t=0 endif if (d3) vb=v1j if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif else vb=v1m if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo1) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) ab=ab2 d3=dd2 ba=bb2 ex2=0 tt=tt-1 if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif if (ir2) t=0 endif if (d3) vb=v2j if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v2m if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo2) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) ab=ab3 d3=dd3 ba=bb3 ex3=0 tt=tt-1 if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif if (ir3) t=0 endif if (d3) vb=v3j if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v3m if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) ab=ab4 d3=dd4 ba=bb4 ex4=0 tt=0 if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (d3) vb=v4j if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v4m if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo4) c=0.4*log(sqr(z^mm)) endif endif endif endif endif if (vb) if (d3) if (ab) z=z*z+c ;Spiderjul John Horner c=c*sp+z else z1=z^p-1 ;Quasinewton Puskas Istvan z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+0.56+ph/100-0.5*zold ;Phoenix Mike Wareman zold=z z=z1 else z2=fn1(z)+c ;Many_mods Linda Allison z1=cos(z2) z=c*(1-z1)/(1+z1) endif elseif (d3) if (ab) z2=z*z ;Julia Puskas Istvan z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb ;Bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) if (dm) z=z*z+c+c*c-dp ;Double Mandel else z2=z*z ;Mandel Puskas Istvan z=z2*z2+p6*z2+c-p0 endif else z3=z ;Secant Mike Wareman z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<ba } ---------------------------------end-------------------------------------

1 0

FOTD 17-11-12 (A Twist of Reason [?])
by Jim Muth 18 Nov '12

18 Nov '12

FOTD -- November 17, 2012 (Rating ?) Fractal visionaries and enthusiasts: NEW FORMULA ALERT! At least I don't think I've posted it before. Today's image is the first in a series of distorted Mandelbrot sets. The distortion is created by applying the 'exp' function to different initial values of 'C'. Doing this creates the effect of viewing the M-set from the point determined by the value assigned the (p3) parameter. The farther from this point, the features lie, the smaller they appear. In today's image the value is +0.255, which places the viewer deep in East Valley and greatly enlarges the surrounding area. Today's image is its own parent fractal, though due to the nature of the exponential function, there are a multitude of parent fractals. The name "A Twist of Reason" indicates that there is nothing at all unreasonable about the Mandelbrot distortion. The same may not be true of the upcoming images however. The rating of a question mark shows my uncertainty as to the true value of the image. The calculation time of 10 seconds will simply fly by. It will take a bit longer to see the finished image on the web sites, but doing so will be more convenient. Check the finished image at: <http://www.crosscanpuzzles.com/Archives.html> and the hi-def variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back inages are at: <http://www.Nahee.com/FOTD/> Total sun and a temperature of 52F 11C made today a day to be remembered here at Fractal Central. The next FOTD will be posted in the proper spacetime. Until whenever and wherever this might be, take care, and have a good time taking it easy. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= A_Twist_of_Reason { ; time=0:00:10.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotFNC function=exp periodicity=6 center-mag=-3.39731/3.1415927/0.2989/1/180 inside=0 params=2/0/0/0/0.255/0 float=y maxiter=1500 colors=000Xd8Xe7Xf7Wg7UhASiDQjFOkIMlKKmNKnPKoSKpUK\ qXKrZLsaNtcPu`PvZRvXTwUVvSXuQZtN`sLbrJdqHfpKhoMjnP\ lmRnlUpkWrjZti`vhcvgevfgughtghshhrhhpihoihmjikjihk\ ifkidlibli`ljZmjXmjVnjTnjRojPokNpkLpkJqkHqkGqkInhJ\ lfLjdMhbOf`PdZRaXS_VTYTVWRWUPYSNZPL`NJaLHcJFdHDeFB\ gGEhHHiIJkJMlKPmLRoMUpNXqOZsPatQduRfwSixTlyUn4AW5G\ Y6M_7R`8Xb9acAgeBlfCrhCwiBtgAqfAoe9lc9ib8ga7d_7aZ6\ _Y6XX5UV4SU4PT3MR3KQ2HP2FOGKQTOSfTUsXWtVUtUTtTSuSR\ uRQuQPvPOvONvNMwMLwLKwKIwJHxIGxHFxGEyFDyECyDBzCAzB\ 9zA8z97wABuBFsBIqCMoDQmDTjEXhF`fFcdGgbHk`HnXEhUBcQ\ 8ZN5UQQVSiVXgQaeLfdHWSBMF5LI7KL9KNBJQDITFIVHHYJG`L\ GbNFePEhREjSIXTMJUP6UOdsLcrIbqFapCap9`o6_n3Zm0Zm2X\ n4Wn6Vn8UnAToCSoERoGQoIPpKOpMNpOMpQLqSKqUJqWIqVLmV\ OjURfUTcUW`TZXTaUTcRUaVV`ZV_aWYeXXhXWlYUoZTsZSvYTr\ YUoYUkXVhXWdXWaXXZWYVWYSWZOV_LV_HV`EV`BQWLMSVINdEJ\ mHKlKLkNMkQNjTOiWPiZQhaRg } frm:MandelbrotFNC {; Jim Muth b=p1, z=p2, c=p3+fn1(pixel): z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

1 0

Arrival
by Albrecht 17 Nov '12

17 Nov '12

Hi, this is the (almost) total view of the Fractal-Journey image, therefore the title. Looking closely you will detect a lot of structures and elements not seen before. Another slow one like all border-defined images but available for immediate watching in full HD on Hal?s server. http://www.emarketingiseasy.com/Albrecht/71635XE.GIF Happy zooming! Albrecht -----------------start-par---------------------------- 71635xe { ; Arrival ; time 23.17 1600/1200 ; newt-sec-phoen-bees-mmods ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=cos/exp/exp/sin passes=t center-mag=-0.105102/-0.00180651/0.6699414/1.1324/\ -90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/716\ 35.03564901002/14253.2207090221/151024.0204808192/\ 384.32768524288/384.00482000595/128.3007683001/256\ .3007682001/512.2007681001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=-4 periodicity=0 rseed=-2436 colors=000zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8K\ J8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriA\ tm9vq8xu7zz5zz4zz3<4>zj4zg4zc4<3>zS5zP5zL6zI6zE6wE\ 6tD6<6>vAIv9Kv9M<3>x7Sy7Uy6Wz6Yz5_<3>f5Ma5IW4E<2>_\ 4H<3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0g\ y0h<3>u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4K\ W0Qc<3>5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<3>civf\ lvinvlqvotvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP\ 8FL8CI<3>SCCXCAaB9<3>uA2zA0xA0<12>SA1QA1NA1<3>D92<\ 6>UXAW`BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJoSFlWAi\ _5fc0ce7_jFRoNIzb0zj0000zr0 } frm:multifractal_10 { ; Albrecht Niekamp Jan2005 ;RP2 Left: 5 Digits_Channel:1_main 2_outside 3_inside1 4_inside2 5_inside3 ; Frms: 0_off 1_Sec 2_Mand(2) 3_Bees 4_Jul 5_Mmod 6_Phoen 7_Newt 8_Spid ; Right: 2 Digits_MMods_Number of sides 2 Dig_Phoenix 2 Dig_Spider ; 1 Dig_TransReset_main :0_no 1_dblmand 2_Iter-res 3_both +5_warp ; 4 Dig_TransReset_Ch2-5:0_no 1_z-reset 2_Iter-res 3_both +5_warp ;IP2 Left: 5 Digits_Bailout Number for Channels 1 to 5 ; Right: Variab: 4 Digits_Mand/Jul(2 var) 2 Digits_Secant 4 Digits_Bees ;RP3 Left: 2 Digits_Newtonvariable 4 Digits_Colour1 ; Right: 5 Digits_Colour2 5 Digits_Colour3 ;IP3 Left: Main: 5 Digits_Warp-factor (fn1 is used) ; Right: 5 Digits_Colour4 6 Digits_Colour5 ;RP4 Left: Outside: 5 Digits_Warp-factor (fn2 is used) ; Right: Outside: 4 Dig+1 fractaldig_bord-out 4 Dig+1 fractaldig_bord-in ;IP4 Left: Inside1_Maxiter ; Right: Inside1_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn2 used) 4 Dig+1 fractaldig_border1 ;RP5 Left: Inside2_Maxiter ; Right: Inside2_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn3 used) 4 Dig+1 fractaldig_border2 ;IP5 Left: Inside3_Maxiter ; Right: Inside3_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn4 used) 4 Dig+1 fractaldig_border3 ; Altnat: Left: 1_Lake effect enabled (Inside3 disabled) ; Right: 2 Digit_Frequency 2 Digit_Waterlevel 2 Digit_Amplitude ; le=0 z=pixel da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+11111 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==4)+(d==5)+(d==8)+(d==9) d4=d3==0 vb=d>5 sc=d==2 mo=d==6 px=d==7 ab=px+(d==3)+(d==5)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>1 sc1=d==2 mo1=d==6 px1=d==7 v1m=mo1+px1 v1j=d>7 dd1=v1j+(d==4)+(d==5) ab1=px1+(d==3)+(d==5)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=d>1 sc2=d==2 mo2=d==6 px2=d==7 v2m=mo2+px2 v2j=d>7 dd2=v2j+(d==4)+(d==5) ab2=px2+(d==3)+(d==5)+(d==9) d=trunc(dd/10) ex3=d>1 sc3=d==2 mo3=d==6 px3=d==7 v3m=mo3+px3 v3j=d>7 dd3=v3j+(d==4)+(d==5) ab3=px3+(d==3)+(d==5)+(d==9) d=dd-d*10 ba=imag(p5) mi3=trunc(ba) dd=(d>1)+(mi3>1) ex4=dd==2 sc4=d==2 mo4=d==6 px4=d==7 v4m=mo4+px4 v4j=d>7 dd4=v4j+(d==4)+(d==5) ab4=px4+(d==3)+(d==5)+(d==9) ; mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 dm=(d==2)+(d==4) ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex1+ex0+ex2+ex3+ex4 ; d=real(p3) dd=trunc(d) da=(d-dd)*10000000000 pp=trunc(dd/10000) ba1=dd-10000*pp ba2=trunc(da/100000) ba3=da-100000*ba2 ; d=imag(p3) sfac=trunc(d) da=(d-sfac)*100000000000 ba4=trunc(da/1000000) ba5=da-ba4*1000000 ; d=real(p4) ofac=trunc(d) da=(d-ofac)*10000000000 bh=trunc(da/100000)/10 bl=(da-bh*1000000)/10 bs=bl/2 ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) da=round((d-dd)*10000000000) d=trunc(dd/10000) dd=dd-d*10000 bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/1000) dd=dd-d*1000 bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/100) dd=dd-d*100 bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/10) dd=dd-d*10 bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=round(dd) bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) ; d=da p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 dp=p6+p0/100 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=d==3 fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 ; d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=d==3 fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 ; if (mi3==1) d=(ba-mi3)*1000000 fr=round((trunc(d/10000))*10) ;lake effect by S.Gallet d=d-fr*1000 lv=(trunc(d/100))/100 d=d-lv*10000 am=d/100 u=real(rotskew*pi/180) t=exp(-flip(u)) bo=1/real(magxmag) q=bo/0.75*imag(magxmag) dd=tan(imag(rotskew*pi/180)) da=2*q*t rs=2*bo*(dd+flip(1))*t zz=center+(-q-bo*dd-flip(bo))*t z=z-zz d=imag(conj(da)*z)/imag(conj(da)*rs) le=d<=lv if (le) dd=lv-d z=z+2*dd*(1+am*sin(fr*dd^0.2))*rs endif z=z+zz else da=(ba-mi3)*100000000000 d=trunc(da/10000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=d==3 fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 endif ; if (vb) if (d3) if (ab) z=z*le+pixel*(le==0) ;Spider c=p1 else z=z*le+pixel*(le==0) c=p1 ;newton endif elseif (ab) c=z ;Phoenix z=z*le+pixel*(le==0) else c=0.4*log(sqr(z^mm)) ;many mods z=0 endif elseif (d3) if (ab) c=p1 ;Julia z=z*le+pixel*(le==0) else ;bees c=p1 z=z*le+pixel*(le==0) endif elseif (ab) c=z ;Mandel z=0 else c=z ;Secant z=z*le+pixel*(le==0) endif t=0 bo=|z| p=pp z0=p7 zold=(0.0,0.0) cb=p9 ba=bb0 : if (tt) t=t+1 if (ex0) ex0=t<mi1 if (bo>bs) u=2*(fn1(t/sfac)) ex0=0 if (ir0) t=0 endif if (d4) z=z*u if (mo) c=0.4*log(sqr(z^mm)) else c=pixel endif else z=z*le+pixel*(le==0) cb=p9*u c=p1*u p=pp*u endif tt=tt-1+ex0 endif elseif ((ex1)&&bo>bl) if (bo<bh) d3=dd1 ba=bb1 ab=ab1 ex1=0 tt=tt-1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif if (ir1) t=0 endif if (d3) vb=v1j if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif else vb=v1m if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo1) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) ab=ab2 d3=dd2 ba=bb2 ex2=0 tt=tt-1 if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif if (ir2) t=0 endif if (d3) vb=v2j if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v2m if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo2) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) ab=ab3 d3=dd3 ba=bb3 ex3=0 tt=tt-1 if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif if (ir3) t=0 endif if (d3) vb=v3j if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v3m if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) ab=ab4 d3=dd4 ba=bb4 ex4=0 tt=0 if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (d3) vb=v4j if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v4m if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo4) c=0.4*log(sqr(z^mm)) endif endif endif endif endif if (vb) if (d3) if (ab) z=z*z+c ;Spiderjul John Horner c=c*sp+z else z1=z^p-1 ;Quasinewton Puskas Istvan z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+0.56+ph/100-0.5*zold ;Phoenix Mike Wareman zold=z z=z1 else z2=fn1(z)+c ;Many_mods Linda Allison z1=cos(z2) z=c*(1-z1)/(1+z1) endif elseif (d3) if (ab) z2=z*z ;Julia Puskas Istvan z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb ;Bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) if (dm) z=z*z+c+c*c-dp ;Double Mandel else z2=z*z ;Mandel Puskas Istvan z=z2*z2+p6*z2+c-p0 endif else z3=z ;Secant Mike Wareman z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<ba } --------------------------------------------end-----------------------

1 0

Trapped Cosine
by Mike Frazier 17 Nov '12

17 Nov '12

This fractal uses a modified Paul Carlson orbit trap coloring method with the parallel resistor formula. Disconnected minibrots and long arms make it easier to avoid overlap issues I have had with this method in the past. Here is a link to an image: http://dl.dropbox.com/u/33642054/image/trapped_cosine_1200_5.jpg The Fractint compatible PAR file for the image is: Trapped_Cosine { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20121117_1037 passes=1 float=y center-mag=-3.240788740145593/-5.614587198083252e-\ 15/8333333437.5/1/0/0 params=0.03/0.3/8/30/6/0.25/0/0/0/0 maxiter=500 inside=255 outside=summ colors=000fOz<28>I0Kz0f<28>O08z88<28>O00zW0<28>c40\ zz0<28>aG00zR<28>0C40zz<28>0CCGGz<28>00O000<12>000\ z88 } frm:F_20121117_1037 { ; Epicycloid_Mset based on Astroid_Mset ; Astroid_Mset copyright (c) Paul W. Carlson, 1997 ; Epicycloid_Mset by Mike Frazier, 2011 ;**************************************************** ; Always use floating point math and outside=summ. ; ; Parameters: ; real(p1) = a factor controlling the width of the curves ; imag(p1) = radius of the curve ; real(p2) = number of color ranges ; imag(p2) = number of colors in each color range ; real(p3) = number of cusps, even integers ; imag(p3) = cusp amplitude (0 to 1) ; ; Note that the equation variable is w, not z. ; Initialize cindex to the index of the background color ; Formula modified to avoid color index 0 which can not ; be used with outside=summ in FractInt v20.04 ;**************************************************** w=0, c=pixel, c1=pixel+1, c2=pixel-1, z=0, cindex=254,; Background color bailout=0, iter=0, range_num=0, i=(0,1), r=imag(p1), f=real(p3)+1, b=imag(p3), ;**************************************************** ; In the accompanying par file, ; we have 8 color ranges with 30 colors in each range ; for a total of 240 colors. The first range starts at ; color 1. Pixels will use color 254 when |w| > 1000. ; Other values can be used here as long as the product ; of num_ranges times colors_in_range is less than 255. ; Color 254 is reserved for the background color and ; color 255 can be used for the inside color. ;**************************************************** num_ranges=real(p2), colors_in_range=imag(p2), ;**************************************************** ; Real(p1) controls the width of the curves. ; These values will usually be in the range 0.001 to 0.1 ;**************************************************** width=real(p1), index_factor=(colors_in_range-1)/width: ;**************************************************** ; The equation being iterated. Almost any equation ; that can be expressed in terms of a complex variable ; and a complex constant will work with this method. ; This example uses the parallel resistor formula ;**************************************************** ww=w*w, w=1/(1/(-1*ww*(cos(w)-1)+c1)+1/(ww*ww+c2)), ;**************************************************** ; The orbit trap curve is an epicycloid. ; Any two-dimensional curve can ; be used which can be expressed in parametric form in ; terms of the angle from the origin. ;**************************************************** ang=atan(imag(w)/real(w)), astroid=r*(cos(ang)-b*cos(f*ang)+i*(sin(ang)-b*sin(f*ang))), ;**************************************************** ; If the orbit point is within some distance of the curve, ; set cindex to the index into the colormap and set the bailout ; flag. Note: the way we use the "distance" here has ; the effect of turning the curves inside-out in the image. ;**************************************************** distance=abs(|w|-|astroid|), if(distance<width&&iter>1), cindex=index_factor*distance+range_num*colors_in_range+1, bailout=1, endif, ;**************************************************** ; Cycle through the range numbers (0 thru num_ranges - 1) ; With two color ranges, even iterations use color ; range 0, odd iterations use color range 1. ;**************************************************** range_num=range_num+1, if(range_num==num_ranges), range_num=0, endif, ;**************************************************** ; Since we are using outside=summ, we have to subtract ; the number of iterations from z. ;**************************************************** iter=iter+1, z=cindex-iter, ;**************************************************** ; Finally, we test for bailout ;**************************************************** bailout==0&&|w|<1000 } -- Mike Frazier www.fracton.org

1 0

Fractal_Journey
by Albrecht 17 Nov '12

17 Nov '12

Hi, yesterday I posted the "Mystery" which was a zoom into an inside-out conversion of an otherwise normal and pretty fractal. That?s what it is: The outside became the empty circle inside and the inside was converted into the looks and structure of the outer frame. Today I?m presenting the reconversion. As it was a zoom, I had no idea what to expect. Here it is without any editing. Judge yourself. Albrecht --------------------------------start-par------------------------------ 71635XC { ; Fractal_Journey ; Time 46.21 1600/1200 ; Conversion of Mystery Image ; back to regular reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=cos/exp/exp/sin passes=t center-mag=0.0104739/-0.881323/3.318983/0.8831 params=-0.05825983458967864/0.3785210730307932/716\ 35.03564901002/14253.2207090221/151024.0204808192/\ 384.32768524288/384.00482000595/128.3007683001/256\ .3007682001/512.2007681001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=-4 periodicity=0 rseed=-2436 colors=000zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8K\ J8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriA\ tm9vq8xu7zz5zz4zz3<4>zj4zg4zc4<3>zS5zP5zL6zI6zE6wE\ 6tD6<6>vAIv9Kv9M<3>x7Sy7Uy6Wz6Yz5_<3>f5Ma5IW4E<2>_\ 4H<3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0g\ y0h<3>u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4K\ W0Qc<3>5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<3>civf\ lvinvlqvotvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP\ 8FL8CI<3>SCCXCAaB9<3>uA2zA0xA0<12>SA1QA1NA1<3>D92<\ 6>UXAW`BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJoSFlWAi\ _5fc0ce7_jFRoNIzb0zj0000zr0 } frm:multifractal_10 { ; Albrecht Niekamp Jan2005 ;RP2 Left: 5 Digits_Channel:1_main 2_outside 3_inside1 4_inside2 5_inside3 ; Frms: 0_off 1_Sec 2_Mand(2) 3_Bees 4_Jul 5_Mmod 6_Phoen 7_Newt 8_Spid ; Right: 2 Digits_MMods_Number of sides 2 Dig_Phoenix 2 Dig_Spider ; 1 Dig_TransReset_main :0_no 1_dblmand 2_Iter-res 3_both +5_warp ; 4 Dig_TransReset_Ch2-5:0_no 1_z-reset 2_Iter-res 3_both +5_warp ;IP2 Left: 5 Digits_Bailout Number for Channels 1 to 5 ; Right: Variab: 4 Digits_Mand/Jul(2 var) 2 Digits_Secant 4 Digits_Bees ;RP3 Left: 2 Digits_Newtonvariable 4 Digits_Colour1 ; Right: 5 Digits_Colour2 5 Digits_Colour3 ;IP3 Left: Main: 5 Digits_Warp-factor (fn1 is used) ; Right: 5 Digits_Colour4 6 Digits_Colour5 ;RP4 Left: Outside: 5 Digits_Warp-factor (fn2 is used) ; Right: Outside: 4 Dig+1 fractaldig_bord-out 4 Dig+1 fractaldig_bord-in ;IP4 Left: Inside1_Maxiter ; Right: Inside1_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn2 used) 4 Dig+1 fractaldig_border1 ;RP5 Left: Inside2_Maxiter ; Right: Inside2_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn3 used) 4 Dig+1 fractaldig_border2 ;IP5 Left: Inside3_Maxiter ; Right: Inside3_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn4 used) 4 Dig+1 fractaldig_border3 ; Altnat: Left: 1_Lake effect enabled (Inside3 disabled) ; Right: 2 Digit_Frequency 2 Digit_Waterlevel 2 Digit_Amplitude ; le=0 z=pixel da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+11111 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==4)+(d==5)+(d==8)+(d==9) d4=d3==0 vb=d>5 sc=d==2 mo=d==6 px=d==7 ab=px+(d==3)+(d==5)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>1 sc1=d==2 mo1=d==6 px1=d==7 v1m=mo1+px1 v1j=d>7 dd1=v1j+(d==4)+(d==5) ab1=px1+(d==3)+(d==5)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=d>1 sc2=d==2 mo2=d==6 px2=d==7 v2m=mo2+px2 v2j=d>7 dd2=v2j+(d==4)+(d==5) ab2=px2+(d==3)+(d==5)+(d==9) d=trunc(dd/10) ex3=d>1 sc3=d==2 mo3=d==6 px3=d==7 v3m=mo3+px3 v3j=d>7 dd3=v3j+(d==4)+(d==5) ab3=px3+(d==3)+(d==5)+(d==9) d=dd-d*10 ba=imag(p5) mi3=trunc(ba) dd=(d>1)+(mi3>1) ex4=dd==2 sc4=d==2 mo4=d==6 px4=d==7 v4m=mo4+px4 v4j=d>7 dd4=v4j+(d==4)+(d==5) ab4=px4+(d==3)+(d==5)+(d==9) ; mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 dm=(d==2)+(d==4) ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex1+ex0+ex2+ex3+ex4 ; d=real(p3) dd=trunc(d) da=(d-dd)*10000000000 pp=trunc(dd/10000) ba1=dd-10000*pp ba2=trunc(da/100000) ba3=da-100000*ba2 ; d=imag(p3) sfac=trunc(d) da=(d-sfac)*100000000000 ba4=trunc(da/1000000) ba5=da-ba4*1000000 ; d=real(p4) ofac=trunc(d) da=(d-ofac)*10000000000 bh=trunc(da/100000)/10 bl=(da-bh*1000000)/10 bs=bl/2 ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) da=round((d-dd)*10000000000) d=trunc(dd/10000) dd=dd-d*10000 bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/1000) dd=dd-d*1000 bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/100) dd=dd-d*100 bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/10) dd=dd-d*10 bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=round(dd) bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) ; d=da p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 dp=p6+p0/100 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=d==3 fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 ; d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=d==3 fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 ; if (mi3==1) d=(ba-mi3)*1000000 fr=round((trunc(d/10000))*10) ;lake effect by S.Gallet d=d-fr*1000 lv=(trunc(d/100))/100 d=d-lv*10000 am=d/100 u=real(rotskew*pi/180) t=exp(-flip(u)) bo=1/real(magxmag) q=bo/0.75*imag(magxmag) dd=tan(imag(rotskew*pi/180)) da=2*q*t rs=2*bo*(dd+flip(1))*t zz=center+(-q-bo*dd-flip(bo))*t z=z-zz d=imag(conj(da)*z)/imag(conj(da)*rs) le=d<=lv if (le) dd=lv-d z=z+2*dd*(1+am*sin(fr*dd^0.2))*rs endif z=z+zz else da=(ba-mi3)*100000000000 d=trunc(da/10000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=d==3 fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 endif ; if (vb) if (d3) if (ab) z=z*le+pixel*(le==0) ;Spider c=p1 else z=z*le+pixel*(le==0) c=p1 ;newton endif elseif (ab) c=z ;Phoenix z=z*le+pixel*(le==0) else c=0.4*log(sqr(z^mm)) ;many mods z=0 endif elseif (d3) if (ab) c=p1 ;Julia z=z*le+pixel*(le==0) else ;bees c=p1 z=z*le+pixel*(le==0) endif elseif (ab) c=z ;Mandel z=0 else c=z ;Secant z=z*le+pixel*(le==0) endif t=0 bo=|z| p=pp z0=p7 zold=(0.0,0.0) cb=p9 ba=bb0 : if (tt) t=t+1 if (ex0) ex0=t<mi1 if (bo>bs) u=2*(fn1(t/sfac)) ex0=0 if (ir0) t=0 endif if (d4) z=z*u if (mo) c=0.4*log(sqr(z^mm)) else c=pixel endif else z=z*le+pixel*(le==0) cb=p9*u c=p1*u p=pp*u endif tt=tt-1+ex0 endif elseif ((ex1)&&bo>bl) if (bo<bh) d3=dd1 ba=bb1 ab=ab1 ex1=0 tt=tt-1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif if (ir1) t=0 endif if (d3) vb=v1j if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif else vb=v1m if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo1) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) ab=ab2 d3=dd2 ba=bb2 ex2=0 tt=tt-1 if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif if (ir2) t=0 endif if (d3) vb=v2j if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v2m if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo2) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) ab=ab3 d3=dd3 ba=bb3 ex3=0 tt=tt-1 if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif if (ir3) t=0 endif if (d3) vb=v3j if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v3m if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) ab=ab4 d3=dd4 ba=bb4 ex4=0 tt=0 if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (d3) vb=v4j if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v4m if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo4) c=0.4*log(sqr(z^mm)) endif endif endif endif endif if (vb) if (d3) if (ab) z=z*z+c ;Spiderjul John Horner c=c*sp+z else z1=z^p-1 ;Quasinewton Puskas Istvan z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+0.56+ph/100-0.5*zold ;Phoenix Mike Wareman zold=z z=z1 else z2=fn1(z)+c ;Many_mods Linda Allison z1=cos(z2) z=c*(1-z1)/(1+z1) endif elseif (d3) if (ab) z2=z*z ;Julia Puskas Istvan z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb ;Bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) if (dm) z=z*z+c+c*c-dp ;Double Mandel else z2=z*z ;Mandel Puskas Istvan z=z2*z2+p6*z2+c-p0 endif else z3=z ;Secant Mike Wareman z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<ba } -------------------------------------end-------------------------------

1 0

Mystery
by Albrecht 16 Nov '12

16 Nov '12

Hi, this is a MOST unsusual image. Got it using border-out values for bailout instead of border-in. The In-version is a pretty multistructural one and then this. Can anybody tell me what happened? Invisible mandels seem to be outside with their heads turned to the inside. Jim, or Paul, if listening, what do you think? Note the FRM version with an improved input section. Albrecht -----------------------start-par------------------ 71635x { ; Mystery ; time 28.57 1600/1200 ; Newt-secant-phoen-bees-mmods reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=cos/exp/exp/sin passes=t center-mag=0.0104739/-0.881323/3.318983/0.8831 params=-0.05825983458967864/0.3785210730307932/716\ 35.03564901002/14253.2207090221/151024.0204808192/\ 384.32768524288/384.00482000595/128.3007681001/256\ .3007682001/512.3007683001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=-4 periodicity=0 rseed=-2436 colors=000zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8K\ J8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriA\ tm9vq8xu7zz5zz4zz3<4>zj4zg4zc4<3>zS5zP5zL6zI6zE6wE\ 6tD6<6>vAIv9Kv9M<3>x7Sy7Uy6Wz6Yz5_<3>f5Ma5IW4E<2>_\ 4H<3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0g\ y0h<3>u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4K\ W0Qc<3>5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<3>civf\ lvinvlqvotvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP\ 8FL8CI<3>SCCXCAaB9<3>uA2zA0xA0<12>SA1QA1NA1<3>D92<\ 6>UXAW`BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJoSFlWAi\ _5fc0ce7_jFRoNIzb0zj0000zr0 } frm:multifractal_10 { ; Albrecht Niekamp Jan2005 ;RP2 Left:5 Dig_Chan: (1)shape (2)outside (3)inside1 (4)inside2 (5)inside3 ; Frm:0_off 1_Sec 2_Mand(2) 3_Bees 4_Jul 5_Mmod 6_phoen 7_newt 8_spid ; Right:2 Dig_MMods_Number of sides 2 Dig_Phoenix 2 Dig_Spider ; 1 Dig_TransReset-Shape: 0_no 1_DblMand 2_Iter-res 3_both +5_warp ; 4 Dig_TransReset-Ch 2-5:0_no 1_z-reset 2_Iter-res 3_both +5_warp ;IP2 Left: 5 Digits_Bailout Number for Channels 1 to 5 ; Right: Variab: 4 Digits_Mand/Jul(2 var) 2 Digits_Secant 4 Digits_Bees ;RP3 Left: 2 Digits_Newtonvariable 4 Digits_Colour1 ; Right: 5 Digits_Colour2 5 Digits_Colour3 ;IP3 Left: Shape: Warp-factor (fn1 is used) ; Right: 5 Digits_Colour4 6 Digits_Colour5 ;RP4 Left: Outside: Warp-factor (fn2 is used) ; Right: Outside: 4 Dig+1 fractaldig_bord-out 4 Dig+1 fractaldig_bord-in ;IP4 Left: Inside1_Maxiter ; Right: Inside1_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_warp factor (fn2 used) 4 Dig+1 fractaldig_border1 ;RP5 Left: Inside2_Maxiter ; Right: Inside2_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_warp factor (fn3 used) 4 Dig+1 fractaldig_border2 ;IP5 Left: Inside3_Maxiter ; Right: Inside3_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp factor (fn4 used) 4 Dig+1 fractaldig_border3 ; Altnat: Left: 1_Lake effect enabled (Inside3 disabled) ; Right: 2 Digit_Frequency 2 Digit_Waterlevel 2 Digit_Amplitude ; le=0 z=pixel da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+11111 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==4)+(d==5)+(d==8)+(d==9) d4=d3==0 vb=d>5 sc=d==2 mo=d==6 px=d==7 ab=px+(d==3)+(d==5)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>1 sc1=d==2 mo1=d==6 px1=d==7 v1m=mo1+px1 v1j=d>7 dd1=v1j+(d==4)+(d==5) ab1=px1+(d==3)+(d==5)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=d>1 sc2=d==2 mo2=d==6 px2=d==7 v2m=mo2+px2 v2j=d>7 dd2=v2j+(d==4)+(d==5) ab2=px2+(d==3)+(d==5)+(d==9) d=trunc(dd/10) ex3=d>1 sc3=d==2 mo3=d==6 px3=d==7 v3m=mo3+px3 v3j=d>7 dd3=v3j+(d==4)+(d==5) ab3=px3+(d==3)+(d==5)+(d==9) d=dd-d*10 ba=imag(p5) mi3=trunc(ba) dd=(d>1)+(mi3>1) ex4=dd==2 sc4=d==2 mo4=d==6 px4=d==7 v4m=mo4+px4 v4j=d>7 dd4=v4j+(d==4)+(d==5) ab4=px4+(d==3)+(d==5)+(d==9) ; mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 dm=(d==2)+(d==4) ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex1+ex0+ex2+ex3+ex4 ; d=real(p3) dd=trunc(d) da=(d-dd)*10000000000 pp=trunc(dd/10000) ba1=dd-10000*pp ba2=trunc(da/100000) ba3=da-100000*ba2 ; d=imag(p3) sfac=trunc(d) da=(d-sfac)*100000000000 ba4=trunc(da/1000000) ba5=da-ba4*1000000 ; d=real(p4) ofac=trunc(d) da=(d-ofac)*10000000000 bh=trunc(da/100000)/10 bl=(da-bh*1000000)/10 bs=bl/2 ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) da=round((d-dd)*10000000000) d=trunc(dd/10000) dd=dd-d*10000 bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/1000) dd=dd-d*1000 bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/100) dd=dd-d*100 bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/10) dd=dd-d*10 bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=round(dd) bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) ; d=da p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 dp=p6+p0/100 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=d==3 fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 ; d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=d==3 fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 ; if (mi3==1) d=(ba-mi3)*1000000 fr=round((trunc(d/10000))*10) ;lake effect by S.Gallet d=d-fr*1000 lv=(trunc(d/100))/100 d=d-lv*10000 am=d/100 u=real(rotskew*pi/180) t=exp(-flip(u)) bo=1/real(magxmag) q=bo/0.75*imag(magxmag) dd=tan(imag(rotskew*pi/180)) da=2*q*t rs=2*bo*(dd+flip(1))*t zz=center+(-q-bo*dd-flip(bo))*t z=z-zz d=imag(conj(da)*z)/imag(conj(da)*rs) le=d<=lv if (le) dd=lv-d z=z+2*dd*(1+am*sin(fr*dd^0.2))*rs endif z=z+zz else da=(ba-mi3)*100000000000 d=trunc(da/10000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=d==3 fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 endif ; if (vb) if (d3) if (ab) z=z*le+pixel*(le==0) ;Spider c=p1 else z=z*le+pixel*(le==0) c=p1 ;newton endif elseif (ab) c=z ;Phoenix z=z*le+pixel*(le==0) else c=0.4*log(sqr(z^mm)) ;many mods z=0 endif elseif (d3) if (ab) c=p1 ;Julia z=z*le+pixel*(le==0) else ;bees c=p1 z=z*le+pixel*(le==0) endif elseif (ab) c=z ;Mandel z=0 else c=z ;Secant z=z*le+pixel*(le==0) endif t=0 bo=|z| p=pp z0=p7 zold=(0.0,0.0) cb=p9 ba=bb0 : if (tt) t=t+1 if (ex0) ex0=t<mi1 if (bo>bs) u=2*(fn1(t/sfac)) ex0=0 if (ir0) t=0 endif if (d4) z=z*u if (mo) c=0.4*log(sqr(z^mm)) else c=pixel endif else z=z*le+pixel*(le==0) cb=p9*u c=p1*u p=pp*u endif tt=tt-1+ex0 endif elseif ((ex1)&&bo>bl) if (bo<bh) d3=dd1 ba=bb1 ab=ab1 ex1=0 tt=tt-1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif if (ir1) t=0 endif if (d3) vb=v1j if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif else vb=v1m if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo1) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) ab=ab2 d3=dd2 ba=bb2 ex2=0 tt=tt-1 if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif if (ir2) t=0 endif if (d3) vb=v2j if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v2m if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo2) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) ab=ab3 d3=dd3 ba=bb3 ex3=0 tt=tt-1 if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif if (ir3) t=0 endif if (d3) vb=v3j if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v3m if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) ab=ab4 d3=dd4 ba=bb4 ex4=0 tt=0 if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (d3) vb=v4j if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v4m if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo4) c=0.4*log(sqr(z^mm)) endif endif endif endif endif if (vb) if (d3) if (ab) z=z*z+c ;Spiderjul John Horner c=c*sp+z else z1=z^p-1 ;Quasinewton Puskas Istvan z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+0.56+ph/100-0.5*zold ;Phoenix Mike Wareman zold=z z=z1 else z2=fn1(z)+c ;Many_mods Linda Allison z1=cos(z2) z=c*(1-z1)/(1+z1) endif elseif (d3) if (ab) z2=z*z ;Julia Puskas Istvan z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb ;Bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) if (dm) z=z*z+c+c*c-dp ;Double Mandel else z2=z*z ;Mandel Puskas Istvan z=z2*z2+p6*z2+c-p0 endif else z3=z ;Secant Mike Wareman z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<ba }

1 0

FOTD 14-11-12 (Julia Intrusion [7])
by Jim Muth 15 Nov '12

15 Nov '12

FOTD -- November 14, 2012 (Rating 7) Fractal visionaries and enthusiasts: The formula behind today's image takes 0.8 part of Z^(-5.8) and subtracts 0.8 part of Z(-9.9) from it on each iteration before adding (1/C). The resulting parent fractal is little more than a mostly open ellipse with its longer axis in the vertical direction and eight patches of debris arranged in a ring just inside the perimeter of this ellipse. Today's scene is located in the debris along the negative X-axis at the western edge of the open ellipse. The name "Julia Intrusion" refers to the 'almost' Julia set at the center. Such miniature Julia sets in Mandelbrot images indicate that an unseen Mandelbrot set or minibrot lies hidden beneath the surface detail of the image. The shape of the Julia set corresponds to the part of the M-set over which it lies. A bit of the underlying Mandelbrot set shows through the surface Julia set as the bright bluish debris filling the left half of the J-set. The rating of a 7 is based mostly on the coloring, which in turn was created by the outside=tdis option. The calculation time of one minute has been rounded for convenience, but the parameter file will run in about this time on most SOTA (State of the Art) computers. Those with machines that lack art appreciation may view the image on one of the web sites. The image has already been calculated and is posted at: <http://www.crosscanpuzzles.com/Archives.html> with high-definition variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are available at: <http://www.Nahee.com/FOTD/> After a few early morning clouds, the day passed with total sun and a temperature of 46F +8C. The next FOTD will be posted in the near future. Until whenever, take care, and ask questions. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Julia_Intrusion { ; time=0:08:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-0.89492913214/+0.01017421388/579726/1/\ -80/0 params=0.8/-5.8/-0.8/-9.9/0/0/0/0 float=y maxiter=15000 inside=0 outside=tdis periodicity=6 colors=000QfNWcNa`OgYOmVPsSPyQPvONsMMpLLmJKjIJgGHd\ FGaDFZBEWADT8BQ7AN59K48H27E16J58N8ARBBVEDZHFbKGfNI\ jQKnTLoRJpPHpNFqLDrJBrH9sF7tD5tC4oG7jK9eNB`REWVGRY\ IcaKceNchPclRcoTclVciXcfYmnOmnPmnQmnQmnRmnSmoTmoTz\ oUzoVzoWzoWzpXzpYzpZzpZzp_zp`zqazqazqbzqczqdzqdFqe\ FrfErgErgDrhDriCrjCsjBskBslAsmAsm9sn9to8tp8tp7tq7t\ r6ts5ut6ts7tr7sq8sq8sp9roArnAqnBqmBqlCpkDpkDpjEoiE\ ohFnhGngGnfHmeHmeImdJlcJlbKkbKkaLk`Mj`Mj_NiZNiYOiY\ PhXPhWQhVQgVRgUSfTSfSTfSTeRUeQVePVdPWdOWcNXcMYcMYb\ LZbKehJbfK`dKZbKXaKV_KTYKRXKPVLNTLLRLJQLHOLFMLCKKD\ LLDLLDMMDMMDNNDNNDOODOODPPDPPDPQDQQDQRDRRDRSESSEST\ ETTETUEUUEUVEUVEVWEVWEWXEWXEXYEXYEYZEYZEYZFZ_FZ_F_\ `F_`F`aF`aFabFabFbcFbcFbdFcdFceFdeFdfGefGegGfgGfhG\ ghGgiGgiGhjGhjGikGikGjlGjlGkmGkmFmnGlmGlmGkmGkmHkm\ HjmHjmHjmHimIimIilIhlIhlIglJglJglJflJflKflKelKekKe\ kKdkLdkLckLckLckLbkMbkMbk } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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MFRX194h
by Albrecht 15 Nov '12

15 Nov '12

Hi, I?m presenting this image because it has a story. About 10 years ago, when I did not think about my multifractal project, I was experimenting and testing combinations of formulas. The results later partly went into the project. As I always was in a hurry the image was not finished and the experiments went on. Later, when I looked at it I saw that the Many-mods holes contained small fractal images which you could zoom into. But the data were lost and I couldn?t finish it, but always kept it. Just lately, cleaning up my working folder, I stumbled on some old experimental formulas, tested them and voila! one was the correct one. So here it is. Albrecht ----------------------------------start-par------------------------------- MFRX194h { ; An_early_Wonder ; Time 27.48 1600/1200 ; Multifrac_236 reset=2004 type=formula formulafile=mfr.frm formulaname=multifrac_236 ismand=y function=exp/exp/exp passes=t center-mag=-1.19904e-014/1.59872e-014/0.3704381 params=0.4546494949186682/-0.6008903775139622/384.\ 0001/256.512/2084.0008/768.256/768.1536/2560.1025/\ -4/2 float=y maxiter=2048 inside=maxiter outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=20009C<19>0bo0cq0es<3>0kz<25>09C08A068<2>02\ 2000211<22>keOmgPoiQqjRslSunT<2>zsX<25>CB7A96875<3\ >000400<23>o00q00s00<3>z00<25>C00A00800<3>000<23>e\ eegggiiijjjlllnnn<2>sss<18>NNNLLLJJJ<3>DDDCCCAAA<3\ >222000022<3>08A } frm:multifrac_236 { ; d=real(p2) fac1=trunc(d) b1=(d-fac1)*10000 ; d=imag(p2) mi1=trunc(d) p6r=trunc((d-out1)*10000) if (mi1<0) mi1=-mi1 endif ; d=real(p3) ba=trunc(d) p6i=trunc((d-ba)*10000) if (ba<0) ba=-ba endif p6=p6r,p6i ; d=imag(p3) fac2=trunc(d) b2=(d-fac2)*10000 ; d=real(p4) mi2=trunc(d) fac3=trunc((d-mi2)*10000) ; d=imag(p4) b3=trunc(d) mi3=trunc((d-b3)*10000) ; d=real(p5) vb=(d<0) If (vb) d=-d endif d1=trunc(d) d=trunc((d-d1)*100) ab1=(d==10)+(d==11) ab=(d==1)+(d==11) ir1=(d1>1000) d1=d1-1000*ir1 wo=(d1>100) d1=d1-100*wo tj=(d1<10) d1=d1-10*(tj==0) v1=(d1==3) v2=(d1==4) d1=(d1==2)+(d1==4) ; d=imag(p5) st=(d<0) if (st) d=-d endif d2=trunc(d) ab2=((d-d2)>0) ir2=(d2>1000) d2=d2-1000*ir2 ni=2*(d2>100) st=st*(ni==0) d2=d2-50*ni mj=(d2<10) d2=d2-10*(mj==0) v3=(d2==3) v4=(d2==4) d2=(d2==2)+(d2==4) d3=(ismand==0) t=0 u=1 bx=ba start=2-st-ni if (ismand) z=0 if (vb) c=0.4*log(sqr(pixel^p6i)) else c=pixel endif else c=p1 z=pixel endif : ba=bx if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) else z2=sin(z)+c sqz2=cos(z2) z=c*(1-sqz2)/(1+sqz2) ba=p6 endif else if (ab) q=sqr(z) z=real(q)+flip(real(z*q))+c else z=z*z+c endif endif bo=|z| If (wo) t=t+1 if ((t<mi1)+(bo>b1)) u=2*(fn1(t/fac1)) if (ismand) z=z*u c=pixel if (vb) c=0.4*log(sqr(pixel^p6i)) endif else z=pixel c=p1*u endif wo=0 if (ir1) t=0 endif endif else if (start) t=t+1 if (start==2) if ((t>mi2)+(bo>b2)) u=2*(fn2(t/fac2)) ab=ab1 if (d1) if (tj) z=pixel endif c=p1*u vb=v2 d3=vb else d3=0 z=z*u c=z if (mj) z=0 endif vb=v1 if (vb) p6=mi2,p6i c=0.4*log(sqr(pixel^p6i)) endif endif start=1 if (ir2) t=0 endif endif else if ((t>mi3)+(bo>b3)) u=2*(fn3(t/fac3)) ab=ab2 if (d2) if (tj) z=pixel endif c=p1*u vb=v4 d3=vb else d3=0 z=z*u c=z if (mj) z=0 endif vb=v3 if (vb) p6=mi3,p6i c=0.4*log(sqr(pixel^p6i)) endif endif start=0 endif endif endif endif bo<=ba } ------------------------------------------------end-------------------------------------------------------

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Alien Toy
by Albrecht 15 Nov '12

15 Nov '12

Hi, I got a present for you - a beautiful alien toy. Have fun playing and exploring! ----------------------start-par--------------------------------------------------------------- 16731x { ; Alien_Toy ; 0.11.71 1600/1200 ; sec-phoen-newt-bees-sec reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=0.0763248/-0.491648/16.48972/1.0471/-54\ .1932378046361691/-6.44479795856680848 params=-0.05825983458967864/0.3785210730307932/167\ 31.32595752213/25234.0311091622/151024.0204808192/\ 384.32768524288/384.00482000595/128.2007683001/256\ .2007683001/384.8007683001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=000000zr0zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>L\ Q8KM8KJ8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>\ qeBriAtm9vq8xu7zz5zz4zz3<4>zj4zg4zc4<3>zS5zP5zL6zI\ 6zE6wE6tD6<6>vAIv9Kv9M<3>x7Sy7Uy6Wz6Yz5_<3>f5Ma5IW\ 4E<2>_4H<3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>\ y0fz0gy0h<3>u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAA\ G7FO4KW0Qc<3>5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<\ 3>civflvinvlqvotvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa\ <3>8JP8FL8CI<3>SCCXCAaB9<3>uA2zA0xA0<12>SA1QA1NA1<\ 3>D92<6>UXAW`BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJo\ SFlWAi_5fc0ce7_jFRoNIzb0zj0 } frm:multifractal_10 { ; Albrecht Niekamp Jan2005 ; ;RealP2 Left: 5 Digits_Channels: (1)shape (2)outside (3)inside1 (4)inside2 (5)inside3 ; Frm: 0_off 1_Secant 2_Mand(2) 3_Bees 4_Jul 5_Mmods 6_Phoen 7_Newt 8_Spid ; Right: 2 Digits_ManyMods_Number of sides 2 Digits_Phoenix 2 Digits_Spider ; 1 Digit_ TransitionReset - Shape: 0_no 1_DbleMand 2_Iter-reset 3_both +5_warp ; 4 Digits_TransitionReset - Ch 2-5: 0_no 1_z-reset 2_Iter-reset 3_both +5_warp ;ImagP2 Left: 5 Digits_Bailout Number for Channels 1 to 5 ; Right: Variables: 4 Digits_Mand/Jul (2 var) 2 Digits_Secant 4 Digits_Bees ;RealP3 Left: 2 Digits_Newtonvariable 4 Digits_Colour1 ; Right: 5 Digits_Colour2 5 Digits_Colour3 ;ImagP3 Left: Shape: Warp-factor (fn1 is used) ; Right: 5 Digits_Colour4 6 Digits_Colour5 ;RealP4 Left: Outside: Warp-factor (fn2 is used) ; Right: Outside: 4 Digits+1fractal digit_Border-out 4 Digits+1 fractaldigit_border-in ;ImagP4 Left: Inside1_Maxiter ; Right: Inside1_Transition: 1_maxiter 2_borderout 3_borderin +5_maxiter+border ; 5 Digits_warp factor (fn2 is used) 4 Digits+1 fractaldigit_border1 ;RealP5 Left: Inside2_Maxiter ; Right: Inside2_Transition: 1_maxiter 2_borderout 3_borderin +5_maxiter+border ; 5 Digits_warp factor (fn3 is used) 4 Digits+1 fractaldigit_border2 ;ImagP5 Left: Inside3_Maxiter ; Right: Inside3_Transition: 1_maxiter 2_borderout 3_borderin +5_maxiter+border ; 5 Digits_Warp factor (fn4 is used) 4 Digits+1 fractaldigit_border3 ; Alternate : Left: 1_Lake effect enabled (Inside3 disabled) ; Right: 2 Digits_Frequency 2 Digits_Waterlevel 2 Digits_Amplitude ;fn(1) shared by many-mods+bees ; le=0 z=pixel da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+11111 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==4)+(d==5)+(d==8)+(d==9) d4=d3==0 vb=d>5 sc=d==2 mo=d==6 px=d==7 ab=px+(d==3)+(d==5)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>1 sc1=d==2 mo1=d==6 px1=d==7 v1m=mo1+px1 v1j=d>7 dd1=v1j+(d==4)+(d==5) ab1=px1+(d==3)+(d==5)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=d>1 sc2=d==2 mo2=d==6 px2=d==7 v2m=mo2+px2 v2j=d>7 dd2=v2j+(d==4)+(d==5) ab2=px2+(d==3)+(d==5)+(d==9) d=trunc(dd/10) ex3=d>1 sc3=d==2 mo3=d==6 px3=d==7 v3m=mo3+px3 v3j=d>7 dd3=v3j+(d==4)+(d==5) ab3=px3+(d==3)+(d==5)+(d==9) d=dd-d*10 ba=imag(p5) mi3=trunc(ba) dd=(d>1)+(mi3>1) ex4=dd==2 sc4=d==2 mo4=d==6 px4=d==7 v4m=mo4+px4 v4j=d>7 dd4=v4j+(d==4)+(d==5) ab4=px4+(d==3)+(d==5)+(d==9) ; mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 dm=(d==2)+(d==4) ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex1+ex0+ex2+ex3+ex4 ; d=real(p3) dd=trunc(d) da=(d-dd)*10000000000 pp=trunc(dd/10000) ba1=dd-10000*pp ba2=trunc(da/100000) ba3=da-100000*ba2 ; d=imag(p3) sfac=trunc(d) da=(d-sfac)*100000000000 ba4=trunc(da/1000000) ba5=da-ba4*1000000 ; d=real(p4) ofac=trunc(d) da=(d-ofac)*10000000000 bh=trunc(da/100000)/10 bl=(da-bh*1000000)/10 bs=bl/2 ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) da=round((d-dd)*10000000000) d=trunc(dd/10000) dd=dd-d*10000 bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/1000) dd=dd-d*1000 bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/100) dd=dd-d*100 bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/10) dd=dd-d*10 bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=round(dd) bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) ; d=da p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 dp=p6+p0/100 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=d==3 fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 ; d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=d==3 fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 ; if (mi3==1) d=(ba-mi3)*1000000 fr=round((trunc(d/10000))*10) ;lake effect by S.Gallet d=d-fr*1000 lv=(trunc(d/100))/100 d=d-lv*10000 am=d/100 u=real(rotskew*pi/180) t=exp(-flip(u)) bo=1/real(magxmag) q=bo/0.75*imag(magxmag) dd=tan(imag(rotskew*pi/180)) da=2*q*t rs=2*bo*(dd+flip(1))*t zz=center+(-q-bo*dd-flip(bo))*t z=z-zz d=imag(conj(da)*z)/imag(conj(da)*rs) le=d<=lv if (le) dd=lv-d z=z+2*dd*(1+am*sin(fr*dd^0.2))*rs endif z=z+zz else da=(ba-mi3)*100000000000 d=trunc(da/10000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=d==3 fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 endif ; if (vb) if (d3) if (ab) z=z*le+pixel*(le==0) ;Spider c=p1 else z=z*le+pixel*(le==0) c=p1 ;newton endif elseif (ab) c=z ;Phoenix z=z*le+pixel*(le==0) else c=0.4*log(sqr(z^mm)) ;many mods z=0 endif elseif (d3) if (ab) c=p1 ;Julia z=z*le+pixel*(le==0) else ;bees c=p1 z=z*le+pixel*(le==0) endif elseif (ab) c=z ;Mandel z=0 else c=z ;Secant z=z*le+pixel*(le==0) endif t=0 bo=|z| p=pp z0=p7 zold=(0.0,0.0) cb=p9 ba=bb0 : if (tt) t=t+1 if (ex0) ex0=t<mi1 if (bo>bs) u=2*(fn1(t/sfac)) ex0=0 if (ir0) t=0 endif if (d4) z=z*u if (mo) c=0.4*log(sqr(z^mm)) else c=pixel endif else z=z*le+pixel*(le==0) cb=p9*u c=p1*u p=pp*u endif tt=tt-1+ex0 endif elseif ((ex1)&&bo>bl) if (bo<bh) d3=dd1 ba=bb1 ab=ab1 ex1=0 tt=tt-1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif if (ir1) t=0 endif if (d3) vb=v1j if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif else vb=v1m if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo1) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) ab=ab2 d3=dd2 ba=bb2 ex2=0 tt=tt-1 if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif if (ir2) t=0 endif if (d3) vb=v2j if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v2m if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo2) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) ab=ab3 d3=dd3 ba=bb3 ex3=0 tt=tt-1 if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif if (ir3) t=0 endif if (d3) vb=v3j if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v3m if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) ab=ab4 d3=dd4 ba=bb4 ex4=0 tt=0 if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (d3) vb=v4j if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v4m if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo4) c=0.4*log(sqr(z^mm)) endif endif endif endif endif if (vb) if (d3) if (ab) z=z*z+c ;Spiderjul John Horner c=c*sp+z else z1=z^p-1 ;Quasinewton Puskas Istvan z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+0.56+ph/100-0.5*zold ;Phoenix Mike Wareman zold=z z=z1 else z2=fn1(z)+c ;Many_mods Linda Allison z1=cos(z2) z=c*(1-z1)/(1+z1) endif elseif (d3) if (ab) z2=z*z ;Julia Puskas Istvan z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb ;Bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) if (dm) z=z*z+c+c*c-dp ;Double Mandel else z2=z*z ;Mandel Puskas Istvan z=z2*z2+p6*z2+c-p0 endif else z3=z ;Secant Mike Wareman z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<ba } -------------------------------------------------------end---------------------------------------

1 0

FOTD 13-11-12 (Ghostly Intruder [6.5])
by Jim Muth 13 Nov '12

13 Nov '12

FOTD -- November 13, 2012 (Rating 6.5) Fractal visionaries and enthusiasts: Today's image in a perturbed Mandelbrot set has a blue wedge intruding into the background. At first, this wedge appears to be totally out of place, with no connection at all to the surface pattern, but if the parameters are changed to 0,0, the connection will become perfectly clear. I named the image "Ghostly Intruder" because of this mysterious brilliant blue wedge, which is actually the ghost of a valley of an everyday Mandelbrot bud. The rating of 6-1/2 indicates that the image, which was done in haste, leaves much to be desired. The calculation time of 15 seconds will pass in a flash, but the web sites are still less of a hassle. View the finished wonder-image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> And check the hi-def variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are available at: <http://www.Nahee.com/FOTD/> The overnight rain ended shortly after daybreak, leading to a partly cloudy day with a temperature of 46F +8C. Fractal cat Nicholas is eagerly awaiting the arrival of his new companion in a day or so. The next FOTD, maybe better, maybe worse, will be posted in the appropriate time. Until whenever, take care, and keep your cool. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Ghostly_Intruder { ; time=0:00:15.00 SF5 at 2000MHZ reset=2004 type=mandel center-mag=-0.7070327249/\ -0.2812099475/1318/1/-111.1/0 params=-0.45/0.27 float=y maxiter=32767 bailout=16 inside=0 logmap=17 periodicity=6 colors=00050Y60X70W80V90UA0TB0SC1RD2QE3PF4OG5KH6HI\ 7II8JI8KJ9KJ9LJ9MKANKANKAOLBPLBQLBQLCRMCSMCTMDTNDU\ NDVNEWOEWOEXOFYPFZPFZPG_PG`QGaQHaQHbRHcRIdRIdSIeSJ\ fSJgSJgTIhTIhUIhUHhUHhVHhVHiVGiWGiWGiWFiXFiXFjXFjY\ EjYEjYEjZDjZDkZDk_Dk_Ck`Ck`Ck`ClaBlaBlaBlbAlbAlbAm\ cAmc9mc9md9md8md8ne8ne8ne7nf7nf7ne6sf7ng7jg7fh8ai8\ Yi7Qi8Uh9XgA_fBbeCedEccGbbIaaK``LZ`MY`NX`OV`PW`QWa\ RXaSYaTZaUZaV_aW`aX`aYaaZbbYaaZbaZb`Zc`Zc_Zc__d__d\ Z_dZ_eY_eY`fX`fX`fX`gW`gW`gVahVahUaiUaiUaiTbjTbjSb\ jSbkSbkRclRclQclQcmPcmPcmPdnOdnOdoNdoNdoMepMepMepL\ eqLeqKfrKfrKfrJfsJfsIfsIgtHgtHguHguGmuGmvFmvFmvEmw\ EmwEmxDmxDmxCmyCmyCmyDmxDmwDmwDmvDrzDrzDrzDrzDrzDr\ zErzErzErzErzErzErzErzErzErzErzEzzFzzFzzFzzFzzFzzF\ zzFzzFzzFzzFzzFzzGzzGzzGzzGzzGzzGzzGzzGzzGzzGzzGzz\ HzzHzzHzzHzzHzzHzzHzzHzzHzzHzzHzzHzzHzzGzzGzzFzzFz\ zEzzEzzEzzDzzDzzCzzCzzBzz } END PARAMETER FILE=========================================

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Web Opposition
by Mike Frazier 13 Nov '12

13 Nov '12

This fractal makes a web in a very different way than the Web Rings fractal I posted previously. By pure chance, this fractal has an area with two closely spaced spirals that rotate in opposite directions. The opposite rotation seems to cause arms to connect the two spirals. I zoomed in using mostly trial and error to find this fractal. The last zoom was particularly surprising as it changed the rings into a mesh. The equation is: z = 1 / (1 / ((z ^ 3) * tan(z) + pixel + 1) + 1 / (z ^ 4 + pixel - 1)) Here is a link to an image: http://dl.dropbox.com/u/33642054/image/web_opposition_1200_5.jpg The Fractint compatible PAR file for the image is: Web_Opposition { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20121113_0951 passes=1 float=y center-mag=0.706758545849994/0.2398003577709398/15\ 686274705.88235/1/17/0 params=1/1/4/4/-1/0/1/0/0/0 maxiter=2000 inside=0 logmap=128 periodicity=6 colors=000JqzLqzNqzPrzRrzTszVszXszZtz`tzbuzduzfuzh\ vzjvzlwznwzpwzrxztxzvyzxyzzzzyzzxzzwzzuzztzzszzqzz\ pzzozzmzzlzzkzzizzhzzgzzgzzgzzgyyfyyfxyfxxexxewwew\ wevwdvvduvduucuuctucttbstbssbrsbrsarraqraqq`pq`pq`\ op_op_oo_no_noZmnZmnZlmYlmYlmYklXklXjkXjkXikWijWij\ WhiVhiVgiVghVfhUfgUfgUegTefTdfTdeSdeSceScdSbdRbcRa\ cRacQabQ`bQ`aP_aP_aPZ`PZ`OZ_OY_OY_NXZNXZNWYMWYMWYM\ VXMVXLUWLUWLTWKTVKTVKSUKSUJRUJRTJQTIQSIQSIPSHPRHOR\ HOQHNQGNQGNPGMPFMOFLOFLOELNEKNEKMEJMDJMDILDILCIKCH\ KCHKBGJBGJBFIBFIAFIAEHAEH9DG9DG9CG9CF8CF8BE8BE7AE7\ AD79D69C69C68C68B57B57A56A46A469459358348348337237\ 23622612611511500400401502603713814915A16A17B27C28\ D29E2AF3AG3BH3CH3DI3EJ4EK4FL4GM4HN5HN5IO5JP5KQ5LR6\ LS6MT6NU6OU7OV7PW7QX7RY7SZ8S_8T_8U`8Va9Vb9Wc9Xd9Ye\ 9ZfAZfA_gA`hAaiBajBbkBclBdlBemCenCfoCgpChqDhrDisDj\ sDktDluElvEmwEnxEoyFpzHpz } frm:F_20121113_0951 { ; Similar to the parallel resistance formula a=real(p1),b=real(p2)-1,d=imag(p1),f=imag(p2), z=0,c1=pixel-p3,c2=pixel-p4: z=1/(1/(a*(z^b)*tan(z)+c1)+1/(d*(z^f)+c2)), |z|<100 } -- Mike Frazier www.fracton.org

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Web Rings
by Mike Frazier 13 Nov '12

13 Nov '12

This fractal makes a web of interconnected rings. You can see the pattern I used to add the rings by zooming out. The technique is the same one that usually adds longer arms to a fractal. To perform the technique, you repeatedly zoom in on ever smaller self similar structures. In this fractal, each time you do that it adds one more ring. The equation is: z = 1 / (1 / ((z ^ 3) * sinh(z) + pixel + 1) + 1 / (z ^ 4 + pixel - 1)) Here is a link to an image: http://dl.dropbox.com/u/33642054/image/web_rings_1200_5.jpg The Fractint compatible PAR file for the image is: Web_Rings { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20121113_0850 passes=1 float=y center-mag=-2.730493261162895/-4.958068276404781e-\ 14/44444445000/1/0/0 params=1/1/4/4/-1/0/1/0/0/0 maxiter=2000 inside=0 periodicity=6 colors=000mnjjligihcgg`deYadU_cRXaOU`KS_HPYEMXAKW7\ HU4ET0BR3DS6GT9IUDLWGOXJQYNT_QW`TYaX`c_bdbeefhgijh\ lmippkpnipkgphepecpcap`_pYYoVWoTUoQSoNQoKOoIMoFKoC\ In9FnBGnEInGJnJLnLNnOOnRQoTSoWToYVo`XobYoe_phanjak\ lbincfpdcseasfZrgWriUqjRplOpmMooJopGnrEmsBmu8lv5kx\ 7kw9kvBluDltFmsHmrJnqLnpNnnPomRolTpkVpjXqiZqh`rgbr\ fesdcpeamfZjgXfiUcjS`kPXmNUnKRoIOpFKrDHsAEt8Av57w3\ 4x00z33y67x9AvCEuFHtILrLOqOSoRVnUZmXak_ejbhielghof\ lsdjqegofdmgajiZhjWfkTdmQanO_oLYqIWrFTsCRu9Pv6Nw3K\ y0Iz3Ky6Mx9OvCQuFTsIVrLXqOZoSanVclYek`gjcjhflginel\ pdtsiqphnlfkiehfcecbb`aZX_WUZTRYQOWNKVKHUHESEBRA8Q\ 85PA8QEBRHESKHUNKVQOWTRYWUZZX_b`aecbhfckienlfqphts\ iurhvpfwneylcyk`yjYxiVxhTxhQxgNwfKweHwdFvdCvc9vb6u\ a4vb6vc9vdCwdFweHwfKxgNxhQxhTxiVyjYyk`ylczlfzmiwmh\ tlfqlenkcliaif_fcXd`VaZTZWQWTOUQMRNJOLHMIFJFCGCAD9\ 7FB9IEBLHEPMJUSPZYUcb_hhd } frm:F_20121113_0850 { ; Similar to the parallel resistance formula a=real(p1),b=real(p2)-1,d=imag(p1),f=imag(p2), z=0,c1=pixel-p3,c2=pixel-p4: z=1/(1/(a*(z^b)*sinh(z)+c1)+1/(d*(z^f)+c2)), |z|<100 } -- Mike Frazier www.fracton.org

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Walk on the Wildside
by Albrecht 13 Nov '12

13 Nov '12

"Walk on the Wildside" sorry, once again as the links belonged to yesterdays image Hi, I hope Lou Reed doesn?t mind I use his songtitle. Music and images have so much in common that sometimes, after I?ve created a new one, just have to use a songtitle. Happened before (The Original Flying Machine) and will happen again. With this image I scratched a little bit deeper into the surface of my formula. Just a little bit, the variations are literally infinite, so I dont expect to loose inspiration. In the par-file you will see a different version of the formula with a "readable" input section, the disadvantage being that the lines are too long so you have to use a printout or a second screen. Hal?s link shows the regular version of the frm. Jim, you talked about lack of inspiration - how about some cooperation? After all it?s just the two of us - more or less - producing images for Fractint. It?s not necessary to create a new image from the scratch. Just zoom out and change the sequence of formulas in line 3 of the Z-screen. All images done with multifractal_10 have these 5 numbers in the title. Secondly the reset commands after the dot. The first six numbers are the variables ( two each) for many-mods, phoenix and spider. The last five are the reset commands for each section - shape, outside, inside 1-3. Each modification will produce a different image, reset changes only of they are "active". With Hal?s link you get a full HD version (1600/1200) instantly. Watching the image first time was something of a shock as the structures are new and extraordinary. How about you? . http://www.emarketingiseasy.com/Albrecht/13657D.PAR http://www.emarketingiseasy.com/Albrecht/13657D.GIF -----------------------------------start-par--------------------------------------------- 13657d { ; Walk-on-the-Wildside ; 0.15.32 1600/1200 ; sec-bees-phoen-mmods-newt reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=0.28279/-5.57193e-015/26.88172/1/-90/-1\ .23373533611470521e-014 params=-0.05825983458967864/0.3785210730307932/136\ 57.64595701112/14235.4911030602/152048.0404808048/\ 384.1604894048/384.00482000595/128.1007683001/256.\ 1007683001/384.1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=0003J83G64D3<17>kkammcpoe<3>zwm<6>cYO`UKYQG\ <3>KA0000<43>000<4>000330<11>110110110<3>000KA4<7>\ gcOjgRmjT<3>zzc<9>UOFRKDOGA<3>A00<9>f0Ci0Dl0F<3>z0\ K<6>Z0EV0DR0C<3>A08004000<26>000<4>000<9>X0a_0dc0h\ <3>p0w<4>_0dX0aU0Y<2>K0NH0JG0NE1R<3>7UX6`Z4h_2oa0w\ c<14>3LA } frm:multifractal_10 { ; Albrecht Niekamp Jan2005 ; ;RealP2 Left: 5 Digits_Channels: (1)shape (2)outside (3)inside1 (4)inside2 (5)inside3 ; Frm: 0_off 1_Secant 2_Mand(2) 3_Bees 4_Jul 5_Mmods 6_Phoen 7_Newt 8_Spid ; Right: 2 Digits_ManyMods_Number of sides 2 Digits_Phoenix 2 Digits_Spider ; 1 Digit_ TransitionReset - Shape: 0_no 1_DbleMand 2_Iter-reset 3_both +5_warp ; 4 Digits_TransitionReset - Ch 2-5: 0_no 1_z-reset 2_Iter-reset 3_both +5_warp ;ImagP2 Left: 5 Digits_Bailout Number for Channels 1 to 5 ; Right: Variables: 4 Digits_Mand/Jul (2 var) 2 Digits_Secant 4 Digits_Bees ;RealP3 Left: 2 Digits_Newtonvariable 4 Digits_Colour1 ; Right: 5 Digits_Colour2 5 Digits_Colour3 ;ImagP3 Left: Shape: Warp-factor (fn1 is used) ; Right: 5 Digits_Colour4 6 Digits_Colour5 ;RealP4 Left: Outside: Warp-factor (fn2 is used) ; Right: Outside: 4 Digits+1fractal digit_Border-out 4 Digits+1 fractaldigit_border-in ;ImagP4 Left: Inside1_Maxiter ; Right: Inside1_Transition: 1_maxiter 2_borderout 3_borderin +5_maxiter+border ; 5 Digits_warp factor (fn2 is used) 4 Digits+1 fractaldigit_border1 ;RealP5 Left: Inside2_Maxiter ; Right: Inside2_Transition: 1_maxiter 2_borderout 3_borderin +5_maxiter+border ; 5 Digits_warp factor (fn3 is used) 4 Digits+1 fractaldigit_border2 ;ImagP5 Left: Inside3_Maxiter ; Right: Inside3_Transition: 1_maxiter 2_borderout 3_borderin +5_maxiter+border ; 5 Digits_Warp factor (fn4 is used) 4 Digits+1 fractaldigit_border3 ; Alternate : Left: 1_Lake effect enabled (Inside3 disabled) ; Right: 2 Digits_Frequency 2 Digits_Waterlevel 2 Digits_Amplitude ;fn(1) shared by many-mods+bees ; le=0 z=pixel da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+11111 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==4)+(d==5)+(d==8)+(d==9) d4=d3==0 vb=d>5 sc=d==2 mo=d==6 px=d==7 ab=px+(d==3)+(d==5)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>1 sc1=d==2 mo1=d==6 px1=d==7 v1m=mo1+px1 v1j=d>7 dd1=v1j+(d==4)+(d==5) ab1=px1+(d==3)+(d==5)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=d>1 sc2=d==2 mo2=d==6 px2=d==7 v2m=mo2+px2 v2j=d>7 dd2=v2j+(d==4)+(d==5) ab2=px2+(d==3)+(d==5)+(d==9) d=trunc(dd/10) ex3=d>1 sc3=d==2 mo3=d==6 px3=d==7 v3m=mo3+px3 v3j=d>7 dd3=v3j+(d==4)+(d==5) ab3=px3+(d==3)+(d==5)+(d==9) d=dd-d*10 ba=imag(p5) mi3=trunc(ba) dd=(d>1)+(mi3>1) ex4=dd==2 sc4=d==2 mo4=d==6 px4=d==7 v4m=mo4+px4 v4j=d>7 dd4=v4j+(d==4)+(d==5) ab4=px4+(d==3)+(d==5)+(d==9) ; mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 dm=(d==2)+(d==4) ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex1+ex0+ex2+ex3+ex4 ; d=real(p3) dd=trunc(d) da=(d-dd)*10000000000 pp=trunc(dd/10000) ba1=dd-10000*pp ba2=trunc(da/100000) ba3=da-100000*ba2 ; d=imag(p3) sfac=trunc(d) da=(d-sfac)*100000000000 ba4=trunc(da/1000000) ba5=da-ba4*1000000 ; d=real(p4) ofac=trunc(d) da=(d-ofac)*10000000000 bh=trunc(da/100000)/10 bl=(da-bh*1000000)/10 bs=bl/2 ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) da=round((d-dd)*10000000000) d=trunc(dd/10000) dd=dd-d*10000 bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/1000) dd=dd-d*1000 bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/100) dd=dd-d*100 bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/10) dd=dd-d*10 bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=round(dd) bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) ; d=da p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 dp=p6+p0/100 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=d==3 fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 ; d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=d==3 fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 ; if (mi3==1) d=(ba-mi3)*1000000 fr=round((trunc(d/10000))*10) ;lake effect by S.Gallet d=d-fr*1000 lv=(trunc(d/100))/100 d=d-lv*10000 am=d/100 u=real(rotskew*pi/180) t=exp(-flip(u)) bo=1/real(magxmag) q=bo/0.75*imag(magxmag) dd=tan(imag(rotskew*pi/180)) da=2*q*t rs=2*bo*(dd+flip(1))*t zz=center+(-q-bo*dd-flip(bo))*t z=z-zz d=imag(conj(da)*z)/imag(conj(da)*rs) le=d<=lv if (le) dd=lv-d z=z+2*dd*(1+am*sin(fr*dd^0.2))*rs endif z=z+zz else da=(ba-mi3)*100000000000 d=trunc(da/10000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=d==3 fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 endif ; if (vb) if (d3) if (ab) z=z*le+pixel*(le==0) ;Spider c=p1 else z=z*le+pixel*(le==0) c=p1 ;newton endif elseif (ab) c=z ;Phoenix z=z*le+pixel*(le==0) else c=0.4*log(sqr(z^mm)) ;many mods z=0 endif elseif (d3) if (ab) c=p1 ;Julia z=z*le+pixel*(le==0) else ;bees c=p1 z=z*le+pixel*(le==0) endif elseif (ab) c=z ;Mandel z=0 else c=z ;Secant z=z*le+pixel*(le==0) endif t=0 bo=|z| p=pp z0=p7 zold=(0.0,0.0) cb=p9 ba=bb0 : if (tt) t=t+1 if (ex0) ex0=t<mi1 if (bo>bs) u=2*(fn1(t/sfac)) ex0=0 if (ir0) t=0 endif if (d4) z=z*u if (mo) c=0.4*log(sqr(z^mm)) else c=pixel endif else z=z*le+pixel*(le==0) cb=p9*u c=p1*u p=pp*u endif tt=tt-1+ex0 endif elseif ((ex1)&&bo>bl) if (bo<bh) d3=dd1 ba=bb1 ab=ab1 ex1=0 tt=tt-1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif if (ir1) t=0 endif if (d3) vb=v1j if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif else vb=v1m if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo1) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) ab=ab2 d3=dd2 ba=bb2 ex2=0 tt=tt-1 if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif if (ir2) t=0 endif if (d3) vb=v2j if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v2m if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo2) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) ab=ab3 d3=dd3 ba=bb3 ex3=0 tt=tt-1 if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif if (ir3) t=0 endif if (d3) vb=v3j if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v3m if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) ab=ab4 d3=dd4 ba=bb4 ex4=0 tt=0 if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (d3) vb=v4j if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v4m if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo4) c=0.4*log(sqr(z^mm)) endif endif endif endif endif if (vb) if (d3) if (ab) z=z*z+c ;Spiderjul John Horner c=c*sp+z else z1=z^p-1 ;Quasinewton Puskas Istvan z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+0.56+ph/100-0.5*zold ;Phoenix Mike Wareman zold=z z=z1 else z2=fn1(z)+c ;Many_mods Linda Allison z1=cos(z2) z=c*(1-z1)/(1+z1) endif elseif (d3) if (ab) z2=z*z ;Julia Puskas Istvan z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb ;Bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) if (dm) z=z*z+c+c*c-dp ;Double Mandel else z2=z*z ;Mandel Puskas Istvan z=z2*z2+p6*z2+c-p0 endif else z3=z ;Secant Mike Wareman z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<ba } ---------------------------------------------------------end----------------------------

1 0

Walk on the Wildside
by Albrecht 13 Nov '12

13 Nov '12

"Walk on the Wildside" Hi, I hope Lou Reed doesn?t mind I use his songtitle. Music and images have so much in common that sometimes, after I?ve created a new one, just have to use a songtitle. Happened before (The Original Flying Machine) and will happen again. With this image I scratched a little bit deeper into the surface of my formula. Just a little bit, the variations are literally infinite, so I dont expect to loose inspiration. In the par-file you will see a different version of the formula with a "readable" input section, the disadvantage being that the lines are too long so you have to use a printout or a second screen. Hal?s link shows the regular version of the frm. Jim, you talked about lack of inspiration - how about some cooperation? After all it?s just the two of us - more or less - producing images for Fractint. It?s not necessary to create a new image from the scratch. Just zoom out and change the sequence of formulas in line 3 of the Z-screen. All images done with multifractal_10 have these 5 numbers in the title. Secondly the reset commands after the dot. The first six numbers are the variables ( two each) for many-mods, phoenix and spider. The last five are the reset commands for each section - shape, outside, inside 1-3. Each modification will produce a different image, reset changes only of they are "active". With Hal?s link you get a full HD version (1600/1200) instantly. Watching the image first time was something of a shock as the structures are new and extraordinary. How about you? http://www.emarketingiseasy.com/Albrecht/20105A.PAR http://www.emarketingiseasy.com/Albrecht/20105A.GIF -----------------------------------start-par--------------------------------------------- 13657d { ; Walk-on-the-Wildside ; 0.15.32 1600/1200 ; sec-bees-phoen-mmods-newt reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=0.28279/-5.57193e-015/26.88172/1/-90/-1\ .23373533611470521e-014 params=-0.05825983458967864/0.3785210730307932/136\ 57.64595701112/14235.4911030602/152048.0404808048/\ 384.1604894048/384.00482000595/128.1007683001/256.\ 1007683001/384.1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=0003J83G64D3<17>kkammcpoe<3>zwm<6>cYO`UKYQG\ <3>KA0000<43>000<4>000330<11>110110110<3>000KA4<7>\ gcOjgRmjT<3>zzc<9>UOFRKDOGA<3>A00<9>f0Ci0Dl0F<3>z0\ K<6>Z0EV0DR0C<3>A08004000<26>000<4>000<9>X0a_0dc0h\ <3>p0w<4>_0dX0aU0Y<2>K0NH0JG0NE1R<3>7UX6`Z4h_2oa0w\ c<14>3LA } frm:multifractal_10 { ; Albrecht Niekamp Jan2005 ; ;RealP2 Left: 5 Digits_Channels: (1)shape (2)outside (3)inside1 (4)inside2 (5)inside3 ; Frm: 0_off 1_Secant 2_Mand(2) 3_Bees 4_Jul 5_Mmods 6_Phoen 7_Newt 8_Spid ; Right: 2 Digits_ManyMods_Number of sides 2 Digits_Phoenix 2 Digits_Spider ; 1 Digit_ TransitionReset - Shape: 0_no 1_DbleMand 2_Iter-reset 3_both +5_warp ; 4 Digits_TransitionReset - Ch 2-5: 0_no 1_z-reset 2_Iter-reset 3_both +5_warp ;ImagP2 Left: 5 Digits_Bailout Number for Channels 1 to 5 ; Right: Variables: 4 Digits_Mand/Jul (2 var) 2 Digits_Secant 4 Digits_Bees ;RealP3 Left: 2 Digits_Newtonvariable 4 Digits_Colour1 ; Right: 5 Digits_Colour2 5 Digits_Colour3 ;ImagP3 Left: Shape: Warp-factor (fn1 is used) ; Right: 5 Digits_Colour4 6 Digits_Colour5 ;RealP4 Left: Outside: Warp-factor (fn2 is used) ; Right: Outside: 4 Digits+1fractal digit_Border-out 4 Digits+1 fractaldigit_border-in ;ImagP4 Left: Inside1_Maxiter ; Right: Inside1_Transition: 1_maxiter 2_borderout 3_borderin +5_maxiter+border ; 5 Digits_warp factor (fn2 is used) 4 Digits+1 fractaldigit_border1 ;RealP5 Left: Inside2_Maxiter ; Right: Inside2_Transition: 1_maxiter 2_borderout 3_borderin +5_maxiter+border ; 5 Digits_warp factor (fn3 is used) 4 Digits+1 fractaldigit_border2 ;ImagP5 Left: Inside3_Maxiter ; Right: Inside3_Transition: 1_maxiter 2_borderout 3_borderin +5_maxiter+border ; 5 Digits_Warp factor (fn4 is used) 4 Digits+1 fractaldigit_border3 ; Alternate : Left: 1_Lake effect enabled (Inside3 disabled) ; Right: 2 Digits_Frequency 2 Digits_Waterlevel 2 Digits_Amplitude ;fn(1) shared by many-mods+bees ; le=0 z=pixel da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+11111 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==4)+(d==5)+(d==8)+(d==9) d4=d3==0 vb=d>5 sc=d==2 mo=d==6 px=d==7 ab=px+(d==3)+(d==5)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>1 sc1=d==2 mo1=d==6 px1=d==7 v1m=mo1+px1 v1j=d>7 dd1=v1j+(d==4)+(d==5) ab1=px1+(d==3)+(d==5)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=d>1 sc2=d==2 mo2=d==6 px2=d==7 v2m=mo2+px2 v2j=d>7 dd2=v2j+(d==4)+(d==5) ab2=px2+(d==3)+(d==5)+(d==9) d=trunc(dd/10) ex3=d>1 sc3=d==2 mo3=d==6 px3=d==7 v3m=mo3+px3 v3j=d>7 dd3=v3j+(d==4)+(d==5) ab3=px3+(d==3)+(d==5)+(d==9) d=dd-d*10 ba=imag(p5) mi3=trunc(ba) dd=(d>1)+(mi3>1) ex4=dd==2 sc4=d==2 mo4=d==6 px4=d==7 v4m=mo4+px4 v4j=d>7 dd4=v4j+(d==4)+(d==5) ab4=px4+(d==3)+(d==5)+(d==9) ; mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 dm=(d==2)+(d==4) ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex1+ex0+ex2+ex3+ex4 ; d=real(p3) dd=trunc(d) da=(d-dd)*10000000000 pp=trunc(dd/10000) ba1=dd-10000*pp ba2=trunc(da/100000) ba3=da-100000*ba2 ; d=imag(p3) sfac=trunc(d) da=(d-sfac)*100000000000 ba4=trunc(da/1000000) ba5=da-ba4*1000000 ; d=real(p4) ofac=trunc(d) da=(d-ofac)*10000000000 bh=trunc(da/100000)/10 bl=(da-bh*1000000)/10 bs=bl/2 ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) da=round((d-dd)*10000000000) d=trunc(dd/10000) dd=dd-d*10000 bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/1000) dd=dd-d*1000 bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/100) dd=dd-d*100 bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/10) dd=dd-d*10 bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=round(dd) bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) ; d=da p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 dp=p6+p0/100 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=d==3 fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 ; d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=d==3 fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 ; if (mi3==1) d=(ba-mi3)*1000000 fr=round((trunc(d/10000))*10) ;lake effect by S.Gallet d=d-fr*1000 lv=(trunc(d/100))/100 d=d-lv*10000 am=d/100 u=real(rotskew*pi/180) t=exp(-flip(u)) bo=1/real(magxmag) q=bo/0.75*imag(magxmag) dd=tan(imag(rotskew*pi/180)) da=2*q*t rs=2*bo*(dd+flip(1))*t zz=center+(-q-bo*dd-flip(bo))*t z=z-zz d=imag(conj(da)*z)/imag(conj(da)*rs) le=d<=lv if (le) dd=lv-d z=z+2*dd*(1+am*sin(fr*dd^0.2))*rs endif z=z+zz else da=(ba-mi3)*100000000000 d=trunc(da/10000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=d==3 fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 endif ; if (vb) if (d3) if (ab) z=z*le+pixel*(le==0) ;Spider c=p1 else z=z*le+pixel*(le==0) c=p1 ;newton endif elseif (ab) c=z ;Phoenix z=z*le+pixel*(le==0) else c=0.4*log(sqr(z^mm)) ;many mods z=0 endif elseif (d3) if (ab) c=p1 ;Julia z=z*le+pixel*(le==0) else ;bees c=p1 z=z*le+pixel*(le==0) endif elseif (ab) c=z ;Mandel z=0 else c=z ;Secant z=z*le+pixel*(le==0) endif t=0 bo=|z| p=pp z0=p7 zold=(0.0,0.0) cb=p9 ba=bb0 : if (tt) t=t+1 if (ex0) ex0=t<mi1 if (bo>bs) u=2*(fn1(t/sfac)) ex0=0 if (ir0) t=0 endif if (d4) z=z*u if (mo) c=0.4*log(sqr(z^mm)) else c=pixel endif else z=z*le+pixel*(le==0) cb=p9*u c=p1*u p=pp*u endif tt=tt-1+ex0 endif elseif ((ex1)&&bo>bl) if (bo<bh) d3=dd1 ba=bb1 ab=ab1 ex1=0 tt=tt-1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif if (ir1) t=0 endif if (d3) vb=v1j if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif else vb=v1m if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo1) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) ab=ab2 d3=dd2 ba=bb2 ex2=0 tt=tt-1 if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif if (ir2) t=0 endif if (d3) vb=v2j if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v2m if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo2) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) ab=ab3 d3=dd3 ba=bb3 ex3=0 tt=tt-1 if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif if (ir3) t=0 endif if (d3) vb=v3j if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v3m if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) ab=ab4 d3=dd4 ba=bb4 ex4=0 tt=0 if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (d3) vb=v4j if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v4m if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo4) c=0.4*log(sqr(z^mm)) endif endif endif endif endif if (vb) if (d3) if (ab) z=z*z+c ;Spiderjul John Horner c=c*sp+z else z1=z^p-1 ;Quasinewton Puskas Istvan z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+0.56+ph/100-0.5*zold ;Phoenix Mike Wareman zold=z z=z1 else z2=fn1(z)+c ;Many_mods Linda Allison z1=cos(z2) z=c*(1-z1)/(1+z1) endif elseif (d3) if (ab) z2=z*z ;Julia Puskas Istvan z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb ;Bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) if (dm) z=z*z+c+c*c-dp ;Double Mandel else z2=z*z ;Mandel Puskas Istvan z=z2*z2+p6*z2+c-p0 endif else z3=z ;Secant Mike Wareman z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<ba } ---------------------------------------------------------end----------------------------

1 0

FOTD 12-11-12 (Root of Epsilon [5])
by Jim Muth 13 Nov '12

13 Nov '12

FOTD -- November 12, 2012 (Rating 5) Fractal visionaries and enthusiasts: Today's image is one of the sights we discover on a journey into the parent Z^(1.64872)+C Mandeloid as it appears 130 levels down the infinite hyperladder. This parent is a near-symmetrical oval-shaped main bay with two large irregular buds, one on the north and one on the south shore lines. The image for today lies in the debris field on the northwest shore line of the main bay. The name "Root of Epsilon" refers to the exponent of Z, which by some strange twist of fate is the square root of 'epsilon'. The rating of 5 is not much. I admit the lack, but the calculation time of 1-1/3 minute is not much of a wait either. And the web sites can cut down even this brief wait. The finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> High-definition variations are online at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are available at: <http://www.Nahee.com/FOTD/> Too many clouds spoiled the temperature of 66F 19C here at Fractal Central today. The next FOTD will be posted within a day or so. Until next time, take care, and grow with the times. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Root_of_Epsilon { ; time=0:01:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-0.489177619169/+0.70722309564/8645276 params=1.64872/0/-130/0 float=y maxiter=3600 inside=0 logmap=107 periodicity=6 colors=000EVbAVe7Uf4VdJWbXX`_YZXYXUYVKYTAYR7YP7YN7\ `R7bV7dZ7baVWfQP`LJVHDPC7J81EB3HD5KF7NI9QKBTMDWOFZ\ RH`TJcVLfXNi_PlaRocTreVthXkkYbm_Vp`MraEtcFveFzgGmi\ GciHUfHKcHDcJNcKXcLfcMpcNyoOynPymPymPylPylQykQykQy\ jQyjUxicwimvirvjvukztlztmzsozrpzrrzqrzprzpnzqkzrla\ rnZsoWtqTtrQutNvuKvwHwxEwyBnlPe`bYPpTMdOKTJHHFF5LK\ 7QO8VSA_WBe_DjcEogGtkHyoIvmKtlMqjNoiPlgQjfSgdUecVb\ aX``YYZ_WYaTWbRVdPUeSTaVSYYRU`QQcPNfOJiNFlMBoL7qL4\ jN3cP3XR3RS3KU3DW36Y30Z3ApGCqJEqMGqOIqRKqUMqWOqZQq\ `SqcUqfWqhYqk_qmZomZmmYlmYjmYhmXgmXemXdmWbmW`mV_mV\ YmVWmUYmUZmUZmTZkTaiTcgTceSccScaSc_SmYSmWTmUUmTVmS\ WmQWmPXmOYnMZmLZmK0mw6msBmoGmlLmhQzeVza_zYdzVizRcz\ OczKczHczEczCcz9cz7cz4cz2cz6czAczDczHczKczOczRczVs\ zZtzatzeuzhuzlvzovzsvzvozphzjzzdzzZzzTzzNzzHzzBzz6\ zzDzzJzzPzzVzz`zzfzzlzzgzzbzzZzzUzzPzzLzzGzzBzz7zz\ BzzEzzHzzKzzNzzQzzUzzXzz_ } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

1 0

Birds in the Sun
by Albrecht 12 Nov '12

12 Nov '12

Hi, as you can guess from the title this is an image in "natural" colours. Nothing spectacular, but beautiful if you ask me. If you cannot generate it or want to avoid the 16min it needs you can get it from Hal?s homepage: http://www.emarketingiseasy.com/Albrecht/20105A.PAR http://www.emarketingiseasy.com/Albrecht/20105A.GIF. The par-file also contains the frm. As more users now have the possibility to watch the multifractal images, thanks to Hal, I?d be happy to get some feedback. . Albrecht --------------------------------start-par-------------------------------------------- 20105A { ;Birds_in_the_Sun ; mandel-secant-mmods ; Time 0.15.16 1600/1200 reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=cos/exp/exp/sin passes=t center-mag=-1.30865464456818600/+0.000023479072921\ 85/243.5358/1.1324/-90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/201\ 05.03564960102/25234.2207090221/151024.0204808192/\ 384.32768524288/384.00482000595/128.1007683001/256\ .1007683001/256.2007683001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=n0B00z<78>vv4ww3ww2<2>zz0zz0zy0<77>z40z30z2\ 0<3>y01y01x02<3>u05u06t06<8>l0Ek0Fj0G<57>50u40v30w\ <3>00z000 } -------------------------------------------end---------------------------------------------

1 0

Buried in the "Dust of Time"
by Albrecht 12 Nov '12

12 Nov '12

Hi, the image is available in full HD 1600/1200 on Hal?s homepage. http://www.emarketingiseasy.com/Albrecht/55555K.gif Maybe, after a second look you?ll like it. Thank you, Hal! Albrecht

1 0

FOTD 11-11-12 (FOTD for Nov-11 [5])
by Jim Muth 11 Nov '12

11 Nov '12

FOTD -- November 11, 2012 (Rating 5) Fractal visionaries and enthusiasts: Today's image rates a 5. It is one that would normally be discarded, but I made it FOTD for today because I have decided to show the fractals that usually head straight for the trash can. I also have a serious case of fractalist's block. The parent fractal is the same shapeless one that gave us yesterday's image. The scene lies in the same general area as yesterday's image. The central minibrot appears split directly down the middle. The name "FOTD for Nov-11" simply states a fact. The calculation time of 1-1/4 minutes is brief enough to bring no impatience, yet slow enough to let a bit of anticipation build. The finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> High-definition variations are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are online at: <http://www.Nahee.com/FOTD/> Near perfect Autumn weather prevailed here at Fractal Central today, with cloudless skies, light breezes and a temperature of 61F 165C. The next fractional fractal will be posted before long, very likely in 24 hours. Until whenever, take care. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= FOTD_for_Nov-11 { ; time=0:01:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=mandelbrotbc3 function=ident center-mag=-1.227133792556/+0.007005797985/2555911 params=2.236/0/4/0 float=y maxiter=2700 inside=0 logmap=-132 periodicity=6 colors=000OJSLTaJbjlbpfVe`NWVFMP8CS9GVAKXAN_BRaBVd\ CYfCaiDdkDhnElpEosFsuFvrEspEpnDmlDjjCghCdfBacBZaAW\ _ATY9QW9NU8KS8IODFLICHNAES7AX47a2Bc7FdBJeFNfKRgOVh\ SYiXaj`ekdilimmmqnqtouolskjqggocem_clW`jRZhNWfJUeF\ ScBPa7N_3LZ4NY4PX4RW4TW4VV4XU4ZU5`T5bS5dR5fR5hQ5jP\ 5kP9bRDUSHLULCVP4WR3TS3RT3PU3NV3LX3JY3HZ3F_3D`3BbE\ CdOCfYDhgDjqDf`KbKQZ3WZ4UZ5SZ6RZ7PZ8OZ9MZALZBJZCHZ\ DGZEEZFDZGBZHAXKCWNEVQFUTHTWIRYKQ`LPcNOfONiQMkRLgU\ LdWK`ZKY`KVcJReJOhJLjIHmIEoZMaZNaZN`ZO`ZO__P__P__Q\ Z_QZ_QY_RY_RX_SX_SW_TW_TW_UV_UV`VU`VU`VT`WT`WS`XS`\ XS`YR`YR`ZQ`ZQ`_P`_PXZMZ_O`_Pb`Rd`SfaThaVjbWlbYncZ\ pc_rdatdbwcbvdcudctecsecrfcqfcpgcogcnhcmhclickicjj\ cijdhkdgkdfldelddmddmdcndbndaod`od_pdZpdYqeXqeWreV\ reUseTseSteRteQuePueOveNveMwfNveOueOtdPsdPsdQrcQqc\ RpcSpbSobTnbTmaUmaUl`Vk`Vj`Wj_Xi_Xh_YgZYgZZfZZeY_d\ Y_dX`cXabXaaWbaWb`Wc_VcZV } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

1 0

FOTD 10-11-12 (Split Opinion [6])
by Jim Muth 10 Nov '12

10 Nov '12

FOTD -- November 10, 2012 (Rating 6) Fractal visionaries and enthusiasts: Today's image shows another image in a fractional fractal. The fractional exponent of the image is 2.236, which, not accidental- ly, is the square root of 5. This expression was calculated 4 levels up the hyperladder with no function applied. The parent fractal produced by this operation is little more than a shapeless blob with a prominent split along the X-axis. But some distance west of the main mass, just north of the X-axis, lies a totally cut-off minibrot. Today's scene lies in an East-type valley of this minibrot. The rating of 6 indicates that inspiration for the fractal was lacking. The name "Split Opinion" points to the split along the X-axis. The relatively fast calculation time of 1-1/2 minutes assures that not too much time will have been wasted if the image fails to satisfy. Check the finished image at: <http://www.crosscanpuzzles.com/Archives.html> and high-definition variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are online at: <http://www.Nahee.com/FOTD/> Light rain ruled the early morning here atF.C., while clouds ruled the rest of the day. The light winds and temperature of 55F 13C made the day seem quite comfortable however. The next FOTD will be posted before too long. Until whenever, take care, and my current dis-spirited attitude is not connected to the outcome of the recent election. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Split_Opinion { ; time=0:01:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident center-mag=-1.28787966181/+0.043392037384/2.52e+007 params=2.236/0/4/0 float=y maxiter=3600 inside=0 logmap=224 periodicity=6 mathtolerance=0.05/1 colors=00050X61Y82_93aA4cB5eC6gG7iJ7kN8kQ8lT8lX9m_\ 9mcAnfAniAomBopBpsBptGmuLjuQhvUewZcwc`xhZylWyqUzvR\ zzPvxOswOpvOmtOisOfrNcpN`oNXnNUlNRkMOjMKhMHgMEfMBe\ MFaPJZSNVVRSYVO`ZLcbHffEijAln7or3ru0tr3sp6sn8slBsj\ EshGsfJsdLsbOs`RsZTsXWsVYsQShLNYGINBDC6818A2AC3CE4\ EF5GH6HJ7JL8LM9NOAPQBRSCSTDRTEPTFOTGMSILSJKSKISLHR\ NFROERPDRQFPRGNRIMRJKSLISMHSOFTPETRCTSAUU9UV7UX5VY\ 4V_2V`1Vmzeivbfr_cnY`jVYfSVbQSZNPVLLRI020INFFJDCFA\ 9B7675332gxScsQ`oOYjMVfKSbIPYGMUEIQCFLACH89D668434\ 298v87q76l66g65b54Y44T33O32J22E119004TAZP8UL7QI6LE\ 5HA3D7283142ZN1WL1TJ1QH1OF1LE1IC0GA0D80A7085053021\ OL2MJ1LI1JH1IF1GE1FD1DB1CA1A90970760650430320110qg\ tjalcXeXRZRMSKGLDBE657xs3so2ok2kg2gd2cc2vcEucEtcEr\ cEqcEpmEomEmmDlmDkmDjmDhmDgmDfzDezDczCazC_zCYzBWzB\ VzBmzAmzAmzAmz9mz9mz9mz8mz8zz8zz8zzLzzXzzYzzYzzYzz\ XzzXzzXzzXzzXzzXzzZzz_zz` } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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Four By Four
by Mike Frazier 10 Nov '12

10 Nov '12

This fractal has a lot of four way symmetry which gives it the name Four By Four. I found it by zooming into a four way symmetry in a tiny disconnected fragment of the parent fractal. It is interesting that this formula often generates minibrots in disconnected fragments. The equation is: z = 1 / (1 / ((z ^ 3) * (exp(z) - 1) + pixel + 1) + 1 / (z ^ 4 + pixel - 1)) Here is a link to an image: http://dl.dropbox.com/u/33642054/image/four_by_four_1200_5.jpg The PAR file for the image is: Four_By_Four { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20121110_1031 passes=1 float=y center-mag=-3.543046540411976/-1.700151082216331e-\ 15/410256415384.6154/1/0/0 params=1/1/4/4/-1/0/1/0/0/0 maxiter=2000 inside=0 logmap=12 periodicity=6 colors=000640C80IC0OG0UK0ZO0cS0hW0lZ0ob0sf0uj0xn0y\ r0zv0zz0zv0yr0xn0uj0sf0ob0lZ0hW0cS0ZO0UK0OG0IC0C80\ 640000000630C60I90OC1UF1ZI2cL3hO4lR5oU7sX8u_9xbBye\ CzhEzjFzhEyeCxbBu_9sX8oU7lR5hO4cL3ZI2UF1OC1I90C606\ 30000000620C40I61O82UA3ZC5cE7hG9lIBoKEsMGuOJxQMySP\ zUSzVVzUSySPxQMuOJsMGoKElIBhG9cE7ZC5UA3O82I61C4062\ 0000000610C21I31O43U55Z67c7Ah8Dl9HoALsBOuCTxDXyEaz\ FfzGjzFfyEaxDXuCTsBOoALl9Hh8Dc7AZ67U55O43I31C21610\ 000000500901E02I04M07Q0AU0EY0I`0Mb0Se0Wg0ai0gj0mj0\ tk0yj0tj0mi0gg0ae0Wb0S`0MY0IU0EQ0AM07I04E029015000\ 00000300601901C03F05I07K0AM0DO0HQ0LS0OT0TU0XV0aV0f\ W0jV0fV0aU0XT0TS0OQ0LO0HM0DK0AI07F05C0390160130000\ 0000100300401602703905A07B09C0BD0EE0GE0JF0MF0PG0SG\ 0VG0SF0PF0ME0JE0GD0EC0BB09A07905703602401300100000\ 00000000000000100100200300400500700800900B00C00E00\ F00E00C00B009008007005004 } frm:F_20121110_1031 { ; Similar to the parallel resistance formula a=real(p1),b=real(p2)-1,d=imag(p1),f=imag(p2), z=0,c1=pixel-p3,c2=pixel-p4: z=1/(1/(a*(z^b)*(exp(z)-1)+c1)+1/(d*(z^f)+c2)), |z|<100 } -- Mike Frazier www.fracton.org

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FOTD 09-11-12 (Everyday Minibrot 6])
by Jim Muth 10 Nov '12

10 Nov '12

FOTD -- November 09, 2012 (Rating 6) Fractal visionaries and enthusiasts: Today's image lies at the edge of the infinitely subdivided main spike of the Z^2.00001+C Mandeloid, just east of the large minibrot. This parent very closely resembles a Mandelbrot set, a great magnification being necessary to reveal the difference. I named the image "Everyday Minibrot" because that's what it is. The rating of a 6 indicates a scene that will never set the world afire. The calculation time of 2-1/3 minutes is slow enough to make the image worth less than its cost. The web sites have a better deal however. View the finished image on the official FOTD web site without the need of calculating it. The web site may be accessed at: <http://www.crosscanpuzzles.com/Archives.html> High-definition variations are online at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are posted at: <http://www.Nahee.com/FOTD/> Weather conditions took a decided turn for the better here at Fractal Central today. The sky was mostly sunny, the winds were much lighter, and the temperature reached a high of 54F 12C, making the day pleasant for almost any outdoor activity. START PARAMETER FILE======================================= Everyday_Minibrot { ; time=0:02:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-1.749357747989381/+0.00019329584512746\ /2.0456e+010/1/147.5/0 params=2.00001/0/0/0 float=y maxiter=2250 inside=0 logmap=277 periodicity=6 mathtolerance=0.05/1 colors=000fJOeHOdGOcEOcCObAOa8Oa7OY6MU6LQ6JN6IJ6HF\ 6FB6E86DNAHaKKpUNkcMgmMcpMhtMmwMrzMvzMzzMzrMzmMzhP\ zcRz_TvVVrVXmUPiSPiQPhPPgNPfLPWJKYGV_DfaAqbXabrMco\ JcmHckEciCcg9ce7dcCebGfaKg`Oh_SiZWjY_f_fYamR_oJZpE\ YnCUjAQd8KY6EQ48J7BK9ELBGMDJNFMOHOOQTNYYNfaNnfNvjN\ smVqpansilvpjxwTZhUbaUfVVjO1cG6ZF8UE6PD4KC2FB0AB6F\ DCIEIMF7SC8XD9aE9eFCaHFYIIUKLRLONNRJOUFQXCRVNgTXxQ\ `xOdxMgxKkxIoxGrxEvxCyxBpYBg8GPBL7DTKQ`Xahinouzgrj\ _oWSlGLi1Tj9`kGhlOpmVwnaspepqhmrkisoftrcuudqodmidi\ cdeZdaTdYNdVIeXJeYKfZLf_LgaMgbNhcOhdOYWIONCEF7F74F\ 01VnHWrAWu4Zs7`q9coCenEglGjjJdRLzgNZ`SKVW5P_AN`EL`\ IK`MI`RH`VF`ZE`bC`fB`bLWCEkBGmAIo9Lq9Nr8Pt7Sv6Ux6W\ yDVrJVlQVfWV`bUUhUOoUIuUCqWFmXIjcKfcNccQ_mSXmVTmYQ\ m_MzbUzeUzgczjczmczomzqmzrmzszztzzuzzvzzrzzozzlzzh\ zzezzbzz_zzWzzTzzQzzNzzHzzBzz5zz9zzCzzFzzJzzMzzPzz\ TzzWzzZzzMzzLzzKzzJzzIzzH } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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Albrecht's multifractal_10 fractal, "Multiple Directions"+ a zoom
by Hal Lane 10 Nov '12

10 Nov '12

I put a rendering of Albrecht's multifractal_10 fractal, "Multiple Directions" on my server: http://www.emarketingiseasy.com/TESTS/FOTD/MULTDRCT.GIF And here's an anti-aliased zoom into the top of "Multiple Directions" along the centerline: http://www.emarketingiseasy.com/TESTS/FOTD/MultDrct1.jpg If you calculate other Multifractal_10 fractals, make sure that the capitalization of the first letter of the "formulaname" in the par -- (Multifractal_10 or multifractal_10) is the same as the frm:'s formula name... Albrecht's .par specification -- with the Multifractal_10 formula added is below. - Hal Lane ######################## # hallane(a)earthlink.net ######################## -----------start par------------------------------- 1536164e { ; Multiple Directions ; jul-sec-bees-phoen-mand ; time 24.52 1600/1200 ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=mfr_10.frm formulaname=Multifractal_10 function=sin/exp/exp/sin passes=t center-mag=+1.33193274819753900/-0.000000000005385\ 46/9.345637e+008/1/90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/413\ 62.64595712822/14235.4911030602/152048.0404808048/\ 384.1604894048/384.00482000595/256.1007683001/512.\ 1007683001/768.1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000zzizzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8KJ8<2>I\ 88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriAtm9vq8\ xu7zz5zz4zz3<4>zj4zg4zc4<3>zS5zP5zL6zI6zE6wE6tD6<6\ >vAIv9Kv9M<3>x7Sy7Uy6Wz6Yz5_<3>f5Ma5IW4E<2>_4H<3>P\ 3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0gy0h<3>\ u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4KW0Qc<3\ >5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<3>civflvinvl\ qvotvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI\ <3>SCCXCAaB9<3>uA2zA0xA0<12>SA1QA1NA1<3>D92<6>UXAW\ `BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJoSFlWAi_5fc0c\ e7_jFRoNIzb0zj0000zr0zz1zzCzzT } frm:Multifractal_10 { le=0 z=pixel da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+11111 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==4)+(d==5)+(d==8)+(d==9) d4=d3==0 vb=d>5 sc=d==2 mo=d==6 px=d==7 ab=px+(d==3)+(d==5)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>1 sc1=d==2 mo1=d==6 px1=d==7 v1m=mo1+px1 v1j=d>7 dd1=v1j+(d==4)+(d==5) ab1=px1+(d==3)+(d==5)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=d>1 sc2=d==2 mo2=d==6 px2=d==7 v2m=mo2+px2 v2j=d>7 dd2=v2j+(d==4)+(d==5) ab2=px2+(d==3)+(d==5)+(d==9) d=trunc(dd/10) ex3=d>1 sc3=d==2 mo3=d==6 px3=d==7 v3m=mo3+px3 v3j=d>7 dd3=v3j+(d==4)+(d==5) ab3=px3+(d==3)+(d==5)+(d==9) d=dd-d*10 ba=imag(p5) mi3=trunc(ba) dd=(d>1)+(mi3>1) ex4=dd==2 sc4=d==2 mo4=d==6 px4=d==7 v4m=mo4+px4 v4j=d>7 dd4=v4j+(d==4)+(d==5) ab4=px4+(d==3)+(d==5)+(d==9) mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 dm=(d==2)+(d==4) ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex1+ex0+ex2+ex3+ex4 d=real(p3) dd=trunc(d) da=(d-dd)*10000000000 pp=trunc(dd/10000) ba1=dd-10000*pp ba2=trunc(da/100000) ba3=da-100000*ba2 d=imag(p3) sfac=trunc(d) da=(d-sfac)*100000000000 ba4=trunc(da/1000000) ba5=da-ba4*1000000 d=real(p4) ofac=trunc(d) da=(d-ofac)*10000000000 bh=trunc(da/100000)/10 bl=(da-bh*1000000)/10 bs=bl/2 d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) da=round((d-dd)*10000000000) d=trunc(dd/10000) dd=dd-d*10000 bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/1000) dd=dd-d*1000 bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/100) dd=dd-d*100 bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/10) dd=dd-d*10 bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=round(dd) bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=da p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 dp=p6+p0/100 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=d==3 fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=d==3 fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 if (mi3==1) d=(ba-mi3)*1000000 fr=round((trunc(d/10000))*10) d=d-fr*1000 lv=(trunc(d/100))/100 d=d-lv*10000 am=d/100 u=real(rotskew*pi/180) t=exp(-flip(u)) bo=1/real(magxmag) q=bo/0.75*imag(magxmag) dd=tan(imag(rotskew*pi/180)) da=2*q*t rs=2*bo*(dd+flip(1))*t zz=center+(-q-bo*dd-flip(bo))*t z=z-zz d=imag(conj(da)*z)/imag(conj(da)*rs) le=d<=lv if (le) dd=lv-d z=z+2*dd*(1+am*sin(fr*dd^0.2))*rs endif z=z+zz else da=(ba-mi3)*100000000000 d=trunc(da/10000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=d==3 fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 endif if (vb) if (d3) if (ab) z=z*le+pixel*(le==0) c=p1 else z=z*le+pixel*(le==0) c=p1 endif elseif (ab) c=z z=z*le+pixel*(le==0) else c=0.4*log(sqr(z^mm)) z=0 endif elseif (d3) if (ab) c=p1 z=z*le+pixel*(le==0) else c=p1 z=z*le+pixel*(le==0) endif elseif (ab) c=z z=0 else c=z z=z*le+pixel*(le==0) endif t=0 bo=|z| p=pp z0=p7 zold=(0.0,0.0) cb=p9 ba=bb0 : if (tt) t=t+1 if (ex0) ex0=t<mi1 if (bo>bs) u=2*(fn1(t/sfac)) ex0=0 if (ir0) t=0 endif if (d4) z=z*u if (mo) c=0.4*log(sqr(z^mm)) else c=pixel endif else z=z*le+pixel*(le==0) cb=p9*u c=p1*u p=pp*u endif tt=tt-1+ex0 endif elseif ((ex1)&&bo>bl) if (bo<bh) d3=dd1 ba=bb1 ab=ab1 ex1=0 tt=tt-1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif if (ir1) t=0 endif if (d3) vb=v1j if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif else vb=v1m if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo1) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) ab=ab2 d3=dd2 ba=bb2 ex2=0 tt=tt-1 if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif if (ir2) t=0 endif if (d3) vb=v2j if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v2m if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo2) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) ab=ab3 d3=dd3 ba=bb3 ex3=0 tt=tt-1 if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif if (ir3) t=0 endif if (d3) vb=v3j if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v3m if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) ab=ab4 d3=dd4 ba=bb4 ex4=0 tt=0 if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (d3) vb=v4j if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v4m if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo4) c=0.4*log(sqr(z^mm)) endif endif endif endif endif if (vb) if (d3) if (ab) z=z*z+c c=c*sp+z else z1=z^p-1 z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+0.56+ph/100-0.5*zold zold=z z=z1 else z2=fn1(z)+c z1=cos(z2) z=c*(1-z1)/(1+z1) endif elseif (d3) if (ab) z2=z*z z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) if (dm) z=z*z+c+c*c-dp else z2=z*z z=z2*z2+p6*z2+c-p0 endif else z3=z z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<ba } ---------------------------------------------------

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Multifractal_10
by Albrecht 10 Nov '12

10 Nov '12

Hi, like Jim, every now & then, when the time is right, I will submit an image only using above frm which by now every one should have downloaded. Today?s image came about zooming into one of my MFR-10 basic images and using Lee?s colours. After completion, checking my records I found that an almost identical image is on Lee?s Multifractal DVD. If two people find the same image by chance there must be something special to it! The Mandel in the middle, MIM image I call it, is Jim?s territory- but not completely this time, check it out. As possibly not everyone can generate MFR images I think it would be great if Hal or Paul could make it available for watching/ download . Fractals Are Fun! Albrecht ------------------------------------------Start Par---------------------- 1536704 { ; Unexpected_mandel ; Secant-mmods-bees-phoen-newt ; time 0.07.44 (XP dos shell) ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=mfr.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=-1.50145103141349900/+0.100170572669321\ 20/6662.918/1/-105.000000000013912/1.6730103413742\ 3699e-011 params=-0.05825983458967864/0.3785210730307932/153\ 67.64595767025/14235.4911030602/152048.0404808048/\ 384.1604894048/384.00482000595/256.1007683001/512.\ 1007683001/768.1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000000oNIzb0<2>zz1zzC<2>zzz<3>jqdfo_blU<3>M\ b8<3>LQ8KM8KJ8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBiOD\ jQF<3>qeBriAtm9vq8xu7zz5zz4zz3<8>zY4zV5zS5<3>zE6wE\ 6tD6<10>w8Px8Rx7S<3>z5_<3>f5Ma5IW4E<2>_4H<3>P3DN2C\ K2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0gy0h<3>u1mt1\ ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4KW0Qc<3>5Xc6\ Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<3>civflvinvlqvotv\ sww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI<4>XC\ AaB9fB7<3>zA0<13>SA1QA1NA1<3>D92<6>UXAW`BYcC<3>hrI\ <3>UnXRm_NlcJkgFfpAaz<6>_5fc0ce7_jFR }

2 4

FOTD 08-11-12 (Slightly Deficient 6.5])
by Jim Muth 08 Nov '12

08 Nov '12

FOTD -- November 08, 2012 (Rating 7.5) Fractal visionaries and enthusiasts: The exponent of Z in the past few days' images has been somewhat greater than two. The exponent of today's image is 1.9, which is somewhat less than two and also explains the name "Slightly Deficient". The parent fractal is basically shaped like a Mandelbrot set, as are all such fractional fractals with an exponent close to 2. This parent is rotated about 180 degrees, with two large period-2 buds on the eastern side of the main bay, one north and one south of the X-axis. A large disconnected minibrot lies just east of the southern bud, with a smaller disconnected minibrot nearby. Today's scene with its scrambled minibrot at the center lies not too far from this smaller minibrot. The rating of 7-1/2 is based on the colors. The little math interest is hardly enough to deserve a higher rating. The calculation time of 2-5/6 minutes is reasonable, though slower than would be preferred. Avoid all impatience by viewing the finished image on the official web site at: <http://www.crosscanpuzzles.com/Archives.html> Check the glorious high-definition variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And don't forget the back images at: <http://www.Nahee.com/FOTD/> Decreasing clouds and increasing temperatures prevailed here at Fractal Central today. The high temperature of 46F +8C would have felt warmer if the winds had not been so brisk. The next FOTD will be posted in 24 hours. Until then, take care, and see the official web site for the closing remark. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Slightly_Deficient { ; time=0:02:50.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=+1.519854358476405/-0.2217400613360854/\ 5.712965e+007/1/-95/0 params=1.9/0/1.9/0 float=y maxiter=3200 inside=0 logmap=277 periodicity=6 colors=000A0Q50LA0P50JA0O50IA1M52GA3N54FA5O56IA7N5\ 8HA9LAAZABZA7OADXAEXAFXABUAFRAITAHQAKNAIPAMLAKIAOF\ AKCAN9AL6AH1AJ3AK4AL5AN7AO8AP9AQBASCATDAUFAVGAXHAY\ JTMPXKLaIHeGDiE9y80zF6zSBgGCQ7CTACVDCXFCZIC`KCbNCd\ PCfTChVCjZCl`CndCpfCrjCtlCvpCxrCtoBqkAmg9jd9f`8cX7\ _U6XS6UP5QM4NJ3JH3GE2CB1980660881AA2BC3DD4EF5GH6HJ\ 7JK7KM8MO9NQAPRBQTCSVDTXEVYEW_FYaGZcH`dIafJchKhmLd\ iK`fKXcKU`JQYJMVJISJFPIBMI7JI4GIERNN`RXjVetZcqbamf\ _jjYgm_bk`ZjaUibQhdNifKihIjjFjlCknAklBjkCijDiiEhhF\ ggGgeHfdIfcJebKdaLd`McZGX_Nc_Tj_ZqVcjlVcmUgnTlpSqq\ RvrRzsWss`mtegtjauoWutQuyKotJipIclHZhHTcGN_FHWECSE\ BUE5P_5Tc5WgQhcLlXGqQBvCCuKCtRCtYgmjknhongsoevodok\ YihSbdMXaGRZAV_BY`B`aBdbBgcBjdBneBqfBtgBpdDmbEicGf\ hHbmJ_mKWmMTmNPmPMmQJmRMrPPvOSzMVzLYzK`zIczHfzGizE\ lzDozCzz8zzNzzGzz9zzHzzPzzXzzdzzlzzszzbzzMzz5zzKzz\ ZzzlzzkzzkzzkzzkzzczzWzzO } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

1 0

FOTD 07-11-12 (More of the Same [No Rating])
by Jim Muth 07 Nov '12

07 Nov '12

FOTD -- November 07, 2012 (No Rating) Fractal visionaries and enthusiasts: Today's image lies in the parent fractal that comes about when the expression Z^(2.06)+C is iterated 18 levels up the hyperladder with no function applied. This parent resembles a Mandelbrot set with two main buds and a large split along the negative X-axis. Today's scene is located near the tip of a wedge-shaped area of chaos extending westward just south of the split. The name "More of the Same" indicates that this is the fourth consecutive similar image. The similarity prevents me from giving it a rating. The calculation time of one minute will pass in a flash. The flash may be avoided by viewing the image on one of the web sites. The finished image is at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition variations are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are at: <http://www.Nahee.com/FOTD/> The day dawned cloudy here at Fractal Central, then the clouds hung on for the rest of the day. The forecast hints at snow tonight, but the temperature of 43F +6C would seem to make that unlikely. The next FOTD will be posted in the proper universal time. Until whenever that is, take care, and think positive. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= More_of_the_Same { ; time=0:01:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-1.174308345901659/-0.0904782035179286/\ 6.741058e+012/1/115/0 params=2.06/0/18/0 float=y maxiter=1800 inside=0 outside=tdis periodicity=6 mathtolerance=0.05/1 colors=000nJzjMzfPzcSz_VzWYzT`zPczMezNgzNhzOjzOkzP\ mzPnzPpzQqzQszRtzRvzSwzSyzSzzMvzGszNszUrz`rzfrzdUz\ b6zd3zCBzR5zTTzMbzElz6vzEwzMxzUyzbzz`yzZxzXwzUvzSu\ zQtzOszLrzJqzHpzFozCnzAmz8lz6kz3izE`zQRz`Izl8zfDz`\ IzUNzOSzIXzBbz91zA3zC5zE7zEAzEDzEGzEJzEMzcFzYRTXPT\ VMTUKTXPW_TZbXae`dhdgkhjnlmcWWcXovSjvOevKavFXvLTuH\ OuCJu8Fu4Au06q17m28i38e49a5AY5AU6BQ7CM8CI9DAAAAAAA\ 9AA9AA8AA8AA7AA7AA6AA6AA5AA5AA5AA4AA4AA3A_3La2Mb2M\ d1Nf1Ng1NMMpNNoOOnPPmPQlQRkRSjSTiSThTUgUVfVWeVXdWY\ cXZbY_aY_`Z`__aZ`bY`cXadWbeVcfUcfTbcRaaQa_P`YO_WN_\ UMZSLYQKYOJXMHXKGWIFVGEVEDUCCTABT8AS69S48W4A_4Bc4D\ g4Fk4Go4Is4JoANlFRhKVePZaVaZ_eVdiSimPnpXnrcnsjntqn\ uobqmSnkHki6hi6Pi65g86e97cA7aB8_C9YE9WFAUGBSHBQICO\ KDMLDKMEINFGOFHPFHPFHQFIQFIQFIRFJRFJSFJSFKSFKTFKTF\ LUFLUFLUFOTGQTGSTGVTHXTHZSHaSIcSIeSIhSJjRJlRJoRKqR\ KsRKuNMvKOwGPxDRyASuDUqGW } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

1 0

Fractint for Windows and Multifrac_10
by Albrecht 07 Nov '12

07 Nov '12

Versions 1 to 7 work well with the windows version. In multifrac_8 I added some addtitional code and variables which were needed for the reset commands which handle the transitions between the participating programs. They are resposible for the lack of chaotic portions and supply joint centers in images done with the latest edition. Versions 8 to 10 produce a "Buffer Overrun" as soon as they are loaded and Fractwin crashes instantly. Therefore only users running clean dos can load multifractal, only a few are left. I run multifractal also in the DOS Shell but I need a modified XP Version without net services. I?m sorry to say, that Richard refuses to increase the internal buffer, possibly only 1 line in the source code "STACKSIZE 7684 ; was 7172" and then recompile it. My bugreport is dated Aril 19, 2011 and when I sent a reminder was told to issue a new one, that?s all. The source code is available from http://iteratedynamics.codeplex.com. Can anybody help, maybe Jonathan ? I can imagine some more activity in the forum wouldhelp it survive a little bit longer Albrecht

3 5

FOTD 06-11-12 (Fractal Warming [7])
by Jim Muth 06 Nov '12

06 Nov '12

FOTD -- November 06, 2012 (Rating 7) Fractal visionaries and enthusiasts: Today's little oddity lies in the parent fractal that appears when the expression Z^(2.12)+C is iterated at ground level with no function applied. This parent is shaped like a squashed Mandeloid with a large main bay and a large period-2 bud on the north shore line. Today's scene lies in a minor valley on the west side of this bud. I named the image "Fractal Warming" because of the fiery reds surrounding the central minibrot, and also because of a recent show on TV about the dangers, real or imagined, of 'climate change'. The rating of a 7 is near FOTD average. Some extra effort on the coloring might have raised the rating a point or so. The calculation time of 1-1/3 minutes is well within reason. A bit of additional time might be saved by viewing the image on one or more of the web sites. The image has already been calculated and posted to the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> with hi-def variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are available at: <http://www.Nahee.com/FOTD/> A mix of sun and clouds, with a temperature of 45F +7C made today feel quite like November here at Fractal Central. Fractal cat Nicholas took advantage of the sun when it was shining and his food dish when it was not. The humans made it through election day without becoming too concerned over who might be the winner. Regardless of who wins, the next FOTD will be posted in the near future. Until whenever, take care, and climate change (aka global warming) is real! It has already begun! We had better believe it and start preparing! Do not make the error of thinking we can stop it or even slow it by forcing a few controversial bills through congress or by signing a few emission reduction treaties that are sure to be violated. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Fractal_Warming { ; time=0:01:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident center-mag=-0.429916265389/+0.98567433255/8.6e+007\ /1/-57.5/0 params=2.12/0/0/0 float=y maxiter=2750 inside=0 logmap=186 symmetry=none periodicity=6 colors=000ZYh`YgbZge_fg_ei`dkadnacpbbrcatcarbbpaco\ `dm_ek_ejZfhYgfXheWicWiaVj`UkZTlXSmWSmUQnSOnRNoPLo\ OJpMIpLGqJEqIDqPHkWLfaP`hTWoXQu_LqYJnWIjUGgSFcQD`O\ CYMAUK9RI7NG6KE4GC3DA1A90A809708707607606505405404\ 30330220210110000zCArB9mB9hB9cB9ZB9UA9UA8UA8UA8UA8\ UA8U98U98U97U97U97U87U87U87U87U86U86U76U76U76T76S7\ 5R65R65Q65P65P65O65N54M54M54L543fU3eT3dS3cR3bR3aQ3\ `P3_O2YO2XN2WM2VL2UL2TK2SJ2RI2QI2PH2OG1MF1LF1KE1JD\ 1IC1HC1GB1FA1E90001D91C80A709608607506405304303202\ 1010ttFrrEqqEooDnnDllDkkCiiChhBffBeeBccAbbAaaA__9Z\ Z9XX8WW8UU8TT7RR7QQ6OO6NN6LL5KK5JJ5HH4GG4EE3DD3BB3\ AA2882771551441220110Um9Tl8Tk8Sk8Sj8Sj8Ri8Ri8Rh8Qg\ 8Qg7Qf7Pf7Pe7Pe7Od7Oc7Oc7Nb7Nb7Nc6Oc6Pc6Qm6Rm6Sm6T\ m6Um6Vw6Ww6Xw5Yw5Zw5_w5`w5aw5bz5cz5dz5ez5fz4gz4hz4\ iz4jz4kz4lz4mz4nz4oz3pz3qz3rz3sz3tz3uz3vz3wz3zz3zz\ 2zz0zz0zz0zz0zz0zz0zz0zz0 } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

1 0

FOTD 05-11-12 (Pseudo-Symmetry [6.5])
by Jim Muth 06 Nov '12

06 Nov '12

FOTD -- November 05, 2012 (Rating 6.5) Fractal visionaries and enthusiasts: The name of today's image is "Pseudo-Symmetry". The name refers to the shape of the parent fractal, which came about when I whimsically calculated the expression Z^(2.34)+C at a level 4.32 turns up the hyperspiral. At first glance this figure-eight- shaped parent appears to have 'origin' symmetry, but a closer look reveals that the symmetry is only approximate. Today's scene is located in a valley of a larger minibrot lying on a filament extending from a mis-shapen bud on the northeast shore line of the northern bay of the parent. The semi- symmetrical shape of the minibrot at the center of the image reflects the shape of the parent. The coloring is nothing exceptional, but with the minor math interest, still earns a rating of 6-1/2. The calculation time of 2-2/3 minutes lies within the normal range. As always, calculation may be totally avoided by checking the image on the FOTD web sites. The pre-calculated image is posted on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> with hi-def variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are available at: <http://www.Nahee.com/FOTD/> Today began with clouds here at Fractal Central, but in the afternoon, the sun finally made a brief appearance, its first since October 25. The temperature of 45F +7C was rather chilly for early November. Fractal cat Nicholas' anticipation is building as the arrival date of his new companion Callie nears. She is due on November 14. Meanwhile, the humans simply made it through another day. The next FOTD will be posted when it is ready. Until whenever, take care, and who are you voting against on Tuesday? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Pseudo-Symmetry { ; time=0:02:40.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident center-mag=+0.581511067122/+0.663743919851/1.3e+007 params=2.34/0/4.32/0 float=y maxiter=5000 inside=0 logmap=243 periodicity=6 colors=000pQgnPilOkkOniNpgMrfLtdKvbJxaJzcMydOxeQwf\ SvgUvhWuiYtj_skarlcrmeqngpoiopknqmnrkjsigtgdudavaZ\ wZWxWTyUQwSNwQKvOHrKHmFGhAGc5Fa2F_2EY2EW2DU2DU1CU1\ CT1BS1BR1AQ1AQ00Q19Q19P18N18K17K17K16F06F05F05F04F\ 04F03F03F02F02F01F01F00A09A08A08A08A07A07A07A07A06\ A06A06A06A05A05A05A05A04A04A04A04A03A03A03A03E02D0\ 2B02A02901701601501300200100wytwxswwrmvqmuqmtpctoc\ sncrnUqmUplUpkUokUnjUmiPlhPlhPkgPjfPiePheLhdLgcLfb\ KebKdaKd`Jc`Jb_EaZE`YD`YD_XDZWCYVCXVCXUBWTBVSBUSBT\ RASQASPARP9QO9PN9OM8OM8NL8MK8LJ7KJ7KI7JH6IH6HG6GF5\ GE5FE5ED5DC4CB4CB4BA3A9398388287IDaL7eO2hS4ZV5PY6F\ eCXbGV`KTaPYaTbbYgbalbeqqE8lPQgZgchxcfocdfccYcaPc`\ HmbMmdRmeVmg_mhcmjhmklciecg_cfTcdNccHceNmfTmgZmhdm\ ijmjombgmV`zOTzGMz9FzJSzScz`ozXpzUqzUqzlnzUozUpzUq\ zUqzcrzcszcszctzcuzcvzcwzcxzcyzcyzcxzcwzcvzcvzcuzc\ tzctzcizc_zcQzcGzc6zc9zcB } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

1 0

FOTD 04-11-12 (Two and One Half [7.5])
by Jim Muth 04 Nov '12

04 Nov '12

FOTD -- November 04, 2012 (Rating 7.5) Fractal visionaries and enthusiasts: Things have finally settled down enough here at FC to once again devote energy to the FOTD. Today's image is a scene in the parent fractal that results when the expression Z^(2.5)+C is iterated 5.2 levels up the hyperladder with no function applied. This unimpressive parent resembles a Mandelbrot set rotated so that the area normally on the west faces northwest, with a large jagged bay where its East Valley should be and a main bud that has two equally large sub-buds. Filaments extend from each of these sub-buds, with large minibrots on these filaments. Today's scene lies in the large minibrot on the filament extending from the north sub-bud. This minibrot has two 'main' buds, with a rudimentary bay between them. This bay is the home of today's image. I rated the image at a 7-1/2. If I had had more time, I might have improved the colors enough to raise the rating to an 8. As it is, the image is not all that bad to look at, and well worth the 1-3/4 minutes required to calculate it. The name "Two and One Half" refers to the exponent of Z. The finished image is posted on the official (whatever that means) FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> enriched versions of the image and related images are online at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are available at: <http://www.Nahee.com/FOTD/> Today was cloudy with a temperature of 43F +6C. The fractal cat is doing fine. His new companion is due on November 14. The humans are still in the clean-up process. I have much to say about the big N.E. storm and the things I am hearing about it, but these things are mostly political, with lack of knowledge abounding, and this is a fractal list. I'll soon voice my opinion on the official FOTD web site, where I will be starting a blog where anything goes. The next FOTD will be posted when I get a 'round tuit'. Until whenever, take care, and instead of continuing to blather about the Arctic ice, let's talk about what's happening to the much more plentiful ice in the Antarctic. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Two_and_One_Half { ; time=0:01:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident center-mag=-1.313645604957682/+0.6344385534013239/\ 5.515427e+010/1/-97.5/0 params=2.5/0/5.2/0 float=y maxiter=2250 inside=0 logmap=248 periodicity=6 mathtolerance=0.05/1 colors=00006c07c08c09c0Ac0Cb0Ea0G`0I_0KZ0MY1OX2QX3\ SX4UX4XX9Z_E`aJbdOdfTfiYhkbjnflpgimgfkhcih`fiYdiVb\ jS_jPYkMWkJTlGRlEPiFRgGSeHUcIVaJX_KYYL_WL`VJaUIbTG\ bTFcSDcRCdRAdQ9eP7eP6fO4fN3gN2gS7mXCrUGoSKlQOiOSgL\ WdJ_aHcZFgXCkUAoR8sO6wMAqNDkOGfPK`QNWQQQRULSXFT_AT\ XBRVBQTBORBNOBMMBKKCJICHFCGzzzzzczzCzmBzcFzUJzKMrF\ QpAUkAXc8TW6NO4HG2C71094AB6HD9OEBQGDSIGVJIXLL_NNaO\ PcQSfSUhTWjY_NUWPRSQ`DYd4aZDXULTPTPJaKEiG9qCIZ5CYJ\ 7YW2Yh8bVDfHLXPTNW_EbdqVdlZdhadddd_gdWjdSmdOpXWiQc\ bJkWCsP5zJLsN`lQpfTjeWdeYZe`TebNedHegBei6ekpR7T4lL\ LfDa`6qV9kYCf`EabHXeJSgNXhQciUkjKdcmskzzlVZmSQnQHo\ RJkSKgTLcUN_VOWWPSWQPZfMavJNWOjKWQpjU6QPFPOXWLOPHX\ O8`QLIvHUdvPKfVMS`NtNqZIMOUN28_2d48eEucVfdSSeQHzAG\ zEFzHEzL9z_BzWCzSmz0BzpCzfDzXzzOzzOzzOzzIzzKzzLzzN\ zzGzzJzzMzzizzczzZzzTzzmzz`zzhzzbzzYzzTzzMzzNzzOzz\ ozzezzXzzlzz_zzkzz_zzdzzZ } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

1 0

The return of the FOTD
by Jim Muth 04 Nov '12

04 Nov '12

Fractal visionaries and enthusiasts: We have experienced some problems both here at New FC and back at Old FC. But the problems are under control (I hope) and the FOTD will resume on November 4. Jim Muth

1 0

Cosines Of Three
by Mike Frazier 03 Nov '12

03 Nov '12

In a prior post called Mixing Cosines I substituted a cosine term instead of the usual z to a power in the parallel resistor formula. The cosine added intricate detail to the fractal but if you looked around with this equation you probably noticed there were only z ^ 2 power minibrots in the fractal. Is it possible to increase the order of the minibrots without losing the intricate detail of the cosine? Here is a link to a web page with an image and a formula that attempts to do that: http://www.fracton.org/fmlposts/cosines_of_three.html The PAR file for the image is: CosinesOfThree { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20121102_1610 passes=1 float=y center-mag=-0.3806336003340345/-3.816249585923092e\ -14/53333334000/1/0/0 params=-1/1/0/4/-1/0/1/0/0/0 maxiter=2000 inside=0 periodicity=6 colors=000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O\ 40C10000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40\ C10000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C1\ 0000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C100\ 00C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000\ C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C1\ 0O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O\ 40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40\ ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA\ 0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0h\ I0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0\ oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS\ 0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0u\ a0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0ua0\ ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0ua0ym\ 0zy0ym0ua0oS0hI0ZA0O40C10 } frm:F_20121102_1610 { ; Similar to the parallel resistance formula a=real(p1),b=real(p2),d=imag(p1),f=imag(p2), z=0,c1=pixel-p3,c2=pixel-p4: z=1/(1/(a*z*(cos(z)-1)+c1)+1/(d*(z^f)+c2)), |z|<100 } -- Mike Frazier www.fracton.org

1 0

Mixing Cosine
by Mike Frazier 02 Nov '12

02 Nov '12

Here is another fractal using the parallel resistor formula. The basic formula combines any two powers of z. It seems to make a fractal with pretty much any coefficients you pick. I wondered what would happen if I substituted a cosine for one of the z terms. The cosine seems to add a lot of intricate detail. Here is a link to a web page with an image and a description of what I found: http://www.fracton.org/fmlposts/mixing_cosine.html I will also list the PAR file here for people collecting them from the mail list: Mixing_Cosine { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20121102_1156 passes=1 float=y center-mag=0.5475442691084866/-2.413982470836851e-\ 06/3333.333375/1/0/0 params=-1/1/0/4/-1/0/1/0/0/0 maxiter=2000 inside=0 periodicity=6 colors=000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O\ 40C10000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40\ C10000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C1\ 0000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C100\ 00C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000\ C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C1\ 0O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O\ 40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40\ ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA\ 0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0h\ I0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0\ oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS\ 0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0u\ a0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0ua0\ ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0ua0ym\ 0zy0ym0ua0oS0hI0ZA0O40C10 } frm:F_20121102_1156 { ; Similar to the parallel resistance formula a=real(p1),b=real(p2),d=imag(p1),f=imag(p2), z=0,c1=pixel-p3,c2=pixel-p4: z=1/(1/(a*cos(z)+c1)+1/(d*(z^f)+c2)), |z|<100 } -- Mike Frazier www.fracton.org

1 0

Mixed Up Minibrot
by Mike Frazier 02 Nov '12

02 Nov '12

I haven't posted any fractals for a few months while I was testing Fracton's 3D model code. I really need a faster computer (or faster code) to make them practical. I stopped one model after two weeks of calculations when it still hadn't finished. Doubling the resolution of the model often takes 10 times longer to calculate. Changing the resolution of a model from coarse to good often changes the execution time from minutes to months. Luckily, there are still plenty of fractal adventures to be had in the 2D space where calculations finish in a much more reasonable time. I recently explored fractals using the parallel resistor formula I have posted in the past. I noticed a few things, although there are still many more behaviors to be discovered. Here is a link to a web page with an image and a description of what I found: http://www.fracton.org/fmlposts/mixed_up_minibrot.html I will also list the PAR file here for people collecting them from the mail list: MixedUpMinibrot { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20121101_1707 passes=1 float=y center-mag=-0.3871042832031641/-1.169807668188325e\ -12/1333333350/1/90/0 params=-1/1/8/7/-1/0/1/0/0/0 maxiter=4000 inside=0 periodicity=6 colors=000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O\ 40C10000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40\ C10000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C1\ 0000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C100\ 00C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000\ C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C1\ 0O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O\ 40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40\ ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA\ 0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0h\ I0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0\ oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS\ 0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0u\ a0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0ua0\ ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0ua0ym\ 0zy0ym0ua0oS0hI0ZA0O40C10 } frm:F_20121101_1707 { ; Similar to the parallel resistance formula a=real(p1),b=real(p2),d=imag(p1),f=imag(p2), z=0,c1=pixel-p3,c2=pixel-p4: z=1/(1/(a*(z^b)+c1)+1/(d*(z^f)+c2)), |z|<100 } -- Mike Frazier www.fracton.org

2 2

Can't get it to work
by Dean Norris 02 Nov '12

02 Nov '12

I was using Fractint back in the late 80's. I Just tried to D/L a windows 7 version and unpacked it. I cant find a working exe file. I just get an error message saying it cannot open the file. It tells me it won't work in a 64bit environment. Help Dean

4 7

Re: [Fractint] Mixed Up Minibrot
by jimmckenzie＠earthlink.net 02 Nov '12

02 Nov '12

NNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIICCCCCCCCCCCCCCCCCCCCCEEEEEEEEEEEEEEEEEEEE!!!!!!!!!!!!!!!!!!!!!!!!!!!!! -----Original Message----- From: Mike Frazier Sent: Nov 1, 2012 10:11 PM To: Fractint and General Fractals Discussion Subject: [Fractint] Mixed Up Minibrot I haven't posted any fractals for a few months while I was testing Fracton's 3D model code. I really need a faster computer (or faster code) to make them practical. I stopped one model after two weeks of calculations when it still hadn't finished. Doubling the resolution of the model often takes 10 times longer to calculate. Changing the resolution of a model from coarse to good often changes the execution time from minutes to months. Luckily, there are still plenty of fractal adventures to be had in the 2D space where calculations finish in a much more reasonable time. I recently explored fractals using the parallel resistor formula I have posted in the past. I noticed a few things, although there are still many more behaviors to be discovered. Here is a link to a web page with an image and a description of what I found: http://www.fracton.org/fmlposts/mixed_up_minibrot.html I will also list the PAR file here for people collecting them from the mail list: MixedUpMinibrot { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20121101_1707 passes=1 float=y center-mag=-0.3871042832031641/-1.169807668188325e\ -12/1333333350/1/90/0 params=-1/1/8/7/-1/0/1/0/0/0 maxiter=4000 inside=0 periodicity=6 colors=000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O\ 40C10000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40\ C10000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C1\ 0000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C100\ 00C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000\ C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C1\ 0O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O\ 40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40\ ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA\ 0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0h\ I0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0\ oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS\ 0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0u\ a0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0ua0\ ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0ua0ym\ 0zy0ym0ua0oS0hI0ZA0O40C10 } frm:F_20121101_1707 {; Similar to the parallel resistance formulaa=real(p1),b=real(p2),d=imag(p1),f=imag(p2), z=0,c1=pixel-p3,c2=pixel-p4:z=1/(1/(a*(z^b)+c1)+1/(d*(z^f)+c2)),|z|<100} -- Mike Frazier www.fracton.org

2 1

FOTD 29-10-12 (The Missing Minibrot [5.5])
by Jim Muth 29 Oct '12

29 Oct '12

FOTD -- October 29, 2012 (Rating 5.5) Fractal visionaries and enthusiasts: Today's image lies in the parent fractal that results when 1.5 parts of Z^(-1.24) are combined with 0.19 part of Z^(-7.26) on each iteration before (1/C) is added. This parent is a colossal sprawling thing hundreds of times the size of the default screen, which consists mostly of zig-zag filaments twisted into huge loops. Today's image is located in a more interesting area of the parent, not too far from the origin. I have named such scenes 'dry valleys'. From a distance it appears that minibrots might lie at their centers. The two-way symmetry is certainly there. But at the center of symmetry we find only saddle-shaped blank walls exactly as we find at the center of today's image. The name "The Missing Minibrot" refers to the disappointment at the centers of these dry valleys. The rating of a 5-1/2 indicates that the image leaves much to be desired. And the calculation time of 5 minutes also leaves much to be desired. A better time bargain may be found on the FOTD web sites. Check the finished image at: <http://www.crosscanpuzzles.com/Archives.html> A hi-def rendering is at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are at: <http://www.Nahee.com/FOTD/> Increasing wind and rain prevailed here at Fractal Central today. The wind and rain are the start of the big frankenstorm, which is not due to reach its peak until tomorrow morning. So far, the highest wind gust has been a not-too-impressive 37mph or 50kph, but winds of 70mph, 112kph are expected tomorrow. The rain so far has measured only 0.5 inch or 1.2cm -- also not too impressive. Up to 12 inches, 30cm is expected south of here however before it all ends on Wednesday. The temperature of 50F 10C was quite chilly for a tropical storm. Fractal cat Nicholas watched the goings on with interest, then viciously attacked his toy ball. The next FOTD is due in about 24 hours. If it fails to appear, don't wait up for it. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= TheMissingMinibrot { ; time=0:00:05.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-3.959516711/-0.158776657/874/1/-27.5/0 params=1.5/-1.24/0.19/-7.26/0/0/0/0 float=y maxiter=1200 inside=zmag outside=tdis periodicity=6 colors=000fFnaLmXRlSXlOakJgjEmj9si5xi6te6pa7lY7hU8\ dR8`N9XJ9TFAPBAL8CKADJCEIEFHGGGHHFJJFLKENLDOMCQNBS\ OAUPAVADFBCEBCDBBDCBCCABCABD9AD99D89E88E77E77F66F6\ 5F65I59K5CM4FO4IQ4LS3OU3RW2UY2X_2_a1bc1ee0hg0ki0nb\ ATnT`zjhvlfrmdnncjoagp`cqZ_rXWsWStUPuTLvRHwPDxO9yM\ 6zL7uM8pM8kN9fN9aOAXOBSPBNPCIQCDQD8RD4RNOXXfaUg`Sh\ `Pi_Ni_Kj_IkZFkZDlYAmY8mY5nX3oX1oX6jZAe_E``IXaMSbR\ NcVIdZEeb9ff4gj0hk0jk0jm0km0mn0mp0np0pq0pq0qs0sx0t\ t0ss0sq0qp0qn0pm0pk0ph0ng0ne0md0mb0m`0k_0kW0jV0jzz\ 0zz0zz0zz0yz0xy0vx0tt0ts0sq0qp0pm0nk0mj0mg0ke0jd0h\ b0g_0eY0eW0dV0bS0`Q0_P0YN0YK0WJ0VH1TF1SE1QD1QD2PE2\ NF2MG2KH4JI4JJ4HK4GI5EG5CE5AC5AA5A84A62A51A41A30A2\ 0A10A00A00A00A00A00A00A00A00A00C00C00E20E40G50G92H\ A4HC7JG9JHCKJEKMHMNJMPMNSNNTQKTTMVSMVSNVSNVSPWQPWQ\ QWQQWQSWQSYPTYPTYPV`PV`PW`NW`NY`NY`N_`N_`M``M`aMba\ MbbMdbKdbKebKebKgbKgcJhcJ } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

1 0

FOTD 28-10-12 (Lake of Dreams [7])
by Jim Muth 28 Oct '12

28 Oct '12

FOTD -- October 28, 2012 (Rating 7) Fractal visionaries and enthusiasts: We're preparing for a big storm here at Fractal Central, so I have little time for a detailed discussion. The parent fractal of today's image came about when I subtracted Z^10 from Z^11 and added straight C on each iteration. This parent is a lopsided, 9-1/2 lobed thing with most of the interest along the eastern edge of the large central bay. Today's scene is located in a kind of debris ring surrounding the northern bud attached to the 1-1/2 lobed bay on the east side. The terraced effect was achieved by rendering the scene with the outside set to 'tdis'. The deep-blue coloring adds a rather somber effect, contributing little to the overall worth of the image. The calculation time of 25seconds is no joke. The image really does finish that fast. For convenience if not faster viewing, check the finished image posted at: <http://www.crosscanpuzzles.com/Archives.html> And check the high-definition version at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are online at: <http://www.Nahee.com/FOTD/> Clouds, occasional rain, and increasing wind prevailed here at Fractal Central today, as the 'frankenstorm' approached. The temperature of 54F 12C was within reason. Fractal cat Nicholas had a restless day, apparently picking up the extra activity of the humans. The next FOTD will be posted before too much time has passed -- I hope! If the worst happens, it might not appear for quite a while. Until whenever, take care, and the gods are angry. Let's heed their message. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Visionary_Vision { ; time=0:00:25.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident center-mag=+1.205125057483229/+0.2232655114510676/\ 3.86445e+008/1/126.25/0 params=1/11/-1/10/0/0/0/0 float=y maxiter=750 inside=0 outside=tdis logmap=31 periodicity=10 colors=00053U65Y67a69d6Bh7Dl7Fo7Hs7Jw7Kz8Ly9LxALwk\ MhlOimRjo_zpczrhzsmztqzvzzwzzxzzrzzmtzhm_ccVYbPT`J\ O_DJZ8M`EObKRcQTeWVgaYhg_jmakrchneejfcfh`cjY_kWWmT\ SoQPpOLrLHsJEnKDiKDdLC_LC_KD`ID`HE`GF`FGaEHaDIaCJa\ BKaAKgHMlOOqUQo_cpZapZ`pY_qXYqXXqWWrVUrVTrUSU16Z7B\ cDFhJJmPNrl3rj5ri6rh8rg9rfBreCrdDrcFraGr`Ir_JrZKrY\ MrXNrWPrVQJkkVedf_Y2zP7wQBtQFrQJoQNmQRjQVhRZeRbcRf\ `RjZRnWRDsTRjSdaRvi2ug6ue97le8ne9Qe9SeAUeAWeGYZL_T\ Q`MVaG_XAYUEWRHVOKTLOSJRQGUPDYNA`M8cOBhPEmQHrRKwPI\ uNHoLGmKElIDjGCgFAdD9aB8ZA6W85T64Q53PJGSXSdjdgzzjz\ okrdkoZklTlEIpDAqC2qEAlFHhGOdHV_IaWTbHR`IP_INYJMXJ\ IRIFLHKPIOTISXJW`J_dKchKglLkpLosLpnJqiIreHr`GsXFtS\ EtNDuJCvEBvAAqDEmFIhHMdKQ_MUWOYUJbSEgRAkP5pO1tS6rW\ AqZEobIneMliRklVipZhsbfwfezjdxl_wmWuoStpOrrKqsGouC\ nv8lx4ky0ix2gx3ex4cw5aw6_w7Yv8Wv9UvASvBRsIQpPPmWPj\ bOgiNdpNbvKVoHNiEFcB8Y85W } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

1 0

FOTD 26-10-12 (Lake of Dreams [9.5])
by Jim Muth 27 Oct '12

27 Oct '12

FOTD -- October 26, 2012 (Rating 9.5) Fractal visionaries and enthusiasts: Today's image is a rerun, but it is such a good rerun that I gave it a superior rating of 9-1/2. The image is a scene in the Seahorse Valley area of the Z^2+C Julibrot, sliced in a direction about halfway between the Oblate and Rectangular orientations. The reason for the name "Lake of Dreams" will be obvious once the image is viewed. The ripples on the 'water' appear in perfect perspective, while the coloring so closely resembles water that it makes me thirsy. The calculation time of 45 seconds will add to the enjoyment. Enjoy the serenity of rippling water by viewing the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> without the inconvenience of calculating it. A high-definition rendering is online at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> and the back images are available at: <http://www.Nahee.com/FOTD/> The clouds hung tough here at Fractal Central today. Fractal cat Nicholas carefully checked the hall closet to be sure Cassie was not in there, then settled on the scratching post for most of the afternoon. The humans once again made it through the afternoon with nothing to report. The next FOTD will be posted on Sunday. On Saturday I'll be in Baltimore, checking Old Fractal Central to see it it's prepared for a big storm expected early next week. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Lake_of_Dreams { ; time=0:00:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=-0.130564/0/\ 2.314276/1/90/0 params=40/90/0/90/-0.75/0/0/0/2/0 float=y maxiter=100000 inside=255 logmap=yes periodicity=10 colors=000Q0hR2iS5jT8kUPnVSmWTnXVoYXpZZq_`r`bsadtb\ fuchvejwfkwglxfkzekwdjvciubhtagrafq`ep_doZcnYbmXak\ X`jW_iVZhUZgUYgTXfSWdRVcRUbQTaPS`OR_NQYMPXMPWLOVKN\ UJMSILRHKQGJPGIOFHNEGLDFKCEJBDIBCHABG9AE89D78C67B5\ 6A55944733622511400320640860A80AA09C09E08G07I07K06\ M36O65Q94SB4U93W83Y62_41a31c10c6Ib5Ha5Ha5H`5G_5GY5\ GY5GX5FW5FW5FV5FV4EU4EU4ET4ET4DS4DR4DR4CQ4CQ4CP4CP\ 3BO3BO3BN3BM3AM3AL3AL3AK39K39J39J39I28H28H28G27G27\ F27F27E26D26D26C26C15B15B15A15A1491481481371371361\ 3602502502402301301201201100100000AKQAKmAKmAKmAKmA\ KmAKmAKMAKLAKKAKKAKJAKJAKIAKIAKHAKGXKGWKFVKFTKESKE\ RKDQKDPKCOKBNKBLKAKKAJK9IK9HK8GK7EH7DG6CF6BD5AC59A\ 4893683562452341221110AK`AK_AKZAKYAKXAKWAKVAKUAKUA\ KTAKSAKRAKQAKPAKOAKOAKNAKMAKLUYKTXJSVIQUIPSHORGNPF\ LOEKNDJLCHKCGIBFHAEF9CE8BC7AB68A678567455334222111\ 0ENuDMsDLrL4dL4dL3eL3eAAA } frm:SliceJulibrot4 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

2 1

You folks are asleep at the switch. You let me...
by Hal Lane 27 Oct '12

27 Oct '12

You folks are asleep at the switch. You let me post the parent (and zooms into it) of Jim's FOTD for October 3rd, 2012 with a 16 color EGA-type color map -- instead of his colors. For comparison -- here's an example of the parent fractal with the color map I had previously used for the parent: http://www.emarketingiseasy.com/TESTS/FOTD/F121003YwrongMap.jpg and the same fractal with Jim's colors: http://www.emarketingiseasy.com/TESTS/FOTD/F121003Y.jpg The October web page has the correct color map in all the images for the 3rd now: http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html Jim's FOTD for October 3rd, 2012 has always had the correct color map on my page: http://www.emarketingiseasy.com/TESTS/FOTD/F121003J.jpg - Hal Lane ######################## # hallane(a)earthlink.net ########################

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Some zooms into Albrecht's Strange Beauty Multifractal_10
by Hal Lane 26 Oct '12

26 Oct '12

Here are some zooms into Albrecht's Strange Beauty fractal that uses his Multifractal_10 formula. The fractal has quite a bit of nifty, colorful variety in it. All 640 x 480 non-anti-aliased. They're arranged in increasing zoom depth, with the 2nd and later fractals each a zoom into the previous one: Albrecht's original Strange Beauty fractal: http://www.emarketingiseasy.com/TESTS/FOTD/STRNGBUT.GIF And zooms into it: http://www.emarketingiseasy.com/TESTS/FOTD/STRNGBU2.GIF http://www.emarketingiseasy.com/TESTS/FOTD/STRNGBU3.GIF http://www.emarketingiseasy.com/TESTS/FOTD/STRNGBU4.GIF http://www.emarketingiseasy.com/TESTS/FOTD/STRNGBU5.GIF http://www.emarketingiseasy.com/TESTS/FOTD/STRNGBU6.GIF http://www.emarketingiseasy.com/TESTS/FOTD/STRNGBU7.GIF http://www.emarketingiseasy.com/TESTS/FOTD/STRNGBU8.GIF Has numerical loss of precision: http://www.emarketingiseasy.com/TESTS/FOTD/STRNGBU9.GIF Has extreme numerical loss of precision: http://www.emarketingiseasy.com/TESTS/FOTD/STRNGB10.GIF The parent fractal: http://www.emarketingiseasy.com/TESTS/FOTD/STRNGBUP.GIF And a zoom into the parent: http://www.emarketingiseasy.com/TESTS/FOTD/STRNGB11.GIF - Hal Lane ######################## # hallane(a)earthlink.net ########################

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FOTD 25-10-12 (Starriest Night [9.5])
by Jim Muth 25 Oct '12

25 Oct '12

FOTD -- October 25, 2012 (Rating 9.5) Fractal visionaries and enthusiasts: Today's fractal rates an honest 9.5. A full point and a half is due to the coloring, which is about all the image has going for it. The scene lies in the parent fractal that comes about when the Mandelbrot set is corrupted with Z^(0.94145506) energies. This parent is mostly cut-off beyond the too-small escape radius. What shows of it is shaped like a large teardrop. A larger escape radius would have revealed more of the parent, but would have lost today's scene. The sky part of the image is all outside stuff made visible by the 'bof60' outside fill. The lower part is everyday inside stuff. The name "Starriest Night" was inspired by a well known painting. The calculation time of 3-1/2 minutes will pass slowly at first, but will speed up notably once the calculation reaches the distant horizon about 2/3 of the way down. The finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> A high-definition rendering plus other goodies is online at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are available at: <http://www.Nahee.com/FOTD/> Heavy clouds permitted only a few peeks of sun at Fractal Central today. The temperature of 66F 19C was all right, but it would have been more enjoyable if there had been more sun. Fractal cat Nicholas spent most of the afternoon on the shelf in the southwest window, waiting for the sun that never came. The humans made it through the day as best they could. The next FOTD will be posted soon. Until whenever, take care, and who said fractals cannot be art? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Starriest_Night { ; time=0:03:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basic.frm formulaname=FinDivBrot-2 function=recip logmap=yes passes=1 center-mag=-0.05596778/+0.5609443890/568/\ 1/-91.1/0 params=0.94145506/1.5/1000000/0 float=y maxiter=15000 inside=bof60 periodicity=10 colors=000bzz_nzXgzU`zRVzPPzMLzJJzGHzDFzBDz8By59t5\ 7q53p53n43k33h23e13c03a03_03Y03W03U03T03S03R03Q03P\ 03O03N03M03Mn4rp4ur4xt4zs5xr5wq6vq6up7to7sn7rn8qm8\ ol9nk9mk9ljAkiAjhBihBhgCffCeeCdeDcdDbcEabE`bE_`KUZ\ POYUIWZCVc7Td8Sd9Rd9QdAPdBOeBNeCMeDLeDJeEIeFHfFGfG\ FfGEfHDfICgIBgJ9gK8gK7gL6gM5hM4hN3hO2hO1hP0hP1iQ2i\ Q2iQ3iQ4iR4iR5iR5iR6iS7iS7iS8iS9iT9iTAiTAiTBiUCiUC\ iUDiUEiVEiVFiVFiVGiWHiWHiWIiWIiWGjZEl`CmcAoe8pgCne\ FlcIjaLh`PfZSdXVcWYaUL58M48M39N3968978A88E98FA8GB8\ MCBUEEcGImIOrNRvTVzWYzZ`zadzdgzejzdjz0WU0UT0RT0PS0\ NR0LQ0IQ0GP0EO0CN09N07M05L03L0BO0IQ_PTaWVcbYei_eh_\ ef_eeZedZecZeaZe`Ze_YeYYeXYeWYeVXeTXeSXeRXeQXfOZgM\ `gKbhIdhGfiEhiCjjAlj8nk6pk4rl6o08m09k0Bh0Cf0Ed0Ga0\ H_0JY0KV0MT0NR0PO0RM0SK0UH0VFuXDuXBiXLZXVN`dCanB_o\ BYoAWoAUo9Sp9Rp8Pp8Np8Lp7Jq7zq6zq6zq5zr5zr5zr4zr4z\ r3zs3zs2zs2zs2zs5zt7zt9zt } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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I'm able 2 calc Albrecht's The_Miracle w the comments in; Dev. Q.
by Hal Lane 25 Oct '12

25 Oct '12

I'm able to calculate Albrecht Niekamp's: "The_Miracle" (that uses Multifractal_10) with all the comments in it in the form he posted it on the [Fractint] list serve Oct 23, 2012 -- in VESA video mode 640 x 480 with DOS Fractint v 20.04.4 under WinXP SP3. The video chip built into the system board of my computer only supports VESA video mode: 640 x 480, and the DOS environment for Fractint is able to allow the calculation of his fractal using that video mode. However, when I try to use the 640 x 480 (or 4k x 3k) Disk Video modes, I get: "Insufficient memory to run fractal type 'formula'" Invoking Disk Video mode apparently allocates some additional memory that "breaks the camel's back" -- despite using the hard drive to write the image to. The version of Multifractal_10 *without* comments has this same problem. Here's Albrecht's "The Miracle" at 640 X 480: http://www.emarketingiseasy.com/TESTS/FOTD/T_MIRACL.GIF and a zoom into it: http://www.emarketingiseasy.com/TESTS/FOTD/T_MIRAC2.GIF Question: Any of the developers have any idea of how to get around the Disk Video modes not leaving enough memory for multifractalll-10 to run? Any debug modes lurking around that might help -- say, specifying the allocation of smaller Disk Video buffers? - Hal Lane ######################## # hallane(a)earthlink.net ########################

6 8

FOTD 24-10-12 (Nuclear Newton [8])
by Jim Muth 24 Oct '12

24 Oct '12

FOTD -- October 24, 2012 (Rating 8) Fractal visionaries and enthusiasts: There was no FOTD for October 23 because FL and I spent the day searching for a companion for fractal cat Nicholas. We found a calico cat named Callie, who will be the next fractal cat when she gets her shots and if she gets along with Nico. For today's image I returned to the MandNewt series of formulas, number 10 to be exact. Amidst all the confusion I dredged up today's scene, which despite the off-coloring, still reminds me of a nuclear explosion. I named the image "Nuclear Newton". The most notable feature of the image is the unusually smooth coloring -- smooth, that is, by 256-color GIF standards. The unexpected smoothness earns the image a rating of an 8. The calculation time of 1-2/3 minutes will pass in a flash. With the passes set to 'g' the image will finish even faster, but a few minor bits of detail will be skipped over. Relieve nascent boredom by checking the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> And don't miss the high-definition rendering at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are online at> <http://www.Nahee.com/FOTD/> Today here at Fractal Central seemed more like a day in May than a day in late October. The temperature of 75F 24C was mild enough for any outdoor activity, while the cloudless skies and light breezes made things near perfect. The fractal cat spent much of the time in the sun and the rest of the time hoping for food. The humans made it through the day with nothing to report. The next FOTD will be posted when it is ready. Until whenever that might be, take care, and protest ambiguity. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Nuclear_Newton { ; time=0:01:40.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandNewt10 passes=1 center-mag=-0.115\ 184/0/2.9/1/90/0 params=5/-1/1/0.5/1/5e-031 float=y maxiter=430 inside=255 logmap=yes periodicity=0 colors=0000020020020020020010010010010011212423634\ 845A56C67E66G56H56I56J56K56L56M56N56O56P56Q56R56R5\ 6R56S56S56T56T55T45U45U45U45V45V45W45W45W45X45X45X\ 45Y45Y45Z45Z45Z45_44_34_34`34`34a34a34a34b34b34c34\ c34c34d34d34d34e34e35f36f27f28g29g2Ag2Bh2Ch2Di2Ei2\ Fi2Gj3Hk3Ik3Jl4Km4Ln4Mn4Oo4Qp4Sq5Uq5Wr5Ys5_s5`t6au\ 6bv6cv6dw6ex6fy7gy7hz7iz7iy8jy8jy8jy9ky9ky9lx9lx9m\ xAmxAmxAmxAmxAmxBmxBmxBmwBmwCmwCmwCmwCmwCmwDmwDmwD\ mwDmvDmvEmvEmvEmvEmvEmvFmvFmvFmvFmvFmuGmuGmuGmuGmu\ GmuHmuHmuHmuHmuImtImtImtImtImtJmtJmtJmtJmtJmtKmsKm\ sKmsKmsKmsLmsLmsLmsLmsLmsMmsMmrMmrMmrMmrNmrNmrNmrN\ mrOmrOmrOmqOmqOmqPmqPmqPmqPmqPmqQmqQmqQmqQmpQmpRmp\ RmpRmpRmpRmpSmpSmpSmpSmoSmoTmoTmoTmoTmoUmoUmoUmoUm\ oUmnVmnVmnVmnVmnVmnWmnWmnWmnWmnWmnXmmXmmXmmXmmXmmY\ mmYmmYmmYmmYmmZmlZmlZmlZml_ll_kl_jm_im_hnfgoheooeo\ odqmeqmfqmgqohqqiqtjqwkqz } frm:MandNewt10 {; Jim Muth z=g=pixel, a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), e=real(p3), f=imag(p3): h=z^a+(g-b)*z-g j=c*z^d+g z=z-e*h/j, f <= |h| } END PARAMETER FILE=========================================

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Multifractal_10 - The Big Ball
by Albrecht 24 Oct '12

24 Oct '12

Hi, as it seems nobody has bothered to check or zoom into "Unexpected_mandel" sofar. Other wise you would have detected that something extraspecial is hidden. I enclude two zooms, as different as can be. Also the total view, even that is impressive. To make it clear: This fractal is one of the most unbelievable ones I have ever seen, and I?ve seen a lot. There is beauty, symmetry and diversity everywhere. In addition: Up to now I have seen no cuts or inconsistencies, although it is made up using five different formulas. The reason for that are the various reset commands I used. Only today I enclude the "FRM" just in case somebody has not yet downloaded it. Sorry for beeing a bit drastic but I want to create some curiosity and action in this forum. I?m thrilled to view your reactions. ---------------------------------------------start pars------------------------------------- 1536705 { ; Strange_Beauty ; secant-mmods-bees-phoen-newt ; time 0.05.49 XP Dos shell ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=mfr.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=-1.50137769253409600/+0.100910670672261\ 60/6855.058/1/165.000000000015433/-4.8305803801440\ 5611e-013 params=-0.05825983458967864/0.3785210730307932/153\ 67.64595767025/14235.4911030602/152048.0404808048/\ 384.1604894048/384.00482000595/256.1007683001/512.\ 1007683001/768.1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000000oNIzb0<2>zz1zzC<2>zzz<3>jqdfo_blU<3>M\ b8<3>LQ8KM8KJ8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBiOD\ jQF<3>qeBriAtm9vq8xu7zz5zz4zz3<8>zY4zV5zS5<3>zE6wE\ 6tD6<10>w8Px8Rx7S<3>z5_<3>f5Ma5IW4E<2>_4H<3>P3DN2C\ K2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0gy0h<3>u1mt1\ ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4KW0Qc<3>5Xc6\ Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<3>civflvinvlqvotv\ sww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI<4>XC\ AaB9fB7<3>zA0<13>SA1QA1NA1<3>D92<6>UXAW`BYcC<3>hrI\ <3>UnXRm_NlcJkgFfpAaz<6>_5fc0ce7_jFR } 1536704e { ; Inside_View ; secant-mmods-bees-phoen-newt ; time 0.33.55 XP Dos shell ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=mfr.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=-1.50145147245682100/+0.100169185289958\ 60/843407.3/1/74.9999999981563263/2.46247487678541\ 432e-009 params=-0.05825983458967864/0.3785210730307932/153\ 67.64595767025/14235.4911030602/152048.0404808048/\ 384.1604894048/384.00482000595/256.1007683001/512.\ 1007683001/768.1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000<3>000000304<8>X0a_0dc0h<3>p0w<4>_0dX0aU\ 0Y<2>K0NH0JG0NE1R<3>7UX6`Z4h_2oa0wc<11>2TG2RE3OC<3\ >4D3<17>kkammcpoe<3>zwm<6>cYO`UKYQG<3>KA0000<43>00\ 0<4>000330<11>110110110<3>000KA4<7>gcOjgRmjT<3>zzc\ <9>UOFRKDOGA<3>A00<9>f0Ci0Dl0F<3>z0K<6>Z0EV0DR0C<3\ >A08004000<26>000 } 1536705d { ; The_Big_Ball ; secant-mmods-bees-phoen-newt ; time 0.02.44 XP Dos shell ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=mfr.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=-0.0231296/0.0288228/0.5500051/1/92.499\ 9999999409539/2.09411585294638769e-011 params=-0.05825983458967864/0.3785210730307932/153\ 67.64595767025/14235.4911030602/152048.0404808048/\ 384.1604894048/384.00482000595/256.1007683001/512.\ 1007683001/768.1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000000oNIzb0<2>zz1zzC<2>zzz<3>jqdfo_blU<3>M\ b8<3>LQ8KM8KJ8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBiOD\ jQF<3>qeBriAtm9vq8xu7zz5zz4zz3<8>zY4zV5zS5<3>zE6wE\ 6tD6<10>w8Px8Rx7S<3>z5_<3>f5Ma5IW4E<2>_4H<3>P3DN2C\ K2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0gy0h<3>u1mt1\ ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4KW0Qc<3>5Xc6\ Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<3>civflvinvlqvotv\ sww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI<4>XC\ AaB9fB7<3>zA0<13>SA1QA1NA1<3>D92<6>UXAW`BYcC<3>hrI\ <3>UnXRm_NlcJkgFfpAaz<6>_5fc0ce7_jFR } frm:Multifractal_10 { ; Albrecht Niekamp Jan2005 ; ;p1 (spider)julia-seed ;real(p2) 5digits : (1)shape (2)outside (3)inside1 (4)inside2 (5)inside3 ;0_off 1_secant 2_mand 3_bees 4_jul 5_m_mods 6_phoen 7_newt 8_spider ; input2: 2digits_many-mods 2digits_phoenix 2digits_spider ; 1digit_shapereset:0_no 1_dblmandel 2_iter-reset 3_both +5_warp ; 4digits reset : 0_no 1_z-reset 2_iter-reset 3_both +5_warp ;imag(p2)(-) 5digits_colour(bailout) number ; input2 : 4digits(-)_mand/jul 2digits_secant 4digits_bees ;real(p3) 2digits_newt 4digits_colour1, 5digits_colour2 5digits_colour3 ;imag(p3) shape : factor (fn1), 5digits_colour4 6digits_colour5 ;real(p4) outside: factor (fn2), 4+1digits_bord-out 4digits+fract_bord-in ;imag(p4) inside1: maxit1, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor1 (fn2) 4digits+fract_border1 ;real(p5) inside2: maxit2, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor2 (fn3) 4digits+fract_border2 ;imag(p5) inside3: maxit3, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor3 (fn4) 4digits+fract_border3 ; optional: 1_lake effect, 2digits_frquency 2digits_level 2digits_ampl ;fn(1) shared by many-mods+bees ; le=0 z=pixel da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+11111 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==4)+(d==5)+(d==8)+(d==9) d4=d3==0 vb=d>5 sc=d==2 mo=d==6 px=d==7 ab=px+(d==3)+(d==5)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>1 sc1=d==2 mo1=d==6 px1=d==7 v1m=mo1+px1 v1j=d>7 dd1=v1j+(d==4)+(d==5) ab1=px1+(d==3)+(d==5)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=d>1 sc2=d==2 mo2=d==6 px2=d==7 v2m=mo2+px2 v2j=d>7 dd2=v2j+(d==4)+(d==5) ab2=px2+(d==3)+(d==5)+(d==9) d=trunc(dd/10) ex3=d>1 sc3=d==2 mo3=d==6 px3=d==7 v3m=mo3+px3 v3j=d>7 dd3=v3j+(d==4)+(d==5) ab3=px3+(d==3)+(d==5)+(d==9) d=dd-d*10 ba=imag(p5) mi3=trunc(ba) dd=(d>1)+(mi3>1) ex4=dd==2 sc4=d==2 mo4=d==6 px4=d==7 v4m=mo4+px4 v4j=d>7 dd4=v4j+(d==4)+(d==5) ab4=px4+(d==3)+(d==5)+(d==9) ; mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 dm=(d==2)+(d==4) ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex1+ex0+ex2+ex3+ex4 ; d=real(p3) dd=trunc(d) da=(d-dd)*10000000000 pp=trunc(dd/10000) ba1=dd-10000*pp ba2=trunc(da/100000) ba3=da-100000*ba2 ; d=imag(p3) sfac=trunc(d) da=(d-sfac)*100000000000 ba4=trunc(da/1000000) ba5=da-ba4*1000000 ; d=real(p4) ofac=trunc(d) da=(d-ofac)*10000000000 bh=trunc(da/100000)/10 bl=(da-bh*1000000)/10 bs=bl/2 ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) da=round((d-dd)*10000000000) d=trunc(dd/10000) dd=dd-d*10000 bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/1000) dd=dd-d*1000 bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/100) dd=dd-d*100 bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/10) dd=dd-d*10 bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=round(dd) bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) ; d=da p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 dp=p6+p0/100 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=d==3 fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 ; d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=d==3 fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 ; if (mi3==1) d=(ba-mi3)*1000000 fr=round((trunc(d/10000))*10) ;lake effect by S.Gallet d=d-fr*1000 lv=(trunc(d/100))/100 d=d-lv*10000 am=d/100 u=real(rotskew*pi/180) t=exp(-flip(u)) bo=1/real(magxmag) q=bo/0.75*imag(magxmag) dd=tan(imag(rotskew*pi/180)) da=2*q*t rs=2*bo*(dd+flip(1))*t zz=center+(-q-bo*dd-flip(bo))*t z=z-zz d=imag(conj(da)*z)/imag(conj(da)*rs) le=d<=lv if (le) dd=lv-d z=z+2*dd*(1+am*sin(fr*dd^0.2))*rs endif z=z+zz else da=(ba-mi3)*100000000000 d=trunc(da/10000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=d==3 fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 endif ; if (vb) if (d3) if (ab) z=z*le+pixel*(le==0) ;Spider c=p1 else z=z*le+pixel*(le==0) c=p1 ;newton endif elseif (ab) c=z ;Phoenix z=z*le+pixel*(le==0) else c=0.4*log(sqr(z^mm)) ;many mods z=0 endif elseif (d3) if (ab) c=p1 ;Julia z=z*le+pixel*(le==0) else ;bees c=p1 z=z*le+pixel*(le==0) endif elseif (ab) c=z ;Mandel z=0 else c=z ;Secant z=z*le+pixel*(le==0) endif t=0 bo=|z| p=pp z0=p7 zold=(0.0,0.0) cb=p9 ba=bb0 : if (tt) t=t+1 if (ex0) ex0=t<mi1 if (bo>bs) u=2*(fn1(t/sfac)) ex0=0 if (ir0) t=0 endif if (d4) z=z*u if (mo) c=0.4*log(sqr(z^mm)) else c=pixel endif else z=z*le+pixel*(le==0) cb=p9*u c=p1*u p=pp*u endif tt=tt-1+ex0 endif elseif ((ex1)&&bo>bl) if (bo<bh) d3=dd1 ba=bb1 ab=ab1 ex1=0 tt=tt-1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif if (ir1) t=0 endif if (d3) vb=v1j if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif else vb=v1m if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo1) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) ab=ab2 d3=dd2 ba=bb2 ex2=0 tt=tt-1 if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif if (ir2) t=0 endif if (d3) vb=v2j if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v2m if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo2) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) ab=ab3 d3=dd3 ba=bb3 ex3=0 tt=tt-1 if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif if (ir3) t=0 endif if (d3) vb=v3j if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v3m if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) ab=ab4 d3=dd4 ba=bb4 ex4=0 tt=0 if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (d3) vb=v4j if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v4m if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo4) c=0.4*log(sqr(z^mm)) endif endif endif endif endif if (vb) if (d3) if (ab) z=z*z+c ;Spiderjul John Horner c=c*sp+z else z1=z^p-1 ;Quasinewton Puskas Istvan z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+0.56+ph/100-0.5*zold ;Phoenix Mike Wareman zold=z z=z1 else z2=fn1(z)+c ;Many_mods Linda Allison z1=cos(z2) z=c*(1-z1)/(1+z1) endif elseif (d3) if (ab) z2=z*z ;Julia Puskas Istvan z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb ;Bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) if (dm) z=z*z+c+c*c-dp ;Double Mandel else z2=z*z ;Mandel Puskas Istvan z=z2*z2+p6*z2+c-p0 endif else z3=z ;Secant Mike Wareman z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<ba } ----------------------------------------------------------end par-----------------------------------

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FOTD 22-10-12 (Snake Resurrection [No Rating])
by Jim Muth 22 Oct '12

22 Oct '12

FOTD -- October 22, 2012 (No Rating) Fractal visionaries and enthusiasts: The very first FOTD image was posted 15 years ago on April 11, 1997. It was named "Snaketree". Today's image is a slight reworking of that old image. In an attempt to improve the original image, I zoomed in on the central tree and recolored it. The result IMO is a somewhat improved image, with more contrast and a more prominent center of attention. The name "Snake Resurrection" has nothing to do with snakes rising from the dead. It is simply a comment on the nature of the image. Way back in the prehistoric era of 1997 I wrote a new formula for each image, giving the formula the same name as the image. Thus today's fractal is the only image ever created by the SnakeTree formula, which calculates (-Z)^(1.095) then adds 3.4 instead of (C) on each iteration. The image is a fast one, finishing in its full glory in a modest 33 seconds. The glory is gloriously reflected on the FOTD web sites. The glorious finished image is online at: <http://www.crosscanpuzzles.com/Archives.html> A super-glorious high-definition rendering is available at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are online in total glory at: <http://www.Nahee.com/FOTD/> Today was absolutely perfect here at Fractal Central. The temperature of 68F 20C was perfect, the cloudless sky was perfect, and the gentle wind from the west was perfect. The only improvement I could think of would have been a few puffy clouds to add interest. Fractal cat Nicholas spent a good part of the afternoon in the sun on his shelf. The humans simply spent the afternoon. The next FOTD, maybe a trip into the FOTD past, maybe not, will be posted when it is ready. Until whenever, take care, and let's all drive to Syracuse to join the protest against the obscene profits the greedy big oil companies are making from their unfair gasoline prices. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Snake_Resurrection { ; time=0:00:33.00 SF5 at 2000MHZ reset=1950 type=formula formulafile=apr-97.par formulaname=SnakeTree passes=1 center-mag=1.79478/\ 0/3.110565/0.929/90/0 float=y maxiter=500 inside=0 logmap=yes bailout=100 periodicity=6 sound=off colors=000b8zY3zY0zQ0zY0zg0zo0zY8zHUz0tz0zz0zz0zo0\ zY0zH0zU0zg0ztCzzbzzxjzzQzz3zz0zz0z30z30z000000000\ 000000000000000000000000000000JA9000H97000F86000E7\ 5000D64000C53000B42000A3100092000081000000000Y00Y3\ cY3cYQcYQcYQcYMczMczMczHmzMmzMmzMmzMmzMmzMmzMmzMzz\ QzzQzzQzzQzzQzzQzzQzzQzzUzzUzzUzzUzzUzzUzzUzzQzzUz\ zYzzbzzbzzgzzjzzozzozztzzxzzzzzgzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzz0ozz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz\ 0zz0zt0zz0zz0zz8zzMzzYzzozzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzjzzbzzUzzQzzHzzCzz3zz0zz0zz0zz0zz0zz0zz0zz0zz0\ zz0zz0zz0zz3zz3tz3xz8zz8zzCzzCzzHzzHzzHzzMzzMzzQzz\ QzzHzzQzzUzzYzzbzzgzzjzzozzxzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzozzbzxQzgC\ zQ0z80z00z00z00z30z80zC0zH0zM0zQ0zU0zU0zY0zb0zg0zj\ 0zo0zt0zx0zz0zz0zz0zz0zU0z00zC0zY0zt0zz0zz8zzHzzQz\ zQzzYzzjzzgzzgzzgzzbzzbzz } frm:SnakeTree {; Jim Muth z=pixel: z=(-z)^1.095+3.4 |z| <= 100 } END PARAMETER FILE=========================================

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multifractal_10 environment
by Albrecht 22 Oct '12

22 Oct '12

Am 22.10.2012 06:38, schrieb Albrecht: > Hi Hal, > "What is the exact environment and version of Fractint that you run > multifractal_10 in? <---<<" > > ItÂ´s a modified WINXP (own modification), I call it "Nonet". All > network services and other > unneeded services are deactivated or set to local. So the system is > absolutely safe > and fast. No firewall, antivirus and other junk needed, good for > gaming too. > Processor AMD x4 620, 2.5Ghz, 4GB Ram, Video NV Geforce GTX460. > This has complete VESA support, incl 1600/1200. All times in the > par-files are for this reso. Fractint version 2.04.11. > I cant get full DOS-RAM in regular XP, although I tried to modify > config.nt > and autoexec.nt, so I have to change the system to use email. > Maybe some DOS-scientist can help??. All RAM settings in the pif-file > are set to automatic. > > Albrecht > > > > >

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Here's Albrecht's Beauty_Contest at 640 x 480:
by Hal Lane 22 Oct '12

22 Oct '12

I was just now successful in calculating Albrecht's Beauty_Contest fractal in DOS Fractint under WinXP that uses the version of multifractal_10 with the comments stripped out that's available in recent emails by me and Albrecht. I also stripped the comments in the .par section out as well, but I'm not sure whether I needed to do that. Here's Albrecht's Beauty_Contest at 640 x 480: http://www.emarketingiseasy.com/TESTS/FOTD/BUTYCNTST.GIF - Hal Lane ######################## # hallane(a)earthlink.net ########################

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Multifractal_10 less comments; MFR-10 Instructions
by Hal Lane 22 Oct '12

22 Oct '12

Below are: 1) Albrecht's instructions -- long version -- for how to use his multifractal_10 (MFR-10) formula, and 2) The multifractal_10 formula with all the comments stripped out, (from Albrecht's latest post) -- in hopes of being able to run it in DOS Fractint. Notes: 1) I have not yet run the multifractal_10 less comments below. I plan to give it a try -- I was unsuccessful when attempting to use the version *with* comments in April of 2011 -- I got DOS Fractint errors. 2) You'll need to choose one of Albrecht's parameter sets that he's recently posted to use with the comment-less formula below. - Hal Lane ######################## # hallane(a)earthlink.net ######################## Albrecht's Instructions on How to Use Multifractal_10 ----------------------------------------------------- ;A few words though about multifractal_10. ;It is the final version, it handles 8 basic fractal ;formulas and combines ANY 5 to one multifractal image. ;(1) Secant (Mike Wareman) ;(2) Mandel (Special version Puskas Istvan) ;(3) Bees (Ray Girvan) ;(4) Julia (Special version Puskas Istvan) ;(5) Many mods (Linda Allison) ;(6) Phoenix (Mike Wareman) ;(7) Newton (Special Version Puskas Istvan) ;(8) Spiderjul (John Horner). ;An easy tweak is real(p2) (Z-screen), just list 5 numbers ;of above list in front of the dot. Multiple entries of the ;same number or any other combinations are possible. ;To get the basic image just use one number followed by 4 ;zeros. The sequence of the five numbers defines following: ;Shape - outside - inside1 - inside2 - inside3. ;To activate S.GalletÂ´s "Lake Effect" type "1" in front ;the dot image(p5) and after the dot 6 digits as stated below. ;I did some exploring and testing, did not detect any fractint ;error. Exploring cant be complete. there are far too many ;possibilities, found that any combination delivered an image ;ready to zoom into. ; ; Multifractal_10 composes images using max 5 different formulas ; simultaneously. There are 9 frms to choose from. There are five ; "channels": basic shape, outside and inside 1-3.The transitions ; are controlled by an iteration counter or by border (z) values, ; in and out (bigger or smaller), or iteration and border ; simultaneously. ; ; At the transition points optional resets are provided, either of the ; iteration counter or the z-value (or both), which affect the coloring ; and further iteration. ; ; Five different bailout values can be applied, ranging from 1 to ; one million. The effect is compression or expansion of the colours. ; ; A unique programmable "warp-effect" can be applied to each channel. ; It changes the behaviour and looks of the channels, pending on ; previous iterations, a choosable function and a "warp" factor. Maybe ; this just means a distortion, maybe a 3d effect. ; ; Sylvie Gallet's lake effect is optional, fully integrated and ; works with all formulas, inside3 is shut off if activated. ; ; There now is a second basic "Double mandel" which allows the creation ; of "mandscapes", 2 samples with different insides, symmetric or ; asymmetric are provided. ; ; ; "Debugflag=322" must be deactivated. Please check your SS-tools.ini. ; ; Multifractal_10 Inputs: ; ; Real P2 ; First Input (before the dot) ; 5 Digits : Channels : 1_Basic Shape 2_Outside 3_Inside1 4_Inside2 5_Inside3 ; Frms: 1_Secant 2_Mandel(2) 3_Bees 4_Julia 5_Many Mods 6_Phoenix 7_Newton 8_Spider ; Second Input (after the dot) ; 2 Digits_Many Mods_Number of sides 2 Digits_Phoenix 2 Digits_Spider ; 1 Digit_Reset on Transitions (Shape) 0_no 1_Dble Mandel 2_Iter-reset 3_both +5_warp ; 4 Digits_Reset Channels 2-5 0_no 1_z-reset 2_Iter-reset 3_both +5_warp ; ; Imag P2 ; First Input ; 5 Digits_Colour (Bailout) Number for each channel (5 available) ; Second Input ; Variables : 4 Digits_Mand/Jul (2 var) 2 Digits_Secant 4 Digits_Bees ; ; Real P3 ; First Input ; 2 Digits_Newtonvariable 4 Digits_Colour1 ; Second Input ; 5 Digits_Colour2 5 Digits_Colour3 ; ; Imag P3 ; First Input ; Basic Shape : Warp-factor (fn1 is used) ; Second Input ; 5 Digits_Colour4 6 Digits_Colour5 ; ; Real P4 ; First Input ; Outside : Warp-factor (fn2 is used) ; Second Input ; Outside : 4 Digits+1fractal digit_Border-out 4 Digits+1 fractaldigit_Border-in ; ; Imag P4 ; First Input ; Inside1_Maxiter ; Second Input ; Inside1 : 1 Digit_Transition: 1_maxiter 2_borderout 3_borderin +5_maxiter+border ; 5 Digits_warp factor (fn2 is used) 4 Digits+1 fractaldigit_border1 ; ; Real P5 ; First Input ; Inside2_Maxiter ; Second Input ; Inside2 : 1 Digit_Transition: 1_maxiter 2_borderout 3_borderin +5_maxiter+border ; 5 Digits_warp factor (fn3 is used) 4 Digits+1 fractaldigit_border2 ; ; Imag P5 ; First Input ; Inside3_Maxiter ; Second Input ; Inside3 : 1 Digit_Transition: 1_maxiter 2_borderout 3_borderin +5_maxiter+border ; 5 Digits_Warp factor (fn4 is used) 4 Digits+1 fractal digit_border3 ; Alternate Input Imag P5 ; First Input : 1_Lake effect enabled (Inside3 disabled) ; Second Input : 2 Digits_Frequency 2 Digits_Waterlevel 2 Digits_Amplitude ; ; ; Inputs Multifractal_10: ; ;p1 (spider)julia-seed ;real(p2) 5digits : (1)shape (2)outside (3)inside1 (4)inside2 (5)inside3 ;0_off 1_secant 2_mand 3_bees 4_jul 5_m_mods 6_phoen 7_newt 8_spider ; input2: 2digits_many-mods 2digits_phoenix 2digits_spider ; 1digit_shapereset:0_no 1_dblmandel 2_iter-reset 3_both +5_warp ; 4digits reset : 0_no 1_z-reset 2_iter-reset 3_both +5_warp ;imag(p2)(-) 5digits_colour(bailout) number ; input2 : 4digits(-)_mand/jul 2digits_secant 4digits_bees ;real(p3) 2digits_newt 4digits_colour1, 5digits_colour2 5digits_colour3 ;imag(p3) shape : factor (fn1), 5digits_colour4 6digits_colour5 ;real(p4) outside: factor (fn2), 4+1digits_bord-out 4digits+fract_bord-in ;imag(p4) inside1: maxit1, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor1 (fn2) 4digits+fract_border1 ;real(p5) inside2: maxit2, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor2 (fn3) 4digits+fract_border2 ;imag(p5) inside3: maxit3, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor3 (fn4) 4digits+fract_border3 ; optional: 1_lake effect, 2digits_frquency 2digits_level 2digits_ampl ;fn(1) shared by many-mods+bees ; =========================================================================== =========================================================================== Multifractal_10 Less Comments ----------------------------- ========= Beginning of Formula ============================================ frm:Multifractal_10 { le=0 z=pixel da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+11111 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==4)+(d==5)+(d==8)+(d==9) d4=d3==0 vb=d>5 sc=d==2 mo=d==6 px=d==7 ab=px+(d==3)+(d==5)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>1 sc1=d==2 mo1=d==6 px1=d==7 v1m=mo1+px1 v1j=d>7 dd1=v1j+(d==4)+(d==5) ab1=px1+(d==3)+(d==5)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=d>1 sc2=d==2 mo2=d==6 px2=d==7 v2m=mo2+px2 v2j=d>7 dd2=v2j+(d==4)+(d==5) ab2=px2+(d==3)+(d==5)+(d==9) d=trunc(dd/10) ex3=d>1 sc3=d==2 mo3=d==6 px3=d==7 v3m=mo3+px3 v3j=d>7 dd3=v3j+(d==4)+(d==5) ab3=px3+(d==3)+(d==5)+(d==9) d=dd-d*10 ba=imag(p5) mi3=trunc(ba) dd=(d>1)+(mi3>1) ex4=dd==2 sc4=d==2 mo4=d==6 px4=d==7 v4m=mo4+px4 v4j=d>7 dd4=v4j+(d==4)+(d==5) ab4=px4+(d==3)+(d==5)+(d==9) mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 dm=(d==2)+(d==4) ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex1+ex0+ex2+ex3+ex4 d=real(p3) dd=trunc(d) da=(d-dd)*10000000000 pp=trunc(dd/10000) ba1=dd-10000*pp ba2=trunc(da/100000) ba3=da-100000*ba2 d=imag(p3) sfac=trunc(d) da=(d-sfac)*100000000000 ba4=trunc(da/1000000) ba5=da-ba4*1000000 d=real(p4) ofac=trunc(d) da=(d-ofac)*10000000000 bh=trunc(da/100000)/10 bl=(da-bh*1000000)/10 bs=bl/2 d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) da=round((d-dd)*10000000000) d=trunc(dd/10000) dd=dd-d*10000 bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/1000) dd=dd-d*1000 bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/100) dd=dd-d*100 bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/10) dd=dd-d*10 bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=round(dd) bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=da p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 dp=p6+p0/100 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=d==3 fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=d==3 fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 if (mi3==1) d=(ba-mi3)*1000000 fr=round((trunc(d/10000))*10) d=d-fr*1000 lv=(trunc(d/100))/100 d=d-lv*10000 am=d/100 u=real(rotskew*pi/180) t=exp(-flip(u)) bo=1/real(magxmag) q=bo/0.75*imag(magxmag) dd=tan(imag(rotskew*pi/180)) da=2*q*t rs=2*bo*(dd+flip(1))*t zz=center+(-q-bo*dd-flip(bo))*t z=z-zz d=imag(conj(da)*z)/imag(conj(da)*rs) le=d<=lv if (le) dd=lv-d z=z+2*dd*(1+am*sin(fr*dd^0.2))*rs endif z=z+zz else da=(ba-mi3)*100000000000 d=trunc(da/10000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=d==3 fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 endif if (vb) if (d3) if (ab) z=z*le+pixel*(le==0) c=p1 else z=z*le+pixel*(le==0) c=p1 endif elseif (ab) c=z z=z*le+pixel*(le==0) else c=0.4*log(sqr(z^mm)) z=0 endif elseif (d3) if (ab) c=p1 z=z*le+pixel*(le==0) else c=p1 z=z*le+pixel*(le==0) endif elseif (ab) c=z z=0 else c=z z=z*le+pixel*(le==0) endif t=0 bo=|z| p=pp z0=p7 zold=(0.0,0.0) cb=p9 ba=bb0 : if (tt) t=t+1 if (ex0) ex0=t<mi1 if (bo>bs) u=2*(fn1(t/sfac)) ex0=0 if (ir0) t=0 endif if (d4) z=z*u if (mo) c=0.4*log(sqr(z^mm)) else c=pixel endif else z=z*le+pixel*(le==0) cb=p9*u c=p1*u p=pp*u endif tt=tt-1+ex0 endif elseif ((ex1)&&bo>bl) if (bo<bh) d3=dd1 ba=bb1 ab=ab1 ex1=0 tt=tt-1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif if (ir1) t=0 endif if (d3) vb=v1j if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif else vb=v1m if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo1) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) ab=ab2 d3=dd2 ba=bb2 ex2=0 tt=tt-1 if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif if (ir2) t=0 endif if (d3) vb=v2j if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v2m if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo2) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) ab=ab3 d3=dd3 ba=bb3 ex3=0 tt=tt-1 if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif if (ir3) t=0 endif if (d3) vb=v3j if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v3m if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) ab=ab4 d3=dd4 ba=bb4 ex4=0 tt=0 if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (d3) vb=v4j if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v4m if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo4) c=0.4*log(sqr(z^mm)) endif endif endif endif endif if (vb) if (d3) if (ab) z=z*z+c c=c*sp+z else z1=z^p-1 z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+0.56+ph/100-0.5*zold zold=z z=z1 else z2=fn1(z)+c z1=cos(z2) z=c*(1-z1)/(1+z1) endif elseif (d3) if (ab) z2=z*z z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) if (dm) z=z*z+c+c*c-dp else z2=z*z z=z2*z2+p6*z2+c-p0 endif else z3=z z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<ba } ========= End of Formula ===================================

2 1

FOTD 21-10-12 (Coma Fractrailis [8])
by Jim Muth 21 Oct '12

21 Oct '12

FOTD -- October 21, 2012 (Rating 8) Fractal visionaries and enthusiasts: For years I was disappointed with the higher order fractal images, especially the minibrots, which to me at least, with a few minor differences, all look the same. Then, totally by accident, I stumbled upon the DivideBrot series of formulas. These formulas somehow combine higher order energies with quadratic energies in such a way that the higher order energies affect only the deeper sections of the fractals. Today's image is a typical scene quite deep in its parent fractal, which on the surface is an everyday Mandelbrot set. We need to go only a small distance down into the parent before we spot trouble however. The large minibrot on the main stem is already breaking up, its main bay filling with debris. Today's image lies in the debris strewn about the northeast part of its main bay. I rated the image at an 8, mostly because the prominent order-7 minibrot at the center is one of the most unusual high-order minibrots I have yet found. I might have added a half-point for the coloring, but a second thought said the present rating is high enough. The name "Coma Fractrailis" is an invented phony latin phrase, which is supposed to mean 'fractal with commas'. The seven elements arranged around the minibrot strongly resemble commas. The calculation time of one minute will be faster on modern SOTA machines and slower on older ones. All timing uncertainty may be eliminated however by checking the web sites. View the image without the effort of calculating it by visiting the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> And don't miss the high-definition version at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images and discussions are available at> <http://www.Nahee.com/FOTD/> A mix of sun and clouds, and a temperature of 61F 16C, made conditions near ideal here at Fractal central today. Fractal Nicholas appreciated both the warm sun on the shelf in the southwest window and the blowing leaves, which are still falling. It was apparent however that he missed Cassie sitting nearby. The fractal people had a not-too-cheery day. It's still rather glum here at FC with only one lonely cat trying to keep things active. The next FOTD will be posted before too much time passes. Until whenever, take care, and look to the light. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Coma_Fractrailis { ; time=0:01:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-1.749144546273318/+0.00657273175035928\ /1.140195e+013/1/-13.25/0 params=7/10000000/0/0 float=y maxiter=1800 inside=0 logmap=66 periodicity=6 mathtolerance=0.05/1 colors=000ABU9DZ7FZ4HZ2JZ0LZ4N`8QaCTcGWdJ_eNbgRehV\ hjYlkaqliuzqzzoxzmtznquonrpkmqhmrelsbkt_kuXjvUjsRh\ qPgnNflLeiJcfHbdFabCY`AUY8PW6KV4FS2AO0AK3AE5AC87AA\ 2CD2EF3FI8PKEUNJcPOocUnc_mc_zc`kZaj_aiabhcbfecegdd\ hdcjeblfanf`pg_qgZmeZjdYgcYdbXaaXZ`WW_WTZVQYVNXUKW\ UHVWLUXPUYSUZWU`_UabUbfUcjUemUfqUguUhxUcwRZvOUuLPt\ IKsFFrCAq95p61p35q78qBCqEFqIJqMMqPJoSHnUFmWClYAj_8\ ia5hc3ge1fg1ik8jm8km9lm9mmAmmAmmBmmCmmCmmdiNdiNehO\ ehOfhPfhPghPhgQhgQigRigRjfSjfSkfTkfTleUzeUzeUzeVze\ VzdWzdWzdXzdXzcYzcYzcZzcZzcZzaYz`Xz_WzZVzYVzWUzVTz\ USzTSzSRzRQzPPzOOzNOzMNzLMzJLzILzHKzGJzFIzEIzFHzGH\ zHGzIGzJFzKFzKEzLEzMDzNDzOCzPCzPBzLBzMAzNAzO9zP9zQ\ 8zQ8zR7zS7zT6zU6zV5zV5zT8zRAzPCzPEzPGzPIzPLzPNzPPz\ PRzZTzZVzZXzZVzZTzZRzZPzZNzZLzZJzZHzZFzZDzZEzZEzZF\ zZFzZGzZGzZFzZFzZFzZFzZFzZFzZFzZFzZFzZFzZFzZFzZFzZ\ FzZFzZFzZFzZFzZFzZFzZFzZF } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

1 0

Re: [Fractint] Multifractal_10
by Hal Lane 21 Oct '12

21 Oct '12

Below are a couple of links to where Albrecht's: Multifractal_10 formula was used by Jim Muth -- on April 17th and 24th in 2011. Albrecht's formula and the .par files are in the files pointed to by "Jim's posts" for these dates: FOTD -- April 17, 2011 (No Rating) FOTD -- April 24, 2011 (No Rating) Links to Jim's images, .par files and the formula are on this page: http://tinyurl.com/April-2011-FOTD or: http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd_2011_04_Apr.html Albrecht told me that if someone had memory overflows running his formula in DOS Fractint, that they could try removing all the comments from it, so it might possibly not overrun any buffers... I plan to remove the formula's comments and post it, to make it easier to try to use -- if you've been having a problem running it, as I have had. - Hal Lane ######################## # hallane(a)earthlink.net ########################

1 0

FOTD 20-10-12 (Iterative Bebop [8])
by Jim Muth 21 Oct '12

21 Oct '12

FOTD -- October 20, 2012 (Rating 8) Fractal visionaries and enthusiasts: Today's image takes us into a Mandelbrot set corrupted in its depths by Z^10 energies, where we check a tiny minibrot on the main stem, some distance east of the large minibrot. This tiny minibrot is just starting to change from quadratic to order-10. The change is visible as bits of debris that have just appeared in the normally open areas of the main bay and bud. Today's scene lies in a kind of island that has arisen from the sea in the northern part of the main bay. The most unusual thing in the image is the unexpected patterns surrounding the satellite minibrots. We like to think of the higher-order fractals as being 'all the same', but today's image shows that, when combined with the Mandelbrot set, higher-order images can produce some quite unusual scenes. The name "Cherry Cheese-Cake" came about when I noticed the colors of the main central ring. The rating of an 8 includes the usual bonus for my coloring, which in today's image is perhaps a bit over-rated. The calculation time of 1-5/6 minutes is a reasonable price to pay for today's image, which will certainly surprise those who expect nothing but a lot of moth-eaten circles in an image with so much Z^10 energy. The finished image is posted online and ready to deliver the surprise at: <http://www.crosscanpuzzles.com/Archives.html> A rendering in high-definition is available at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are posted at: <http://www.Nahee.com/FOTD/> Today began with clouds here at Fractal Central. The clouds hung on until midday, when the sun suddenly burst through, bringing a glorious end to the day. The temperature of 59F 15C was a bit hard to enjoy due to the clouds. Nicholas the cat spent a good part of the day watching falling leaves. He also had several bouts of dashing up and down the long hallway, just as he did when Cassie was here to chase him. The next FOTD will be posted when the time is right. Until whenever, take care, and if Nicholas continues chasing and being chased by something invisible, I might have to admit that cat spirits do indeed exist. My credulity should not be so shocking to fractal rationalists however, since I have already stated that information can travel backward in time, as it did during the week preceeding 9-11, and therefore, at least one paranormal phenomenon, (precognition), is true. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Cherry_Cheese-Cake { ; time=0:01:50.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-1.674495682723143/+0.00008260622076861\ /2.610704e+009/1/52/0 params=10/1e+020/0/0 float=y maxiter=7200 inside=0 logmap=53 periodicity=6 colors=000zzzzxszwmzvcztUzpAmn8lhClcFlZIkTMkOPkJSj\ DWj8Zj3ag2Ud1Na1GZ09X02Z27`4Bb5Fd7Jf9NhARjCVkDZfHW\ bLTYOQUSOQVLLZIHaFDeD8hA4l70o54iB7dHA_NDUSGPYJKcMF\ hJB`zzzzzmwwcms8kqKio7fk8cg9`c9Z_AWWBTTBQPCOLDLHDI\ DEGAEFBFFBFFBFFBFFCFFCGFCGFCGFDGFDGFDHFDHFEHFEHFEH\ FEHHHKJJMLLOMNQOPSQRURUWTWYVY_W_aYac_ce`egddggcgjb\ gnagq`gt_gy_hxffxiexjdsjcnhbifadd``b_W`ZRZYMXXHVWD\ UWASVDTWFUWHVXJWXLWXNXYPYYSZYU_ZW_ZY`Z_a_ab_bb_cb_\ cb_`aXZaVW`SU`QS_OP_LNZJLZHIYEGYCEXABX79W54U07W3AY\ 5C_8FaAHcDKeFMfHPhKSjMUlPXnRZpUarWdrTfrWcrY`p`YmbV\ jeSggPdjMalJZoIYpHWqCWc7WR2WE3VH4VK4VN5VP6VS6VV7VY\ 8U_8Ub9UeAUhZGRZLOYPMYUKYZHmsFkrDiqAgp8eo6cn8am9_j\ AagBbdDdaEeZFgWGhTIiQJkNKlKLlGNmHMmHMmHLnILnIKnIKo\ JJoJJoJIpKIpKHpKHnMIpKHqIGsGGtEFuDFwCEuDFtEGsFHqFI\ pGJoHKmILlIMkJNiKOhLPhLPgLQhNTiOVjPXjRZkS`lTblVdmW\ fnXhnZjo_lp`npbpqcrdGCeLB } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

2 1

FOTD 18-10-12 (Iterative Bebop [7.5])
by Jim Muth 18 Oct '12

18 Oct '12

FOTD -- October 18, 2012 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image is named "Iterative Bebop". The name came about when something in the image reminded me of the 'bebop' music that developed in the mid 20th century and promised so much more than it delivered. In fact, only certain present-day 'music' delivers less. IMO, the unabashed popularity of the current 'music' simply shows the lack of sensitivity of the current noise-addicted fans. The parent fractal of today's image came about when I iterated the expression Z^(1.6)+C three levels up the hyperladder with no function applied. This parent resembles a moth-eaten M-set rotated so that its main bud faces southeast. A very prominent disconnected and distorted minibrot lies just north of the main bay of the parent. Today's scene lies in what appears to the East Valley of this minibrot. The minibrot at the center of today's image is of order 1.6, though it bears little resemblance to a typical 1.6 minibrot. The highly fractured surrounding pattern is unusually brilliant, a result of the colors, which took nearly a half hour to get almost right. The calculation time of 2-1/4 minutes is slightly slow. The web sites cam speed up things quite a bit. For maximum speed and convenience the finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> For maximum pleasure it is posted in high-definition at <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> For maximum appreciation the back images are online at: <http://www.Nahee.com/FOTD/> The day began sunny here at Fractal Central, but by mid- afternoon the clouds moved in, with rain expected by night. The temperature reached a comfortable 66F 19C. Nicholas, the remaining fractal cat, spent a good part of the day playing in his cat cube complex. Curiously, he still acts as though an invisible Cassie were in the house, playing with him. I guess no one has told him that cats do not have spirits. The humans spent the day doing human things, such as getting the work finished. The next FOTD will be posted when it is ready. Until whenever, take care, and who knows. Maybe cats do have souls and maybe Nicholas has gotten over his loss so quickly because Cassie is still here, at least to him. (I must ponder the implications of his behavior.) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Iterative_Bebop { ; time=0:02:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-0.66753502154/+1.096587351422/4506788\ /1/-25/0 params=1.6/0/3/0 float=y maxiter=2750 inside=0 logmap=208 periodicity=6 colors=000Ge8Fe7Ed7Dc6Ca6BZ5AV59S47O36L35H24E23A12\ 71130_dzX`qUYlRYaOXUPWGPUGPTHPRHPQHPOIQNIQLJQKJQIJ\ QGKQFKQDLRCLRALR9MR7MR6NR4NR3NO2LM2JK2HI2FF1DD1BB1\ 9110917605403201VzBSuAQq9Om8Mi8Ke7I`6GX5ET5CP4AL38\ G26C2481240PkFOiENgDMeDLdCKbCJ`BI_BHYAGWAGU9FT9ER8\ DP8CO7BM6AK69I58H58F47D46C35A3482362251131010f7oc6\ k`6hY5eW5bT4ZQ4WO3TL3QI3MG2JD2GA1D819506203hY8fW7d\ V7bT6`S6ZQ6XP5VN5TM5RK4PJ4NH4LG3JE3HD3FB2DA2B82971\ 7515413201108wg7sd7oa6l_6hX5eV5aS4ZP4VN3SK3OI2LF2H\ C1EA1A7075032QbcDJKEJ3DI2CH2BG2BF2AE29D29C18B17A17\ 91681571461450340230220110000NAQL9OK8MI8LH7JF6HE6G\ C5EB5DA4B839738526414213101mWniTjeRfbPcZM_WKWSITPG\ PLDLHBIE9EA6A747323n7Ao69p69q69r68sU8tU8uU7vU7wU7x\ Z6yZ6zZ6zZ5zU5zU5zU4zU4zK4zK3zUzzUzzUzzUzzKzzKzzKz\ zKzzKzzKzzKzzKzzKzzKzzKzzKzz3zz2zz2zz2zz2zz2zz1zz1\ zz1zz1zz1zz0zz0zz0zz0zzsz } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 17-10-12 (Spokes and Spirals [7.5])
by Jim Muth 17 Oct '12

17 Oct '12

FOTD -- October 17, 2012 (Rating 7.5) Fractal visionaries and enthusiasts: The parent fractal of today's image is one of the most unpromis- ing of all time -- little more than a large open circle with degenerate buds along its circumference. But the east side of this circle holds hints of Mandelbrot stuff, and as one looks closer, the hints prove to be entire worlds. Today's scene lies in a remote non-critical valley near an unpromising bud in this island of chaos. To create the parent circle, I combined 1/2 part of Z^2 with 1/10 part of Z^3 on each iteration, then and added 1/C. Perhaps the most interesting feature of the image is its combination of open areas, straight spokes and spirals. The spokes and spirals explain the name. The rating of 7-1/2 includes a half-point bonus for my work on the colors. It really did take nearly 1/2 hour to get the colors almost right. The calculation time of 15 minutes will pass slowly. But here is where the FOTD web sites come in handy. Make life easy by checking the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> Make it easier by seeing a high-definition rendering at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> For perpetual enjoyment, the FOTD back images are online at: <http://www.Nahee.com/FOTD/> When the morning fog cleared off, sunshine ruled the roost here at Fractal Central today. A few decorative angel-hair cirrus clouds in the afternoon merely added to the splendor. Fractal cat Nicholas passed the afternoon sleeping in the sun. From the way he sometimes behaves since Cassie's departure, I would assume he is interacting with her conscious left-over energy field. (Could I call it her spirit without arousing the wrath of rationalists who know that conscious spirits do not exist? [I guess it's all right as long as I consider such belief to be merely a comforting and harmless fantasy.]) FL passed the day putting her garden to sleep; I passed the day pondering the mysteries of existence. The next FOTD will be posted when the time is right. Until whenever, take care, and how can we make statements about the existence of things like spirits when we can't even agree on whether the Mandelbrot set actually exists? (I, for one, have seen nothing of the set more than a lot of pictures.) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Spokes_and_Spirals { ; time=0:15:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=t center-mag=-0.307016313251/+0.219156404541/6.96e+9\ /1/-7.5/0 params=0.5/2/0.1/3/0/0/0/0 float=y maxiter=5700 inside=0 logmap=784 periodicity=6 colors=000CDNDEOEFPFGQGHRHISIJTJKUKLVLMWMNXNOYOPZP\ Q_QR`RR_RRYRRXQRZPR_PR`ORbNRcNRdSRgXRjaRmfRpeQndPl\ dOkcQibRgbSfaUdaVc`Wa_Y__ZZZ_XYaVYbUXcSXdRVkJTrCRy\ 5Pz0Oz0Oz1Nz3Nz4Nz5My7Mx8Mw9LvBLuCKtEKsFKrGJqIJpJJ\ pKHnJFlJEjJChJBfI9dI8bI6`I5ZH3XH3VH3TH3RH3TG7UFBWF\ EXEIZEM_DQaCTbCXdB`eBdgAgh9kj9ok8rl8mqEhuJ3hH4dF6`\ D8XBAUACQ8EM6GI4IF3KH6MI8OKAQLCSMETOHVPJXQLZSN`TPa\ URZWOWXLTZIQ_GOaDLbAId8Fe5Cg2Ah0NXjMYiMZhLZgL_fL_e\ K`dKacJacJbbJbaIc`Id_HdZHeYHeYUhbzrzznjvkhthfredoc\ bm``jYZhVXgTVfQTeNRcKPbINaFL`CJ_9HZ7FYCIYGLYKNYOQY\ SSXWVX_XXd_XhaXldWpfWtiWxkWznWzp3Re4Pc7ObAN`DM_GLZ\ JKXLJWOHVRGTVFSZERbDPiCOiBNnCPpCRpDSzDUsDWzEX_EzZE\ zYFzXFzXFzWGzVGzVGzEJz3LzANzMOzYPgiQlrRq4g35e45c46\ b57`58Z69Y79W7AU8BT8E`5C`4B`4Aj39j38j27t16t15t0_z0\ _z0_z0_z0_z0_z0_z0iz0iz0iz0rz0rz0rz0rz0rz0rz0rz0rz\ 0rz0rz0rz0rz0rz0rz0rz0rz0 } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD 08-10-12 (Terminus [7.5])
by JackOfTradeZ＠comcast.net 17 Oct '12

17 Oct '12

. Jim (and Fractal Lady), I offer sincere condolences for your loss. I understand what you are going through. I lost the best, dearest friend I ever had (a White German Shepherd). It has been well over 2 years and I'm still not over it, still have tearing spells. JoTz .

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FOTD 16-10-12 (Forever Onward [8])
by Jim Muth 16 Oct '12

16 Oct '12

FOTD -- October 16, 2012 (Rating 8) Fractal visionaries and enthusiasts: Today's image came about when I combined Z^2 with 0.2 parts of Z^3 on each iteration before adding a very unusual log(c). Since the MandAutoCritInZ formula is meant to produce Mandelbrot images, we are actually using the logarithm of the pixel. The resulting parent fractal is little more than a tiny series of bays spread along the X-axis. Today's scene is located in the East Valley area of a prominent minibrot just north of one of these bays. The name "Forever Onward" suggests the unending detail of fractals. The rating of a solid 8 owes a full point to the coloring, which I spent nearly an hour getting almost just right. The image is one of those rare ones in which a negative logmap gives the best coloring. The calculation time of 45 minutes is excessively slow, but luckily, viewing the image on one of the web sites will reduce the delay of enjoyment notably. The finished image is online at: <http://www.crosscanpuzzles.com/Archives.html> A high-definition rendering is available at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are posted at: <http://www.Nahee.com/FOTD/> Pleasant autumn weather prevailed here at Fractal Central today, with partly cloudy skies and a high of 59F 15C. The remaining fractal cat, Nicholas, passed most of the day on the shelf in the southwest window, watching the world go by, probably remem- bering Cassie. When Cassie was here she would sometimes hide, then suddenly dash out and surprise Nicholas, causing him to leap into the air and get a bristled tail. Monday evening while Nicholas was walking peacefully down the hall, he suddenly leaped into the air and his tail bristled as though Cassie had just surprised him. Science (at least the skeptics) says there are no such things as ghosts, much less cat ghosts. They say belief in unseen things such as ghosts is an outdated superstition carried over from a less enlightened era. Apparently Nicholas has not heard the news however. The humans made it through the day with nothing going wrong, which is easier said than done. The next FOTD will be posted whenever it is posted. Until whenever arrives, take care, and if I had created the world, I certainly could have done a better job. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Forever_Onward { ; time=0:45:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=log passes=1 center-mag=+0.04926340855299391/+0.008282418603709\ 65/3.21828e+009/1/-15/0 params=1/2/0.2/3/0/0/0/0 float=y maxiter=8400 inside=0 logmap=-894 periodicity=6 mathtolerance=0.05/1 colors=000KKaLK`MK_NKZOKZPKYQKXRKWSKVTKVUJUWITYGS_\ FSaDRcCQeAPg9Pj9Ll9Im9Fn9Cq99t96q86n76k66h56e46b36\ _26X18U1AR1BO1DM1EO1GR0IT0JW0LY0M`0Ob0Pf7MiDJlJHoP\ ErVBu`9tbDtcGtdJteMtfPsgSshVsjZskasldrmgrnjromrppr\ qsmkrieqe`qf_pgZphYphXoiWojWokVnkUnlTnmSmnSmnRmoQl\ pPlqKlqKlmKhiKdeKaaKYYKUUURQUPNUNKULHUKEUIBUG8UF9U\ GAUHBUHCUIDUJEUJFUKFcLGcLHcMIcNJcNKcOLcPLcPKmRJmTI\ mVHmXGmZFz`EzbDzdCzfBzhAzjAzkWzepz_rzZtzYzzYzzXzzW\ zzVzzUzzUzzTzzSzzRzzQzzQzzPzzOzzNzzMzzMzzLzz1zzKzz\ JzzIzzIzzHzzGzzFzzFzzEzzDzzCzzBzzBzzAzz9zz8zz7zz7z\ z6zz5zz4zz3zz3zz2zz1zz0xz8uz7rz7pz6zz6jz6hz5ez5bz5\ `z4Yz4Vz4Tz3Qz3Nz3Lz2Iz2Fz2Dz1Az17z15z02z0_z77zB6z\ A6z95z95z85z84z74z74z63z63z53z42z42z32z31z21z21z10\ z10z0Qz1Pz0Oz0Nz0Nz0Mz0Lz0Kz0Kz0Jz0Iz0Hz0Hz0Gz0Fz0\ Ez0Ez0Dz0Cz0Bz0Bz0Az09z08z08z07z06z05z05z04z03z02z\ 02z01z00z0rzapz_nzZlzYkzX } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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IFL
by Mark Christenson 16 Oct '12

16 Oct '12

Damien, I have a question. I submitted my resurrected fractal site for the IFL a few weeks ago and haven't heard anything. Is the submission process inactive? Should I resubmit? Thanks, Mark AKA Bud

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While Jim Muth is not posting FOTD images...
by Hal Lane 14 Oct '12

14 Oct '12

While Jim Muth is not posting FOTD images due to the death of his much-beloved cat, Cassie, I'm posting a few more 'investigations' into the parent fractal of his FOTD for Oct. 8th, 2012. Main page: http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html Click "October" in the 2012 column to get to the October, 2012 page that has these additional images. - Hal Lane ######################## # hallane(a)earthlink.net ########################

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Re: [Fractint] FOTD 08-10-12 (Terminus [7.5])
by RENRAD1＠aol.com 12 Oct '12

12 Oct '12

I'm so very sorry to read of your loss. May cherished memories and a successful search for a candidate for introduction to the household ease the road ahead. sincerely, peter m spencer

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FOTD status
by Jim Muth 12 Oct '12

12 Oct '12

Fractal fans: I would like to put rumors to rest. The FOTD is not terminated forever, but it will be on hold for a while. Here at Fractal Central we are still dealing with the unexpected departure of Cassie, one of the fractal cats. Nicholas, the remaining fractal cat, is slowly adjusting to the loss of his lifelong playmate. We will eventually find a new lady companion for him, but only time will tell if she will be able to fill the void. Meanwhile, I am still exploring and finding interesting fractals, and saving them for future FOTD's. JIM

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FOTD 08-10-12 (Terminus [7.5])
by Jim Muth 08 Oct '12

08 Oct '12

FOTD -- October 08, 2012 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image is named "Terminus". The word implies an ending, and as far as I know, today's fractal might be the final FOTD. On Saturday, fractal cat Cassie was a little lazy. On Sunday morning she was gasping for breath. When we rushed her to the doctor, he said she had severe pneumonia and put her on oxygen, but he told us she probably would not make it. When the phone rang at 2:30 last night, we knew what it meant. Enough said about that, but with no fractal cat activity to comment on, I now see little reason to continue finding and writing about the simple basic fractals I have been finding in my daily searches, which have fascinated me for the past 15 years but were hardly considered great even when I began posting them. For several years, as has been obvious from my closing comments, my interest has been shifting from fractals-101 more to philoso- phy, science, religion and the human condition. I might combine my thoughts and expand them into a book. If I continue with fractals, I might pick up one of the fast modern-day S.O.T.A. machines and join the legion of fractal fans trying, usually futilely, to make a bit of money from fractal stuff such as giant posters, t-shirts, bags, stained glass, coffee mugs, etc. One thing certain however is that I will continue reading and posting comments to the list. If I turn up any truly great fractals, I will post them, with or without comments. Today's image, which rates a 7-1/2, lies in the parent that results when 2 parts of Z^(-2.2) are combined with 0.2 parts of Z^(-12.2) and (1/C) is added on each iteration. This parent resembles a partially obscured 3-leaf clover, with today's image located in a tiny bud on the southern shore line of the eastern bay. The calculation time of 5-3/4 minutes is a bit slow, but hey!, you would not want to miss what could be the final FOTD image. The web sites will make the viewing notably easier. The completed image is online at: <http://www.crosscanpuzzles.com/Archives.html> A high-defenition rendering is at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The entire FOTD library is at: <http://www.Nahee.com/FOTD/> A chilly cloudy day prevailed here at Fractal central today. The temperature topped out at 54F 12C. With the loss of one fractal cat, the humans had a dejected day. The next FOTD might eventually be posted, but that day is not yet in sight. Until then, if ever, take care, put on those rose-colored glasses and look for the bright side. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Terminus { ; time=0:05:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=+0.5131103181014518/-0.5309527846287503\ /1.26e+09/1/35/0 params=2/-2.2/0.2/-12.2/0/0/0/0 maxiter=3600 inside=0 logmap=600 periodicity=6 colors=000VXdhfEbfIUYcRZQLhUTZbS_`JcaS_aU`bW`bY`c_\ `c``db`dd`ef`eg`fi`fk`gm`gn`hp`hr`it`iu`it_jsZjrYj\ rXjqWjpVjpUkoTknSknRkmQklPklOkkNijMgiLehKcgJafI_fH\ YeGWdFUcETbDRaCPaBN`AL_9JZ8HY7FX6DX5C_9GaDJcHNfLQ3\ csjTXlX`4bpqdgshj5amunonln6`jbhlXfk7_gKbiE`h8Zf2Xf\ 4Zc6_c7`_9aY7_dCcTEdR8_eHfNLdN9_fV_N_YNA_ghTNmRNB_\ hvNNtLWC_hqHlpFtoKpnOmmSjlXfk`cjd`iiXhmUgqRguORcSA\ NWELYHJ_KI`NGbQFcUDeXCg_Ahb9je7ki6ml4oo3pr1ru0s0lB\ NSHi8NeETbJY_PcXUhUZmMOkEDi63hCEXIPMHQOHRPGSQGSSFT\ TFUUEVWEVXEWYDX_DY`CYaCZcB_dB`eB`f3425847B59F6BI8C\ M9EPAGTCIWDJZEHaJFcNDeSBgW9i`7kdFl`MlYUmU`mRgmOjlT\ mlYplbslgvllxlpvioufnscmr`lpYkoVjmSilPhjMgiJgNGuRJ\ pUMlYPh`SddV`gYXk`TncPifOehNajMXlMTnLPpKLrJGtJCvI8\ xH4zHEqFNhEW_DdRBmIAvA9tDArFBqHCoKDnNElQFkTGiWHhZI\ faJedKcgLbjM`mN_pO`sO`vOaxObzNczNzzNzzNzzNzzNzzBzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 06-10-12 (The Greatest Mystery [7])
by Jim Muth 07 Oct '12

07 Oct '12

FOTD -- October 06, 2012 (Rating 7) Fractal visionaries and enthusiasts: Fractals are one of the greatest mysteries, but perhaps the greatest mystery of all is the human brain, which by some strange coincidence is brought to mind by today's image. The other day on one of those pop-neuro-science shows on TV, I heard the statement that 'you are your brain'. This sounds harmless enough as long as one does not think too deeply about it, but the deeper one thinks, the less sense the statement makes. If I *am* my brain, as neuro-science claims, and I *have* a brain, which is a fact, then it is stated that my brain has a brain, which makes no sense at all, since there is only one brain. Just what is this mysterious 'I' that has a brain? Maybe the implication is that the 'I' in question is a mere illusion generated by my brain, which would mean the illusion has a brain. Or maybe the illusion is having an illusion of having a brain. Or maybe we should simply state that my brain *is* my brain. Where the heck has reality gone? I thought science was based on reason and common sense. Until neuro-science can get its act together and make clear the process of the generation of self-awareness from unconscious meat, the brain will likely remain the greatest mystery. Since today's image rather resembles a brain, I have named it "The Greatest Mystery". Almost as non-sensical as the world of neuro-science is the world of the fourth spatial dimension, which exists in the world of mathematics, though not in the world of 'reality', makes even less sense. Today's image is a near-Julia scene along the X-axis at the eastern edge of the main bay of the (-Z)^(2.5)+C Mandeloid. It is a four-dimensional scene, since it is double- rotated 1 degree and 1 degree from the exact Julia orientation, and double rotation (around two totally perpendicular axis planes) is not possible in 3-D space. The image, with its two hemispheres, is very close to being a fractal tree. A different view might have made it a tree. But it is not quite close enough to justify a tree-like name. Even with all the image's color and all the reality and illusion talk, I could give the image a rating no higher than a 7. The calculation time of 3-1/4 minutes is within reason, though the web sites are more reasonable. For total reason, check the finished image online at: <http://www.crosscanpuzzles.com/Archives.html> A rendering in hi-def is available at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are at: <http://www.Nahee.com/FOTD/> Clouds, occasional showers and a cooler temperature of 63F 17C prevailed here at Fractal Central today. The fractal cats checked the conditions early, then decided to take it easy. With FL feeling a bit under the weather, the humans simply took it easy. The next FOTD will be posted in a reasonable time. Until whenever, take care, and the distance between two objects is determined by the amount of empty space between them. But empty space is nothing, so how is it possible to have more or less of nothing? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= TheGreatestMystery { ; time=0:03:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot5 passes=1 periodicity=6 center-mag=0.619222/0/8.51924/1/90/0 params=89/0/\ 89/0/0.375/0/0/0/2.5/0 float=y maxiter=10000 inside=0 logmap=yes colors=000100SEDQDCOCBMBALA9J98H88F77E76C65A548447\ 33522311100x7Tt6Rq6Pn5Ok5Mg5Ld4Ja4IZ4GW3FS3DP2CM2A\ J29G17C1691460330181Q60J40D206TpiRmgQkePicOgaNe`Mc\ ZLaXK_VIYUHWSGUQFSOEQNDOLCMJBKHAIF8GE7EC6CA5A84873\ 6524312110T00P00M00J00G00C009006003gbfe`dcZbaY`_WZ\ YUYXTWVRUTQSROQPMPNLNMJLKHJIGHGEGEDECBCB9A98876754\ 53331119SD8RC8QC8PB7OB7NA7MA6L96K96J85I85H85G74F74\ E64D64C53B53A4394284273263152142131021010000tVvqTs\ oSqmRokQmiPkgOheMfcLdaKbZJ`XIYVHWTGURESPDQNCOLBLJA\ JG9HE8FC6DA5A8486364242127ai5SY3JN19BSjXQfUOcSM`QK\ YOIVMGSJEPHDLFBID9FB7C8596364132QgGKZCFQ9AH6583yPP\ vOOtNNrMMpLLnKKlKKjJJhIIfHHdGGbFF`FFZEEXDDVCCSBBQA\ AOAAM99K88I77G66E55C55A4483362241c20cN3cdMcdLccKcc\ JccJccIcbHcbHcbGcaFcaFcaEcaDc`Dm`Cm`Bm`BmZAmYAmX9m\ V9mU9mT8mS8mQ7mP7mO7mM6mL6mkHzK6zJ5zH5zG4zF4zE4zC3\ zB3zA3z82z72z61z51z31z20z } frm:SliceJulibrot5 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=(-z)^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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FOTD 05-10-12 (A Third Opinion [6])
by Jim Muth 06 Oct '12

06 Oct '12

FOTD -- October 05, 2012 (Rating 6) Fractal visionaries and enthusiasts: Today's image is the third scene from the parent fractal of the FOTD of October 3, which explains the name "A Third Opinion". In today's exploration into fractal semi-chaos, we check the situation far out on the zigzag filament that extends northwest from the oversized bud of the parent. Rather than coming to a well-defined limit, this filament disintegrates into ever smaller and more disconnected pieces, ultimately becoming a twisted string of fractal bits, which finally dissipates. The minibrot in today's image lies far out on this filament. It is the last one I could find, though it is certainly not the last minibrot on the filament. Most likely there is no last minibrot. The rating of a 6 indicates that I consider the image to be a come-down from yesterday's image, which was a come-down from the day before. The calculation time of only 10 seconds (plus shipping and handling) is no mistake. The image really is that fast. But it is not available in stores. The finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> But wait! A high definition rendering is posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are posted at: <http://www.Nahee.com/FOTD/> After the early morning fog cleared off, today was really quite pleasant here at Fractal Central, with sunny skies and a temperature of 77F 25C. But it could be the last pleasant day for a while. The weather people forecast rain and much colder temperatures for the next few days. The fractal cats enjoyed the sun, forgetting the extra treats. The humans, who get all the extra treats they want, had an average day. The next FOTD fractal will be posted before too long. Until whenever, take care, and always remain fractally alert. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= A_Third_Opinion { ; time=0:00:10.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident float=y center-mag=-1.196727555403/+2.77816601291/1351948/\ 1/177.5/0 params=1.5/0/51/0 maxiter=1750 inside=0 logmap=31 periodicity=6 colors=000MF`LD_KCWF9QIAOG8LE6H00053D62IA75HB5LG5P\ K5TP4XUAbZFicKnhPtmUyrZzvaztZzqUymPtnKnkFiaCcUAYKB\ VACSwDPmENfFKdOH`cESmBQz9YzEgzJYzNNzSNmXMc`MUeLCiL\ BhKChJDgIEgHEgGFfFGfFGeEHeDIeCIdBJdAKdAKbBM`BOmCQw\ CSwDUhDWhEYhE_hFamFcZGeZGgZHiZHjIHkJIkJIlJImJImJJn\ JJoJJoJJpIKoJJpJJpJJpJJpJJpKJpKJqKJqKJqKIqKIqLIzD5\ zC5zB5zA5z95z85z75z65zOHzeTzvcftbdrabp``n_ZlZzjYzh\ XzgXzeWzcVzaUz_TzYSzWRzUQzTQzVPzXPzYPz_Pz`PzbPzdPz\ ePzgPzhPzjPzlPzmPzoPzpPzoOzoNznMznLzmKzmJzlIzlHzlG\ zkFzkEzjDzjCziBziAzi9zf9zb9zZAzVAzRBzNBzKBzLAzRUzT\ RzUOzVLzXIzYFz_Cz`9za6z_8zYAzXCzVEzTFzSHzQJzOLzNMz\ G6zE5zC4zB3zZfQhf9hfEhfIhfMffQcfUbfSafRafQ`fP_fO_f\ NbfMd_Lf`Ki`KkaJmaJpbIrbItcHwcGwzGwzFwzFwzHtzJpzLl\ zNjzQizThzVgzYfz_ezbdzdczgbzidzgfzehzcizakz_mzYnzW\ pzUrzStzQuzOwzMwzKwzIfzMczMazNZzNWzOTzOQzPOzPTzUXz\ ZazbezgjzlnzplznjzlQzbOza } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 04-10-12 (A Second Opinion [7])
by Jim Muth 05 Oct '12

05 Oct '12

FOTD -- October 04, 2012 (Rating 7) Fractal visionaries and enthusiasts: Today's image is another scene in yesterday's parent fractal, though instead of checking the large bud, we check the east edge of the main bay, just south of the broad peninsula that is trying, though not too successfully, to be an East Valley. The fractal patterns in this area are entirely different from those on the shore line of the large bud. Instead of loops, we see sharp-pointed, rather dark and ominous elements that would make a fitting cover for a paperback horror novel. The name "A Second Opinion" indicates that today's image is the second venture into the same parent fractal, and, as is the case with medical doctors, a second opinion sometimes brings an entirely different outlook. A rating of a 7 is entirely justified, at least in my opinion. The pattern surrounding the tiny central minibrot may be highly fractured, but it is regular enough to make a recognizable, semi-organized minibrot basin. The calculation time of 1-2/3 minutes is fast enough to leave time for fun or business. Time-saving joy may be found at the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> where the finished image is posted. Hi-def joy is online at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are blissfully available at: <http://www.Nahee.com/FOTD/> Heavy clouds, fog and drizzle spoiled the entire morning here at Fractal Central. Some sun broke through in the afternoon, and the temperature reached 72F 22C, but by then the damage had been done and the fractal cats were in unhappy mode, demanding extra treats. The humans had another un-notable day, one that was peaceful to experience but boring to read about. The next FOTD will appear in a reasonable geologic time. Until that wondrous moment arrives, take care, and debate the debate. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= A_Second_Opinion { ; time=0:01:40.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=+0.442996736165/-0.063360789746/6e+007/\ 1/-85/0 params=1.5/0/51/0 float=y maxiter=1750 inside=0 logmap=144 periodicity=6 colors=000MF`LD_KCWF9QIAOG8LE6H00053D62IA75HB5LG5P\ K5TP4XT4bX4h_4mc3rf3wj3wm3wp3wn5wl6rj7mi8hg9ceAYcB\ VbCSwDPmENfFKdOH`cESmBQz9YzEgzJYzNNzSNmXMc`MUeLCiL\ BhKChJDgIEgHEgGFfFGfFGeEHeDIeCIdBJdAKdAKbBM`BOmCQw\ CSwDUhDWhEYhE_hFamFcZGeZGgZHiZHjIHkJIkJIlJImJImJJn\ JJoJJoJJpIKoJJpJJpJJpJJpJJpKJpKJqKJqKJqKIqKIqLIzD5\ zC5zB5zA5z95z85z75z65zOHzeTzvcftbdrabp``n_ZlZzjYzh\ XzgXzeWzcVzaUz_TzYSzWRzUQzTQzVPzXPzYPz_Pz`PzbPzdPz\ ePzgPzhPzjPzlPzmPzoPzpPzoOzoNznMznLzmKzmJzlIzlHzlG\ zkFzkEzjDzjCziBziAzi9zf9zb9zZAzVAzRBzNBzKBzLAzRUzT\ RzUOzVLzXIzYFz_Cz`9za6z_8zYAzXCzVEzTFzSHzQJzOLzNMz\ G6zE5zC4zB3zZfQhf9hfEhfIhfMffQcfUbfSafRafQ`fP_fO_f\ NbfMd_Lf`Ki`KkaJmaJpbIrbItcHwcGwzGwzFwzFwzHtzJpzLl\ zNjzQizThzVgzYfz_ezbdzdczgbzidzgfzehzcizakz_mzYnzW\ pzUrzStzQuzOwzMwzKwzIfzMczMazNZzNWzOTzOQzPOzPTzUXz\ ZazbezgjzlnzplznjzlQzbOza } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 03-10-12 (Silver Horizon [8])
by Jim Muth 03 Oct '12

03 Oct '12

FOTD -- October 03, 2012 (Rating 8) Fractal visionaries and enthusiasts: Today's scene lies in the Mandeloid fractal that results when the formula Z^(1.5)+C is iterated 1.5 levels up the logarithmic hyper-spiral with no function applied. This parent fractal resembles a Mandelbrot set with an oversized main bud on the north shore line of the main bay. Today's scene is located on the southwest shore line of this oversized bud. I rated the image at an 8 because it is one of the finer minibrot scenes I have found in the fractals with exponents between 1 and 2. Although the pattern around the minibrot is filled with discontinuities, they are arranged so that the pattern appears quite regular, with some rather attractive curly filaments extending outward from the minibrot. The unusually brilliant colors also help with the rating. I sometimes wonder whether fractals like today's are actually true fractals at all. It seems to me that the MandelbrotBC3 formula invents a new kind of math, and while using it with its various functions, I am exploring possible alternate mathemati- cal systems rather than real fractals created with accurate math. It really doesn't matter however. The images are fractals, with all the characteristics of fractals, and real or not, they can still be unusually attractive. Do not be deceived by the name "Silver Horizon". The image is not one of those fantastic fractal scenes on other planets. It is a surprisingly attractive scene of just another irregular <2 >1 minibrot. The calculation time of 2 minutes is near the fractal average. The web sites can cut the wait notably. The finished image is online at: <http://www.crosscanpuzzles.com/Archives.html> The image is posted in high-definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are available at: <http://www.Nahee.com/FOTD/> With partly cloudy skies, a temperature of 77F 25C and high humidity, today seemed more like an early August day than an early October day. The fractal cats would have preferred more sun, but they still found enough comfort on their chair by the southwest window. Except for a midday visit by the dryer repairman, who did his job quickly, the humans had a typical day. The next FOTD will be posted at the right time. Until whenever, take care, and I get the feeling that something is wrong with the world, but I can not track it down. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Silver_Horizon { ; time=0:02:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident center-mag=+0.1154933507434394/+0.9603539171372509\ /7.500726e+008/1/-115/0 params=1.5/0/51/0 float=y maxiter=2500 inside=0 logmap=257 periodicity=6 colors=0009P07O05N03L02K02J00I00G00F00E10D20C20B52\ B85DAAFCEGEIHGNGJTGLZFOaHQcJTbLW_KZXIaTGdLOVEVL8`D\ 2e75i59l5Co5Fr5Ju5eu5ovSuz_zzzzzarzXmz3kz5ju5jr7hm\ 8hj8fe9fbAeZBeVBdSCdODbLEbIEaFFaCG_9I_7IZ3JZ2KX0LX\ 0LT0JP2GL5EJ9DFBBCE9AI87L53P31S20W10_00d00f01_2ATA\ LNGXGPdBZk7fp9jtCmzFpzJrzOuzVxzazzeuzkpOFmEDh5Ce5G\ z5Bj5AZ55W52V38S38Q37O37N35K25J25G25F23D23C35E35F3\ 7G58J59K5AL5BO5CP5DQ5ES7FV7GW7IX8J_8Ka8Lb8Nd9Of9Ph\ 9QjASmAToAVpAVrBTpCSoDQoEQmFPkGOkIOjJNhKLhLKfQKeWJ\ eZIdeIdKOaFV_B_Z7fX2mW0uV0zT0zW0xX0vZ0u_0sa0sb0re0\ pf0oh0mj1kk1km2jp2hr2fs2eu2XZ2_X1aW0dV0kT0pS0pQDmQ\ FoNKoJKoGQoDQpAXp8Xp5Xu2Xz0dz0kz0hfCzSAzV9zX9k_8kb\ 8Xe7Xh7Kj5Km53p52s51v30z30z32z9XsDXsIXsOXsTXsZXsdX\ skXsrkkxkkzkkzkkzkkzkkzkkzkkxkzxkzLkz0kz0kz0kz0kz0\ kz0kz0kz0kz0kz0kz0kz0kz0kz0zz0zz0zz0zz0zz0zz0zz0zz\ 0zzozzmzzkzzazzZzzXzzVzzS } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 02-10-12 (Negative Territory [5])
by Jim Muth 02 Oct '12

02 Oct '12

FOTD -- October 02, 2012 (Rating 5) Fractal visionaries and enthusiasts: We appear to be in one of those slow fractal periods here at FC. Today's humdrum image is the best I could dredge up in the day's fractal search. The image is a scene in the East Valley area of a Mandelbrot set corrupted by Z^(-21)+C energies. As is true of all Mandelbrot sets corrupted by negative energies, the deep minibrots retain the Z^2+C appearance. Since there are no minibrots in fractals of pure negative orders, the minibrots in negatively corrupted M-sets have nothing to change into. Perhaps the most surprising thing in today's image is the criticality of the bailout radius, (which is 16 more than the value assigned the real(p2) parameter, or 3.3). Decreasing this value results in a blank screen; increasing it results in the image first becoming more chaotic and finally breaking up and evaporating. The rating of a 5 indicates nothing of exceptional artistic value but implies enough fractal interest to make the brief calculation time of 45 seconds worth the effort. Enjoy extra leisure time by letting someone else do the calcula- tion. View the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> And check the high definition and anti-aliasing at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are posted at: <http://www.Nahee.com/FOTD/> Rain fell here at Fractal Central today. The temperature of 64F 18C was pleasant enough, but with things so wet, it was wasted. The fractal cats saw the weather, then began chasing each other up and down the long hallway. The humans had so many other things to do that they hardly noticed the rain. The next FOTD will be posted in a number of hours. Until whenever, take care, and if you wish to rule the universe, the queue is on the right. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Negative_Territory { ; time=0:00:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip center-mag=+0.3330817092270084/+0.0270745261371607\ /8.007146e+010/1/-166.25/0 params=-21/100000/-12.7\ /0 float=y maxiter=1500 inside=0 outside=real periodicity=6 mathtolerance=0.05/1 colors=000Q_pWdpaiofmogmkgmhgmegmbhm_hmXhmUhmRhmOi\ mLimIimFimCim9gnDfoGdpJcqMaqP`rSZsVYtYWu`VucYr`_pZ\ anXclUejSghQjeNlcLnaJp_GrYEtWCvUApTAjTAdTAZTATTANT\ AHTABTACVDCWGCYJCZMC`PCaSCcVDdYDf`DgcDifDjiDllDmnD\ pyGkwIfuKasMXqOSoPWhP_bPbWQfQQjJQmDKaKFRQ9GX45bE6_\ O7XX7Vf8So8QoINoSKo`IojFosDZbVJNkUZacjSmvIgtObrTXp\ YSncMlhHjmChrOW__JIYOFXSDVWAU`8Sd5Rh3Pb7OYAMTDLOG`\ QTWSe`YgabhVgjOmkHrmBwnQLZ_l0VK6RCC1JIJXOEWUAY_6ee\ 2ejCijLljUojbrjabctx0tb2ldBefKYhTRjaJljCnrFbdIRRLF\ DO30yKgxSkwZnveqvltoipifmccjY`gSYzMVzGmzAQz8RY7S_6\ Ta5Uc3Ve2Wg1Xi0Xk2Ze4_`5`W7oQ8cLAtGBeBDdFEdJFcMGcQ\ IbUJbXKazLazIIpGczDdNBez8fC6g77fN8ea9epzvDztJzrPzp\ Vzn_zlezjkRH3HVSrYMh`T_bZQddHfjdKKYPRRUYLZcEcjM7z0\ uksVzkPpdKfXFYQAOI5EB05J28Q4BX6Dd8GkAJrCLWGE9J7JUF\ TdNboU`nTZnSXnRVnQTnPRmOPmNNmMLmLKmKKkNKjQKhSKgVKe\ YKd_KbbKadK_gKZjKXlKWoKVq } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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FOTD 01-10-12 (NewStuff [Low])
by Jim Muth 01 Oct '12

01 Oct '12

FOTD -- October 01, 2012 (Rating Low) Fractal visionaries and enthusiasts: Today's image has a low rating. Since I did not wish to embarrass myself, I did not state exactly how low, but it would be fair to state that the rating would be notably less than average. (A rating of 4 would be a good guess.) The image lies within the tiny bit of debris inside the Mandelbrot bud that appeared in the background of yesterday's image. Today's image is characterized by a near-hopeless nest of zigzag filaments overlying a totally chaotic background. The filaments are much like those found in the 'Siegel Disk' area of the Mandelbrot set. The name "New Stuff" is a bit misleading, since there is little new stuff in the image, which is really only a casual glance of what lies within a strange little eye-shaped bit of unevaporated debris. The calculation time of 8-1/2 minutes is a bit too much to pay for the image, but once again, the FOTD web sites charge to the rescue, saving both time and frustration. Be part of the charge. View the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> A high-definition version is posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Lots more older images are available at: <http://www.Nahee.com/FOTD/> Despite a few minor clouds here at Fractal Central today, the day brought the impression of a sunny one. The temperature of 68F 20C was quite pleasant for the start of October, and the fractal cats took full advantage of it in their southwest window as they watched the falling leaves outside. The humans made it through another day with nothing out of the ordinary happening, which is boring to report but quite pleasant to experience in person. The next FOTD will be posted whenever it is. Until then, take care, and be of sound constitution, but keep the sound level under control. You wouldn't want your noisy constitution disturbing the peace. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= New_Stuff { ; time=0:08:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=JulibrotMulti2 function=recip passes=1 center-mag=+0.0017245727/+0.0093780664/10151/1/82/0 params=6.5/-6.5/89/0/89/0/-1.626/0/0/0 float=y maxiter=4000 inside=0 logmap=382 periodicity=6 colors=000z1Sm8YfEbYKgRQlrzFgvIXtLNrNOpQOnTPlVRjYS\ h`TfbVdeWbhX`jZZm_Xp`VrZYkX_dWaYUcRSeKRgDTeEUdEVcE\ WbFX`FY_FZZG_YG`XGbTKdPOfMShIWjE_lBcn7gp4kn6il7hj8\ gh9ffAedCdbDc`EbZFaXG`VI_TJZRKYPLXNMWOQXPTXQXYQ_YR\ cYSfZTjZTmZUq_Vt_Vw_Uu`UtaUsbTrcTqdTpeToeSmfSlgSkh\ RjiRijRhkRgkL_fFSaQLh`Enk7tu0zs2xq4wo6vn7tl9sjBriC\ pgEoeGndHlbJk`Lj_MhYOgWQfVReSTgQUiOVkMWmKXoIYqGZsE\ _tKWoQSkWOgaKcgG_lCWjEVhGVfIUdJUbLTaNT_OSYQSWSRUTR\ TVQRXQPYPN_PLaOKbORUUYM_dDek5kj9jiCihFihIhgLhfOgeS\ feVfdYec`ebcdbfdZdaWc_TbYQ`WN_UKZSHXQEWOBVM8Tz5rz2\ ez6RQARZERgIRpLRyLYyLMz1bG4_N7XUAU`DSfGPmNzCMzBKv8\ Jr5In2Hk0Ii1Ih2Ig2If3Id4Ic4Ib5Ia5J_6JZ7JY7JX8JV9JU\ 9JTAJSAKQBKPCKOCKNDKLEKKEKJFKIFLHELHELGEMGDMFDMFDN\ ECNECNDCODBOCBOCBOCBPFDQHFQJHRMJSOLSQMTTOTVQUXSV_U\ VaVWcXXfZXh`YjbYlcjJQiIMhGIgFDfE9eD5eC1_J5VQ9PXCKc\ GFiJKePPaVTZ_j9Rl7Sn5Sp3S } frm:JulibrotMulti2 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p2*0.0055555555555556), b=pi*imag(p2*0.0055555555555556), g=pi*real(p3*0.0055555555555556), d=pi*imag(p3*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), aa=-(real(p1)-2), bb=imag(p1), c=p+flip(q)+p4, z=r+flip(s)+p5: z=(bb)*(z*z*fn1(z^(aa)+bb))+c |z|< 6 } END PARAMETER FILE=========================================

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FOTD 30-09-12 (Fractals-101 [7.5])
by Jim Muth 01 Oct '12

01 Oct '12

FOTD -- September 30, 2012 (Rating ?) Fractal visionaries and enthusiasts: The day we spent yesterday back at Old Fractal Central went quite well. But the fractal cats disapproved of our all day absence and our 10pm return. A quick treat of tuna and cheddar restored their good spirits. Today's image shows both the Mandelbrot and Julia aspects of the same Julibrot scene together at the same time. Since I will attempt to explain how this is possible, I have named the image "Fractals-101". The reddish outer parts outline the Julia aspect of the scene, while the bluish inner parts show the Mandelbrot bud aspect. The bluish Mandelbrot bud near the center is about 60 times its apparent size when it is viewed as a straight Mandelbrot shape. To see the pure Mandelbrot view, reset the real(p2) and real(p3) parameters to zero and reset the magnitude to 60. (The value of 60 is necessary because it is close to the value of the tangent of 89.) But how can a Mandelbrot image be enlarged by merely slicing it at a very sharp angle? The answer lies in the 4-dimensional shape of the high-iteration Mandelbrot features of the Julibrot, which are extended to infinity in two dimensions, and display the typical compact Mandelbrot shapes in the other two dimensions. Imagine an infinitely long cylinder in three dimensions with a circular cross-section. If it is sliced straight across, the slice is a circle. But if it is sliced at an ever increasing angle, the slice is an increasingly stretched oval. And slicing the cylinder along its length produces an infinitely long straight rod. The angle of the slice causes the expansion of one dimension of the slice. In four dimensions we may have an object that is circular in its two compact dimensions and extends to infinity in its two extended dimensions. Such an object may be sliced at two independent sharp angles. Doing this will give a 2-D slice that is stretched in two directions, and if the angles are equal, the cross section will be enlarged proportionally without being stretched. We have a Mandelbrot microscope. The Mandelbrot part of today's image was enlarged just this way. (Unfortunate- ly, we can get no extra magnification of Mandelbrot objects by doing this.) The image itself is pretty routine. The most interesting part is the curiously shaped bluish Mandelbrot bud at the center. The rating of a question mark means I don't really know how to rate the image. The calculation time of 2 minutes is reasonably fast, but the web sites are always there to make things even easier. Be happy! View the finished on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> without the need to calculate it. View the image in high-definition, with lots of added bells and whistles such as anti-aliasing at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> All the thousands of FOTD back images are online at: <http://www.Nahee.com/FOTD/> A mix of sun and clouds, with a temperature of 64F 18C made today quite typical of the end of September here at Fractal Central in Central Pennsylvania. The fractal cats enjoyed the sunny periods on their shelf, and endured the cloudy times in sulk mode. The humans spent most of the day recovering from yesterday's trip to Old Fractal Central, where my sister is putting out food for the neighborhood cats that are starting to gather in increasing numbers for a free meal. The next FOTD will be posted in a reasonable amount of time. Until whenever, take care, and if we suddenly lost all our advanced technology, how many, I wonder, would survive and how many would curl up and expire. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Fractals-101 { ; time=0:02:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=JulibrotMulti2 function=recip passes=1 center-mag=0/0/1.572327 params=6.5/-6.5/89/0/89/0/\ -1.626/0/0/0 float=y maxiter=24000 inside=0 logmap=12 symmetry=xaxis periodicity=6 colors=000S05U17W28Y39_4Aa4Bc5Ce6Dg7Ei8Fk8Gm9HoAIq\ BJtCKwCLuEMsGMqINoKNmMOkOOiQPgSPeUQcVQbUPbUPbUOaUO\ aUNaTN`TM`TM`TM_TL_SL_SKZSKZSJZSJZSJVTKSULPVMLWNIX\ OFYPBZQ8_R5`S2`T9cQGeNNhKUjH`lEgoBnq8us5so9rlDpiGo\ eKmbNl_RkWViTYhQafMdeJhdGkdGkcHkcHlcHlcHlbIlbImbIm\ bImaJmaJmaJnaJn`Kn`Kn`Ko`Kz_Lz_Lz_Lz_LzZMzZMzZMzZM\ zYNzYNzYNzYNzXOzXOzXOzXOzWNzWNzWNzWNzWNzWNzWNzWNzW\ MzWMzWMzWMzWMzWMzWMzWMzWLzWLzWLzWLzWLzWLzWLzWLzVKz\ VKzVKzVKzVKzVKzVKzVKzVJzVJzVJzVJzVJzVEzVJzVJzVJzVJ\ zVIzVIzVIzVIzVIzVIzVIzVIzUHzUHzUHzUHzUHzUHzUHzUHzU\ GzUGzUGzUGzUGzUGzUGzUGzUFzUFzUFzUFzUFzUFzUFzUFzYKz\ XKzXKzXKzXKzXKzXKzWKzWKzWKzWKzWKzWKzVKzVKzVKzVKzVK\ zVKzUKzUKzUKzUKzUKzUKzaKz`Kz`Kz`Kz`Kz`Kz_Kz_Kz_Jz_\ Jz_Jz_JzZJzZJzZJzZIzZIzYIzYIzYIzYIzYIzYIzXHzXHzXHz\ XHzXHzWHzWHzWGzWGzWGzWGzVGzVGzVGzVFzVFzUFzUFzUFzUF\ zUKzKKzKKzMKzLKzLKzKKzKKz } frm:JulibrotMulti2 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p2*0.0055555555555556), b=pi*imag(p2*0.0055555555555556), g=pi*real(p3*0.0055555555555556), d=pi*imag(p3*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), aa=-(real(p1)-2), bb=imag(p1), c=p+flip(q)+p4, z=r+flip(s)+p5: z=(bb)*(z*z*fn1(z^(aa)+bb))+c |z|< 6 } END PARAMETER FILE=========================================

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FOTD 28-09-12 (Injured Starfish [7.5])
by Jim Muth 29 Sep '12

29 Sep '12

FOTD -- September 28. 2012 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image lies in the same parent fractal as yesterday's, but instead of being found near the tiny bud at the eastern extremity, it is located in a valley of a strange-shaped minibrot near the center of a ragged island in the center of the main bay of the parent Mandeloid. I named the image "Injured Starfish". The resemblance to a starfish with missing arms is quite striking. The rating of 7-1/2 includes a half-point bonus for the extra effort necessary to bring out the starfish resemblance. The calculation time of 1-3/4 seconds is a bit slow. But this is no need to worry. The web sites will make the access near instant. The finished image is posted on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The hi-def version is available at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are online at: <http://www.Nahee.com/FOTD/> Lots of clouds and occasional showers left today with a lot to be desired here at Fractal Central. The fractal cats, much less active than the old fractal cats, took it easy most of the day. The humans, always active, had a typical day with a lot to do but nothing to report. There will be no FOTD for September 29, since I'll be going back to Old Fractal Central to check things. Most likely, the next FOTD will be posted on September 30, but as always, there is no guarantee given or implied. Until whenever, take care, and why do people need so many technologi- cal gadgets to distract them from the world? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Injured_Starfish { ; time=0:01:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-0.5823524453967268/+0.0261965516683267\ /1.906265e+009/1/-90/0 params=6.5/-6.5/0/0 float=y maxiter=2500 inside=0 logmap=108 periodicity=6 colors=000GL`GOaGRbGUcBXZ7_UBbWEeYHh_KkaNncQqeTtgW\ wiZzkazmdznezofzpgzqhzqizrjzskztlzulzujzoDzVSmlRmm\ TmjUmgWmeXmbYm__mY`mVbmScmQdmNfmKgoIiqFjsCkzAhz9ez\ 8bz8_z7Xz7Uz6Rz6Oz5Lz5Nz8PzBQzDSzGUzIVzLXzNYzQ_zSa\ zVbzXdz_ezacz`bz_`zZ_zYYzXXzWVzVUzUSzT5W89YAC_BGaC\ JcDMdEQfFThGXjH_lIbmJfoKiqLmsMpuNsvOfiqhhsdfn`eiXd\ eTc`PbWLaSDZI4JP40963B86DA9ECCGEFIGIJILLKONMROOUQz\ XRzVQzUPzSOzRNzQMzOLzNKzMJzLIzKIzJIzIIzHIzGIzGIzFH\ zEHzDHzCHzBHzAHzAHzJGzRGz_FzgFzpEzxEzsFGnFEjFCeFA`\ F8XF6SF4NF2JF2OE2SE2WE2_E2cE2gE2kE2oE2sE3qD4pD5nD5\ mC6lC7jC7iC8hB9fBAeBAdABbACaAC`ABbBBcCBdDBeEBfEBgF\ BhGBiHBjHBkIBlJBmKBnKElKHmKKmKNmKQzKSzKVzKYzK`zKcz\ KezKhzKkzKnzKqzKszKtzJtzJtzJtzIzzczzczzczzmzzmzzmz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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FOTD 27-09-12 (Strange Count [7])
by Jim Muth 27 Sep '12

27 Sep '12

FOTD -- September 27, 2012 (Rating 7) Fractal visionaries and enthusiasts: Today's image gives a glimpse into the disorder that results when a Mandelbrot set is seriously corrupted by negative Z^(6.5) energies. Today's parent M-set is barely recognizable as an M-set. It still has the tiny bud on the X-axis at the eastern edge of the main bay however, and today's image lies deep on a filament associated with this bud. Perhaps the most striking thing in the image is the lack of visible discontinuities, which certainly do exist but are concealed by both the coloring and underlying fractal forms. The name "Strange Count" does not refer to a certain well-known vampire. It refers to the 13 orangish shafts radiating from the central minibrot. The number 13 is not too surprising, since 13 equals (6.5)x(2). Curiously, the northeast shaft, unlike the other 12 shafts, is disconnected from the minibrot. The central minibrot itself is surprising also. Being of order 6.5, this minibrot should have 5.5 lobes and main buds, but at least at today's reasonable distance, it appears to have a full 6 buds and only 5 lobes. The distant appearance is deceiving however. A closer look shows that the northeast lobe, which is larger than the other four, is actually 1-1/2 lobes, making a total of 5.5, and the 2 buds attached to it are only 3/4 buds, making a total of 5.5 buds. So it all adds up, and all is once again right in fractal land. The rating of a 7 is dead average, held down a bit by the color- ing. The image, as are all FOTD images, is worth a quick look however, especially with a calculation time of only 40 seconds. The image will seem more enjoyable when viewed on one of the web sites without the need to calculate it. All problems connected with calculating the parameter file may be avoided by viewing the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> And check the image in high definition on Hal's web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The thousands of back images are online at: <http://www.Nahee.com/FOTD/> The day began with light rain here at Fractal Central, but the rain soon ended, and by midday the sun broke through, leading to a partly cloudy afternoon with a temperature of 70F 21C. The fractal cats passed the day taking it easy. FL spent the day at a nearby fair, while I remained at FC, seeing that nothing impor- tant went undone. The next FOTD will be posted in the proper time. Until whenever, take care, and if high technology were to become our god, I guess I would be an Athiest. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Strange_Count { ; time=0:00:40.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip logmap=46 center-mag=+0.617165311719468/+0.00000000001321963\ /1.687e+011 params=6.5/-6.5/0/0 float=y maxiter=500 passes=1 inside=0 periodicity=6 mathtolerance=.05/1 colors=000fiqhhsdfn`eiXdeTc`PbWLaSDZI5W89YAC_BGaCJ\ cDMdEQfFThGXjH_lIbmJfoKiqLmsMpuNsvO4JP30993BE6DJ9E\ PCGUFIZIJcLLiONnROsUQxXRyVQyUPySOyRNzQMzOLzNKzMJxL\ IwKIvJIuIIsHIrGIqGIpFHoEHmDHlCHkBHjAHiAHdJG`RGX_FT\ gFPpELxEIsFGnFEjFCeFA`F8XF6SF4NF2JF2OE2SE2WE2_E2cE\ 2gE2kE2oE2sE3qD4pD5nD5mC6lC7jC7iC8hB9fBAeBAdABbACa\ AC`ABbBBcCBdDBeEBfEBgFBhGBiHBjHBkIBlJBmKBnKElKHmKK\ mKNmKQmKSmKVmKYmK`mKcmKemKhmKkmKnmKqmKsmKtmJtmJtmJ\ tmItmIumIumHumHumHumGvmGvmGvmFvmFvmF`maGzwIzsKzoMz\ lNzhPzdRzaTzYUzVXzYZz_azaczdfzfhzhkzkmzmpzorzruztw\ zvtztqzsnzqlzpizofzmczlazkZziWzhTzfRzeOzdLzbIzaGz`\ GzaGzbGzcBzZ7zUBzWEzYHz_KzaNzcQzeTzgWziZzkazmdznez\ ofzpgzqhzqizrjzskztlzulzujzoDzVSmlRmmTmjUmgWmeXmbY\ m__mY`mVbmScmQdmNfmKgoIiqFjsCkzAhz9ez8bz8_z7Xz7Uz6\ Rz6Oz5Lz5Nz8PzBQzDSzGUzIVzLXzNYzQ_zSazVbzXdz_ezacz\ `bz_`zZ_zYYzXXzWVzVUzUSzT } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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FOTD 26-09-12 (Double-Take [8])
by Jim Muth 27 Sep '12

27 Sep '12

FOTD -- September 26, 2012 (Rating 8) Fractal visionaries and enthusiasts: Today we ramble into the fractal world that appears when the Mandelbrot set is corrupted by 4.5 negative units of Z^(4.5)+C energies. This parent fractal resembles the parents of the past several days' images, and the image is located in the same tiny east-central bud. But, unlike the situation with straight Z^(n)+C fractals, in today's situation the fractal interest seems to increase as the exponent is raised. I named the image "Double-Take" because it is filled with twin pairs of Z^(4.5) minibrots. The rating of an 8 shows that I consider the image to be a rather good one, at least as far as the underlying forms go. I might have raised the worth to 8-1/2 or so if the brilliant green color palette had not been almost totally created with a stroke of the <enter> key. The calculation time of 30 seconds, like the times of all the recent images, is a rounded approximation. On some machines the parameter file will run faster; on others it will run notably slower. Luckily, the finished image is available on the FOTD web sites, where all uncertainty is eliminated. The image is posted, already calculated, on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> A high-definition rendering is online at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Thousands of FOTD back images and discussions are available at: <http://www.Nahee.com/FOTD/> Clouds were the thing of the day here at Fractal Central today, with only a few peeks of sun. Rain showers simply added to the confusion. The temperature of 70F 21C was pleasant enough . . . as long as the changeable weather was observed from indoors, that is. The fractal cats observed the conditions from their southwest window, complaining every so often about the lack of sun. The humans had another in a long string of everyday week-days. The next FOTD *will* be posted. That's all I can say right now about exactly when. Until whenever, take care, and I see that the dangers of cell- phone radiation are back in the news (on CNN at lunch time today). To read my comments about the dangers, check the FOTD discussions of about 10 years ago. BTW, it's now safe for the phone companies to let the risk of too much cell-phone use be widely known. Almost everyone under the age of 30 is now totally addicted to various wireless devices, which have become just another necessary part of modern day life, and regardless of the risk, they would never give them up. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Double-Take { ; time=0:00:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=+0.4968959677020675/+0.0000000286553292\ /4.433267e+008/1/39/0 params=4.5/-4.5/0/0 float=y maxiter=1600 inside=0 logmap=49 periodicity=6 colors=0002596BC9GFCMIFRLDEDC26PD7`N8mY9ygAiX7VM50\ EIFB2jdPZUINKCBA69TF4E748o36b24Q12DiYpYPbNHQB8DeRc\ dOccLcdOYdQTdTOdVJdXEfZFh`FibFkdGlfGnhGojGqlHsnHtp\ HvrIwtIyvIzxIvtJrqJnnJjkKfhKceK_aLWZLSWLOTMKQMHNMQ\ INYDOf9On4Pv0Pu3St5Us7Wr9YrB_qDapFcoHeoJglHajFWhDR\ eBLc9Ga7A_65b59d4Dg4Hi3Ll2Pn2Tq1Xs0`u0dr3go6jl8miB\ ofDrcGu`IwaMvaPvaSubWubZtbatceschsckrdordrqduqbvm`\ vjZvfXvcVv_TvXRvTPvQNvMLvJJvFHvCGv9IpEKkIMcMOcRQcV\ ScZUcbWcgYck_co`csacracqacpacoacnacmbclbckbcjbcibc\ hbcgbcfZcbWcZTcVPcRMcNJcJGcFCcB9c76c33m08m6DmBImGN\ mLSmQXmVam_emdbmZ_mUXmPUmKRmFPmARmETzHVzLXzOYzR_zV\ azYczadzdfzghzkjznkzqhzrezsczt`zuZzvWzwUzwPzmKzcFz\ UBzLBzWBzeBzoDzkEzgGzcHz_JzXKzTMzPNzLOzIDzOIzIMzCR\ z6Vz0pzmlzjhzgjz`lzVnzOpzIozXozklznjzpgzsezuczvbzv\ azv_zkZz`YzQXzGVzKTzNRzQPzTYzRfzQozPjzSezV`zYWz_Vz\ kUzw_zdezNkz5gz8czARz9Ez9 } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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FOTD 25-09-12 (PI Pie [5])
by Jim Muth 25 Sep '12

25 Sep '12

FOTD -- September 25, 2012 (Rating 5) Fractal visionaries and enthusiasts: Today's image is a hasty one that I found after only a 2-minute search. With so little effort going into its creation, I could give it a rating no higher than a humble 5. The coloring is so hasty that several colors from the GIF default palette remain in several registers. The image is named "PI Pie". The reason for the name is that it was found by the FinDivBrot-2 formula with both positive and negative PI entered as the parameters. The parent fractal is a distorted Mandelbrot set, well on the way to becoming a 'ZexPI' Mandeloid. Today's scene lies near a tiny, 'PI' bud at the point where the X-axis crosses the east edge of the main bay. The image shows a 'PI' minibrot, which is hard to distinguish from a cubic minibrot. The surrounding pattern is even harder to distinguish. The overly brilliant reds surrounding the minibrot are actually part of the GIF default color palette. The calculation time of 1-1/4 minutes will pass quickly. Of course, no guarantee of total fractal satisfaction is given or implied. The image is posted, completely calculated, at: <http://www.crosscanpuzzles.com/Archives.html> A high-definition rendering is online at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are available at: <http://www.Nahee.com/FOTD/> Today began foggy here at Fractal Central. The fog cleared by 9am, and the rest of the morning was sunny, but heavy clouds moved in during the afternoon, with threats of showers. The early morning low of 37F +3C rose quickly to 68F 20C in the afternoon. The fractal cats observed all this with disinterest, while the humans had an everyday day. The next FOTD image will be posted in the properly appointed time. Until whenever, take care, and is the Mandelbrot set animal, vegetable, mineral, or none of the above? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= PI_Pie { ; time=0:01:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip center-mag=+0.30458021054461/-0.00143308920906492/\ 8.461661e+010/1/97.5/0 params=3.14159265358979/\ -3.14159265358979/0/0 float=y maxiter=1800 inside=0 logmap=204 periodicity=6 mathtolerance=0.05/1 colors=0009RD9i2Gk5Mm7So9YqBdsDjuFpwHvyJuvItsItpHs\ nHskGrhGqfFqcFp`EpZElXIhVLdTOaRRYPUUNXQL`NJcJHfFFi\ BDl8Co7Gj6Kf6Oa5SY4WT4_P3cK2gG2kB1o71r3lhzhgsdfl`e\ eYdZUcSQbLNaELZDKXCIUBHSAFQ9EN8CL7BJ7AG68E57B45934\ 7224112000000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLz\ zzLzzz000555888BBBEEEHHHKKKOOOSSSWWW___ccchhhmmmss\ szzz00zG0zV0zj0zz0zz0jz0Vz0Gz00zG0zV0zj0zz0jz0Vz0G\ z00z00zG0zV0zj0zz0jz0Vz0GzVVzbVzjVzrVzzVzzVrzVjzVb\ zVVzbVzjVzrVzzVrzVjzVbzVVzVVzbVzjVzrVzzVrzVjzVbzhh\ zlhzqhzuhzzhzzhuzhqzhlzhhzlhzqhzuhzzhuzhqzhlzhhzhh\ zlhzqhzuhzzhuzhqzhlz00S70SE0SL0SS0SS0LS0ES07S00ron\ i`q`NtT9wNGxHNyBUz5_zAcsEfmIifMm`QpUUsOYvI`pJcmJfm\ KhmKkmLnmLpmLomSnmZmmelmlkmsfmrzmzzrzzqzzqzzqzzpzz\ pzzpzzpzzrzztzzuzzwzzyzzzzzrzzmzzmzzmzzmzzmzzmzzmz\ zmzzmzzmzzpzzqzzmzzmzzmzzmzzzezzkzzqzzvzzszzpzzmzz\ jzzlzzmzzozzpzzfzzXzzNzzD } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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Fractal links
by Mark Christenson 25 Sep '12

25 Sep '12

Hi all. I am cleaning up the links for Bud's Fractal Pages. I will probably have more questions like this. 1) Is fractalforum still around? I clicked on my old link for fractalforum.com and was directed to a hosting page. Thanks...

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FOTD 24-09-12 (Zexpe Recip Zexpe [7])
by Jim Muth 24 Sep '12

24 Sep '12

FOTD -- September 24, 2012 (Rating 7) Fractal visionaries and enthusiasts: Today we check the fractal that results when the Z^(e)+C Mandel- oid is calculated epsilon levels down the hyperladder with the 'recip' function applied. The parent fractal somewhat resembles the standard cubic Mandeloid, but with two East Valleys and a wedge-shaped open area west of the single West Valley. Today's image lies on a filament extending from a tiny bud on the posi- tive X-axis at the eastern edge of the main bay. Perhaps the most unusual feature of the image is its magnitude of over 2*(10^14). Such a magnitude is normally well beyond the resolution range of double precision math, but resolution limits are not fixed, and occasionally an area such as today's, with an exceptionally high limit turns up. Even so, the resolution breakdown is starting to become visible, especially along the normally smooth iteration band edges. The name "Zexpe Recip Zexpe" refers to the way the image was created. The rating of a 7 shows that I am not totally pleased with the image, especially with the colors. The calculation time of 47 seconds has been rounded off as all the calculation times now are. The way to avoid calculation problems is to view the image on one of the FOTD web sites. Find fractal enlightenment and the finished image online at: <http://www.crosscanpuzzles.com/Archives.html> where the finished image and discussion ares posted. Find high-definition happiness at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Enjoy images from the ancient past at: <http://www.Nahee.com/FOTD/> Another near perfect autumn day was appreciated by all here at Fractal Central today. The crisp temperatures in the 60's F, upper teens C, blue skies and puffy clouds made it a day to be remembered. The fractal cats appreciated the activity of the local pigeons, which might become a problem. The humans made it through the day without anything unusually annoying happening. The next FOTD will be posted soon, the most likely time being in 24 hours. Until whenever, take care, and hopefully, whatever the problem, technology will save us. (But don't bet on it.) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Zexpe_Recip_Zexpe { ; time=0:00:47.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=+0.2091342460974785/+0.000005325221225\ 66/2.242649e+014/1/-7.5/0 params=2.71828182845905\ /-2.71828182845905/0/0 float=y inside=0 logmap=74 maxiter=1800 periodicity=6 mathtolerance=0.05/1 colors=000LGANHAQJATLAWNAZPAaRAeTAiUAbTAWO9PJ8ID6A\ 85344755A86DC6GG7JK8NO8QU9TZAXbA_fBbjCenChqEfnGfkH\ fhJfdLf`MfXOfTQfQRfNTfKVfHWfDYf8_f5`d5Xb5Ua5R_5OY5\ LX5I_7Lb9OeBRhCTkEWnGZsCarF`qH`pK`oM`nP`mR`lT`kW`j\ Y`i``hb`UQFaYQhd`unnrllokkmjjjhihghefgcde`cdZbcW`b\ U_aRZ`L_XPY_TXaXWc_VecUhgTjkSlpOpoQonRnmTnmUmlVmkX\ lkYlj_ki`kiajhcjgdiihfgeiebkd`mbYo`VqZWx_Ts`Qo`Nja\ KfaHabEYbBTc8Pc6L`7LY9MWAMTBMQCMODMRGQUJUXMY_PabSe\ eViZRZSNOLJDFF2GK3HP3HU4IY4Jb5Jg5Kl6Kp6Mn9NmBPkDQj\ FRiHTgKUfMWdOXcQYbSXaTWaUW`UV`VU_WU_WTXVTVVTTVTRVT\ PVTNVTLVSJUSHUSFUSDUSBUS9US7UR7UR7TR7TQ7SQ7SP6RP6R\ O6QO6QMOOJQMFSKCTJ9JZ38q7AmACjDDgHFdKG`NIYRJVULSeO\ TXMPPKMGIJ8GG9HFAIEBJDCKCDLCEMBFNAGO9HP8CG0FL4HP8J\ TCLYFNaJPeNQhLRiQRjURjYRkaRlfRljRmnQnvRmtRmrRlpRln\ RllRkjSkhSjfSjdSjbSi`SiZUjYSiXRiWPiWOiVMiVLiUJhUIh\ TGhTFhSDhSChRBhRD`OEULFNJ } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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FOTD 23-09-12 (Cubic Number Field [6])
by Jim Muth 23 Sep '12

23 Sep '12

FOTD -- September 23, 2012 (Rating 6) Fractal visionaries and enthusiasts: There was no FOTD for September 22, when FL and I decided to take an trip down to Carlisle to do some antiquing. We found several interesting old books, but nothing of real value. Today's image, a trip into the crazy world of mixed quadratic and cubic fractals, rates only a 6. The lowly rating is because to me at least, the image appears too . . . well . . . feminine. Those light pastel shades really fail to give the image its proper impact, but it really is a pleasant view of a cubic mini- brot that has no right to appear in its mostly quadratic parent. The parent fractal is basically a Mandelbrot set whose smaller features are starting to change into those of the cubic Mandeloid. The main bud has already split into two lobes, while the East Valley has vanished and been replaced by a tiny cubic bud with curious curving tendrils extending from its two lobes. Today's scene lies deep in one of these curving tendril spirals. The name "Cubic Number Field" sounds like more that it means. This name simply popped into my head as I shut off my thought processes, something every fractal fanatic must do to properly enjoy the tricks of numbers. The calculation time of 42 seconds will make the task of running the parameter file a simple one. The only thing simpler is a trip to one of the FOTD web sites. Leap in joy at the sight of the finished image posted on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> Leap higher by viewing the high-definition rendering at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Go into orbit at the sight of thousands of FOTD back images at: <http://www.Nahee.com/FOTD/> Typical autumn weather prevailed here at Fractal Central today. The temperature hovered around 66F 19C, while the sky was filled with big dark lumpy clouds of the strato-cumulus variety. The fractal cats were more concerned with falling leaves and pigeons than with the outside weather that they never get to experience. The humans had a relaxing day after yesterday's adventure. The next FOTD will be posted promptly. Until whenever, take care, and vote with your head, not your heart. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Cubic_Number_Field { ; time=0:00:42.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip float=y center-mag=+0.2071310995378451/-0.0201790533795087\ /1.3047e+011/1/86.25/0 params=3/-5/0/0 maxiter=1500 inside=0 logmap=103 periodicity=6 mathtolerance=/1 colors=000LBeMCfNDgOEhPFiQGjRHkSIlTJmUKnVLoWMpXNqY\ OrZPs`QvbRvdSufSrhQnjLmjIjgGeaE`W8PAAAbsY_nUXiQUdN\ R_JOVFLSCLO8OLCUMGYOQfS`oVjwYtHxqJwsKwtLwuZmwkdyxW\ zoVxfVvYUtPUrGUqUTifSasRUoTJlV9hSBdPC`MDXJETGFWIDZ\ KBaMAcO8fQ7iS5kU4bR5UN6LK6CI74H7CHCJHHQHMXIRcIWjI`\ qIepKZoLTnNNmOHlPBnTHpXNr`StdYugbnWhhLmbArFn_Mm`Sl\ `Yk`cj``kXZkUWlQUlNRmKPmGMnDKnALj9Mf9Nb9NZ9OV9PR9Q\ N9QJ9ONDNQGLTKKWNIZQHaUFdXEg_GcZH_ZIWZJTYKPYLLYMIY\ QHaTHdWHhZGkaGodGrY_jRrcTefVTiXGlZ4n`AibFdcK_ePVfU\ QhZLicGceIZgJUiKVcHVYEVSBVM8VH5TBJR6XP1iZAUhIFqQ0i\ R5aS9UTEMUIFUMEXKE_JDbHDdGCfNBhUAi`9kf8lm7nt6ozGrp\ PugYwZ`vVbvSdvOfvLhuHjuEluAnu7zo8zj8ze8z_9zV9zQ9zK\ AzFAzAAz5AzBFzHJzMOzSSzXWzWZzV`zUbzTezSgzRizQkzPnz\ OpzNrzMtzRozVkz_gzcczh_zlWzdYzY_zQ`zJbzCczAZz8Uz6Q\ z5Lz3Hz1Cz08z4Bz7DzAFzEIzHKzKMzOOzRRzUTzYVz`Xzc_zg\ azjczmezlczlazl_zlZzSdzKd } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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FOTD 21-09-12 (Herring Run [7])
by Jim Muth 23 Sep '12

23 Sep '12

FOTD -- September 21, 2012 (Rating 7) Fractal visionaries and enthusiasts: Today's image takes us to the Z^(3.003)+C Mandeloid in search of any geometric figures such as triangles or rectangles that might lie there. I had little hope of finding any such figures, since rather than cutting through a stem, the negative X-axis of the Z^(3.003) Mandeloid cuts through the West Valley, which is a mirror of the East Valley. But I did find a very interesting area along the southern edge of the broadened valley, where the elements are broken into herringbone like patterns. Today's scene shows a near-cubic minibrot lying in this herringbone area. I named the image "Herring Run", which is the name of a stream that runs about 1/2 mile from Old Fractal Central back in Baltimore. The image itself holds very little of a fishy nature, though a few vague hints of elephants are visible. The rating of a 7 is what I feel the close-to-average image is worth. The calculation time of 3-1/4 minutes is also about average, making the image an average bargain. An even bigger bargain may be found however on the web sites. The full glory of the finished image may be viewed online at: <http://www.crosscanpuzzles.com/Archives.html> The fuller glory of high-definition is available at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The total glory of all the images may be viewed at: <http://www.Nahee.com/FOTD/> A very pleasant end-of-summer day prevailed here at Fractal Central today. The fractal cats fully enjoyed the temperature of 77F 25C, while the humans, who agree on many issues but not everything, passed the day involved in work. The next FOTD will be posted in the foreseeable future, but probably not on the 22nd. Until whenever, take care, and I heard from the greenies that we need a source of energy that is cleaner and less expen- sive than coal and oil, and exists in a quantity large enough to make us independent of foreign sources. We recently found such a fuel -- natural gas. I thought we were saved, but why are the same greenies now protesting so much about its production. Either the world is crazy or I'm crazy . . . . or maybe we both are. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Herring_Run { ; time=0:03:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotN passes=1 float=y center-mag=-0.388666508437/-0.002122642167/2259652\ /1/-27.5/0 params=3.003/0/0/0/0/0 maxiter=8400 inside=255 logmap=192 periodicity=6 colors=000nALmAKlAJkAIjAGiAEhACgAAf85e61d51W51M51D\ 51451pjnmamfPgeIgeChhPojaubbkVbbOcTGcK8dA1d16b8A`F\ EZLJXSNVYRTdVSjRRgOQeKPcHOaDN_AMY6LW3LUANWHOXOQZVR\ _aSaIVviNfiNfjNgjMgkMgkMgkLhlLhlLhlKhmKimKinJinJin\ JjoIjoIjrEnoIjlMgjQcgT`dXYb`U_dR_hNZgOYgOXgOXgOWgO\ VfOVfOUfOTfOTfPSePRePQePQePPePOePOdPNdPMdPMdQLdQKc\ QKcQJcQIcQHcQHcQGbQFbQFbREbRDbRDaRCaRBaRBaRAaR9aR8\ `R8`S7`S6`S6`S5_S4_S4_S3_S2_S1`R2_S3ZS3ZT4YT4XU5XU\ 6WU6VV7VV7UW8TW8TX9SXARXARYBQYBPZCPZCO_DO_EN_EM`FM\ `FLaGKaGKbHJbIIbIIcJHcJGdKGdKFeLEeMEeMDfNCfNCgOBgO\ BgNAhL9iK9jJ8kI7kH6lG6mE5nD4oC4pB3qA2r81s92rA2rA3r\ B3qB3qC4qC4pD5pD5pE5pE6oF6oF6oG7nG7nH8nH8mI8mJ9mJ9\ mK9lKAlcD2cD2cD2cD2bD2bD2bD2bD2aD2aD2aD2aD2`E1mE1m\ E1mE1mE1mE1zE1zE1zE1zE1zE1zE1zE1zE1zE1zF1zF1zF1zF1\ zF1zF1zF1zF1zF1zF1zF1zF1zF1zF1zF1zF1zG3zH4zI5zJ6zK\ 7zL8zM9zNAzOBzPCzQDzREzzz } frm:MandelbrotN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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over the phone
by Sebastien Helie 22 Sep '12

22 Sep '12

and then 2 home.... walker jonny Jeohva witness, whanted to interest me in the 32_33 nympho predator call kristos... i said i am interest in god but you seem attracted by money, this computer is money at work?! showing my last tess.exe on the background... no serious system 74 or 42 but if your master cannot claim higher than 32 do not try to fix universal cased... holy marijuanna mother of god.... pot a beer -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com

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sorry for fluent discour here
by Sebastien Helie 22 Sep '12

22 Sep '12

but here is the default mojoworld system in position on earth (old file) i think but i do not mount my taught every know and then les groulx, les loup the groulx, the wolf. https://dl.dropbox.com/u/68454194/manicouagan_sts9.bmp -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com

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mac cat drive that...
by Sebastien Helie 22 Sep '12

22 Sep '12

and windows more attracted by deal movie teather... anyway avoide mojoworld and windows 8 just do more plasma system and no creative in multiplication... will to be full of $$ jail + no prodject only self in case i can buy? -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com

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addendum to fractal center 98
by Sebastien Helie 22 Sep '12

22 Sep '12

or advantage... systeme administrator who already existe whanna get copy and past like black dos... in other term avoide toutch screen has much has you can, you will have to do a little if you use mojoworld plasma but i do not think it run under windows hate.,8 -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com

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in french
by Sebastien Helie 22 Sep '12

22 Sep '12

windows version 8 really cheap..... sa veaux pas chere.... mes excitant.dummy at crash test. -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com

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the last IN addendum
by Sebastien Helie 22 Sep '12

22 Sep '12

Arcchk.exe Might be a little poisonous at first but i cannot redo the same pattern on compilation. so it's extremely rare only have the beginning clear.... collection hem! swap hem with you extensive friend M... drink drink less drink more drink non alcoolik beer... drink mad. AND FLY for FLY EARTH for earth man for man and fractal to fractal understanding... -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com

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Correction -- FOTD 20-09-12 (Busy Busier Busiest [6])
by Jim Muth 22 Sep '12

22 Sep '12

FOTD -- September 20, 2012 (Rating 6) Fractal visionaries and enthusiasts: This FOTD is posted a second time because the original posting included the wrong formula in the parameter section. Please delete the first posting. We have another rush in progress here at Fractal Central today. And when time is lacking, the quality and accuracy sometimes suffers. The name of today's image, "Busy Busier Busiest", explains the lowly rating of a modest 6 points. The image las a lot of color action, that's for sure, but like so many current movies, it has too much action and not enough plot. Even the addition of the 'tdis' rendering fails to bring life to the moribund image. The only thing worth noting in the image is the central minibrot, shaped suspiciously like a peanut. The formula behind the scene is Z^(1.7)+C, which I iterated 69 levels up the hyperladder with the 'ident' function applied. This mixture creates a parent fractal that somehow reminds me of a mermaid. A very prominent cut-off minibrot lies south of the main body, with today's image located in a valley of this minibrot. The too-long calculation time of 7 minutes merely adds to the disappointment. But at least with this time aspect, relief may be found on the FOTD web sites. View the completed image online at: <http://www.crosscanpuzzles.com/Archives.html> A high-definition rendering is at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back FOTD's are at: <http://www.Nahee.com/FOTD/> After the early morning fog cleared off here at Fractal Central today, the rest of the day was near ideal, with mostly sunny skies and a temperature of 70F 21C. The fractal cats enjoyed the outside conditions from the inside, but when an unwanted cat wandered by, the dynamic duo leaped to the window and growled their warnings at the intruder. Except for a slightly heated lunch time exchange of opinions about politics and culture, the humans had a quiet day. The next FOTD will be posted in due time. Until whenever, take care, and if only one of the thousands of claims about alien abduction is true, then aliens from space actually are visiting earth. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= BusyBusierBusiest { ; time=0:07:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=+0.5231137961416107/-1.34126660456844/\ 1.53e+008/1/125/0 params=1.7/0/69/0 float=y maxiter=12000 inside=0 outside=tdis periodicity=6 colors=000_ldakbbkadk`fkZgkYikXmmZjkWhiUegRceP`cNZ\ aKW_IUYFRWDQX8PVBOUDNTFMRILQKKPMJNPIMRHLTGJWFIYEH_\ DFbCEdCDfEFcGGaIH_KIXMJVOKTQMQSNOUOMWPJYQH_RFlJH`S\ DP`ADh7Fi9HzBJzDKzFMzHOzIQzKRzMTjOVjQXkRYkT_kVakXc\ kZac2dk__eeVgnW`kXUiYOgZHec5d`8cZBcXDcUGbSJbQLbNOa\ LRaDOXGR_JTaLWcOYeR`gTbiWekZgn`jpclrfothqvktxmvzmt\ xzrzzzzzzzzzzfzodznzKlzdjzKiz`gzKezsozhiZYdaNZdCUf\ 2Pg9OgGOgNNgTNh_MhfMhmLkwKhsLepLblL_iMXeMUbMRZMOWN\ LSNIPNAD9DIGGMNJRUMV_P_fScm_jwVgsRdoNakJ_hFXdBU`7S\ Y9SXASXBSXCSWDSWESWFSWGSVHSVISVJSUKSULSUQMWMSUIYSE\ bQAhO5kOmlN6mNmnN7nNmoN8pN8pMmqMmrMmrMAsMmtM9wJmtM\ ArPBpRBnUClWCjZDh`DfcEdeEbhBdhDbiE`jFZkHXlIVmJTnLR\ oMPpSRuPPsNOqLMpJLnHJmFIkCGiAFh8Df6Ce4Ac29b9TZFkWF\ lVFlVFmUFmUGnTGnTGoSGoSGpRGpRMeLSWGYMAcC5aD8`DB_EE\ ZEHYFKWFMVGPUGSTGVSHYQH_PIbOauObtOcsPerPfqPgpPhoQj\ nQkmQllQmlSljUliVlhXlfZle } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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BUDDAH brot question you have to answer
by Sebastien Helie 22 Sep '12

22 Sep '12

YOU have to answer IN english I'am, but i'am not what i'am. question what i'am I IN french Je suis me ne suis pas ce que je suis qui suis-je? -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com

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IN (2) to analyze under dosbox maybe
by Sebastien Helie 22 Sep '12

22 Sep '12

use to be valide code... give a few INT to higher processor. some may get dirty. on entrance slot.? psy also possible BE IN math also. not automated but a full lot's to do. /************************************************/ /*Arc Library check befor loop and rnd variation*/ /*Sinpix12823 [Sebastien Helie] : 14_05_2011 */ /* */ /* */ /* double user/developper or compilator warning */ /* do a floating point matricial clean up */ /* before any mix of rnd with rotative rectangle*/ /* Note error entry slot while you clean up */ /* usefull # elsewhere. From experience their */ /* is two probleme */ /* 1-3 2-3(4) 1 - slot double number on count+*/ /* 2 - noise entry point */ /* how to clean up.. for now negative psy */ /* work but.. */ /* tech note : you could check the exact */ /* memory position of the error */ /* and by-pass (replace with */ /* jmp or 00 */ /* 0000:0000 */ /* jmp 01c0:0001 --> command PAL */ /* 01c0:0000 [error slot] */ /* :0001 --> memoris it somewhere */ /* intelligence emmergence */ /************************************************/ #include <stdio.h> #include <graphics.h> main (void) { /* request auto detection */ int gdriver = DETECT, gmode, errorcode; int xmax, ymax, loop, loop1; char jump; /* initialize graphics and local variables */ initgraph(&gdriver, &gmode, ""); /* read result of initialization */ errorcode = graphresult(); /* an error occurred */ if (errorcode != grOk) { printf("Graphics error: %s\n", grapherrormsg(errorcode)); printf("Press any key to halt:"); getch(); exit(1); } setcolor(6); xmax = getmaxx(); ymax = getmaxy(); /* draw a diagonal line */ line(0, 0, xmax, ymax); arc(320,240,0,45,100); arc(320,240,0,45,80); arc(320,240,90,135,100); arc(320,240,90,135,80); arc(320,240,180,225,100); arc(320,240,180,225,80); arc(320,240,270,315,100); arc(320,240,270,315,80); do{ for(loop;loop<=480;loop++) { line(0,0+loop,640,480-loop); setcolor(0); line(0,480-loop,640,0+loop); setcolor(6); } loop=0; }while(!kbhit()); /* clean up */ getch(); closegraph(); return 0; } https://dl.dropbox.com/u/68454194/ARCCHK.EXE -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com

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now hotmail?????????
by Sebastien Helie 22 Sep '12

22 Sep '12

is accepted in outlook..they still redject gmail. under http.. it might be a source of error(publicity) ,mushroom season soon!!!!!!!!!!!!!!!! end result under math pixel cynergia https://dl.dropbox.com/u/68454194/Apophysis-120921-202.png pretty and fragile i forgot my flower at the bar (Mac Bar... he do not give me acces to my free gmail?!baby bar?!) keep this under silence excellent beer talkable under the phone to solve.. i may connect with them with videotron but it's full of spam here... -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com

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SOME _SNAKE_MAC????
by Sebastien Helie 22 Sep '12

22 Sep '12

good for money or flash card... https://dl.dropbox.com/u/68454194/MIKE_SNAKE.PNG -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com

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i_bop_fene..sants...
by Sebastien Helie 22 Sep '12

22 Sep '12

IBUPROFEN is a cool publicity... try weed and ibuprofene -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com

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cubic art
by Sebastien Helie 22 Sep '12

22 Sep '12

to drive geometrical binary Harvard graphic for dos drive a perfect ansi...find the new at http://www.harvardgraphics.com/ dos version: exemple: https://dl.dropbox.com/u/68454194/1.bmp a cool easyer way than straight compilation in order to be balanced geomaster. i like google earth altought it hurt a little 9itch on the star space + marsian + moon objected really possible to do nice pictur flight... hurt too much for geostatic also present..like the native has something to solve... -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com

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fracta; humour
by Sebastien Helie 22 Sep '12

22 Sep '12

since i talk about torrent porno drop out actually i drive really down it and feel no current treath. it seem mostly clean but the image become white. out a few team approche kind'a 86.com not has brutal and classified by something who see everything sexual here Is by my best friend i do not always like. but porno star no probleme, masturbation is sexuality....egg KING https://dl.dropbox.com/u/68454194/demotivational-posters-masturbation.jpg the looser. in shit ship. leave for another game.... cat-rat lab knows. https://dl.dropbox.com/u/68454194/samorost1-01.jpg -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com

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FOTD 19-09-12 (Reciprocal of Infinity [7])
by Jim Muth 22 Sep '12

22 Sep '12

FOTD -- September 19, 2012 (Rating 7) Fractal visionaries and enthusiasts: Today's scene is a trip into the parent fractal that results when three negative parts of Z^(-2.3) are combined with one negative part of Z^(-5.6) on each iteration before (1/C) is added. This parent roughly resembles a diamond filled with debris. The southeast point of the diamond has strong Mandelbrot features including a pseudo-main bay and a very prominent straight main spike pointing southeast, which terminates as a filament in the shape of a large broken circle. Today's scene is located near the evaporating southwest edge of the shore line of the 'main bay'. A good part of the image is actually 'inside' stuff made visible by the 'zmag' inside fill. The black inside of the large central minibrot is hand colored. Luckily, none of the inside- the-minibrot color registers also appear outside the minibrot. The name "Reciprocal of Infinity" is a phrase that came to mind as I studied the image. The actual reciprocal of infinity is zero, though there might be different orders of zero (are they technically called infinitesimals?) for the different orders of infinity. I lack the knowledge to recognize the difference. With a rating of a 7, the worth of the image falls right in the middle of the FOTD range. The calculation time of 4-1/4 minutes is a slight drag, but headache relief is always available on the web sites. To avoid a calculation headache check the finished image at: <http://www.crosscanpuzzles.com/Archives.html> A high-definition rendering is at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> All the FOTD back images are online at: <http://www.Nahee.com/FOTD/> After yesterday's washout, when over 3-inches or 8-cm of rain fell, today seemed quite pleasant. The sky cleared just after sunrise, leading to a partly cloudy invigorating day with a high temperature of 68F 21C. The fractal cats, fully invigorated, got into a lively tussle over something only they were aware of. Little Cassie came out on top, while oversized Nicholas sulked away his defeat. The humans passed the mid-week doing totally human things such as finishing the unexpectedly heavy work. The next FOTD will certainly be posted, but I am not saying exactly when. Until whenever, take care, and don't forget to add rice to the list of foods that are hazardous to one's health. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Recip_of_Infinity { ; time=0:04:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip center-mag=+0.4271053768113824/-1.341152341307607/\ 41582/1/-105/0 params=-3/-2.3/-1/-5.6/0/0/0/0 float=y maxiter=1500 inside=zmag periodicity=6 colors=000SimOhkKhiGggCgeBdbBa`BZZBXXBUUBRSBOQBMOZ\ X9US8PN8LI8GE7C97747307BXxDUoERfGOYHLPSVSbdVmnYww`\ qrbkndeif_ehVaiXUbZMX`ERa7LUETNL`GSh9Zp2dw9hvGluMp\ uTttZxt`weavRbvCYnKTgSP`_SbVUdRWfN`jUdm_hpe0000000\ 00UUUmZZUUUhbaeXWbRR_LLXFG_DIbBKe9Mg7Nj5Pm3Rp1Tr0U\ fEOVRIH4NH4RJ4VL5ZN6bP7fR8lT7nV7rWDqWJqWPpWUpW_pWe\ oWhoWkoXnlXqiXqfXqcXq`XqYXqVXqTe_BhaAjb9mc8od7qe6t\ f5vg4xh4wZ5vQ6vH6rGCoFIlEOiDUfC_cCd`KaZSZW_WUgTSoQ\ RiUQdYP_aOVeNQiMLmMGpXSefbWb`XZZXWYXSWXOUXLTXORSQP\ OSOKVMGXKCZJ8kKZxLxZVr9dmCejFfgHfdKgbMg_PhXRhVNfZJ\ daGbeC`h8Zl5XoCVpJTqQRrWPsbNtiLuoKvjGkeC``8RW4GS06\ tS`oUYkVWgWTcXRZZPV_MR`KNaIQcOSdUUeZWgdYhj_ioWgpSe\ qOdqKbrHarSPgbDXm1Nl6PkARjESjIUiNWhRXgVZgZ_a_TX_MS\ _FN_9WgLdnXlugciiVYjMNkDBl50m76n9BnAHnCMnESnFXnHbn\ IgnMhmPimTilWjl_kkbkkfljiljdfb``VWVNSQFTRCUSAVT8WU\ 6XV4YV2RN4LF5F76907PXd0x3 } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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addendum to busy busy (mini error)
by Sebastien Helie 21 Sep '12

21 Sep '12

sorry i forget to copy and past the frame from calculator 1.... mini error. -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com mandel_3 { ; just out of storm reset=2004 type=formula formulafile=2012_6.frm formulaname=escapecard function=sin center-mag=-1.64e-006/2.205e-006/0.6666676 params=-1/1/1/1 inside=0 colors=00000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzzzLzzz000555<3>HHHKKKOO\ O<3>ccchhhmmmssszzz00z<3>z0z<3>z00<3>zz0<3>0z0<3>0zz<2>0GzVVz<3>zVz<3>zV\ V<3>zzV<3>VzV<3>Vzz<2>Vbzhhz<3>zhz<3>zhh<3>zzh<3>hzh<3>hzz<2>hlz00S<3>S0\ S<3>S00<3>SS0<3>0S0<3>0SS<2>07SEES<3>SES<3>SEE<3>SSE<3>ESE<3>ESS<2>EHSKK\ S<2>QKSSKSSKQSKOSKMSKK<2>SQKSSKQSKOSKMSKKSK<2>KSQKSSKQSKOSKMS00G<3>G0G<3\ >G00<3>GG0<3>0G0<3>0GG<2>04G88G<2>E8GG8GG8EG8CG8AG88<2>GE8GG8EG8CG8AG88G\ 8<2>8GE8GG8EG8CG8AGBBG<2>FBGGBGGBFGBDGBCGBB<2>GFBGGBFGBDGBCGBBGB<2>BGFBG\ GBFGBDGBCG000<6>000 } frm:escapecard{;sinpix a=real(p1),b=imag(p1/a),f=real(p2),g=imag(p2/-f) z=0.707106/1.4142,c=fn1(pixel): s=z*a+z*b+z^(-z+1+pixel) t=z*f/z+g m=z^3.001+c z=z+m+t+s |z|<10 }

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BUSY......busy
by Sebastien Helie 21 Sep '12

21 Sep '12

Since i do not emmite during the week mostly cause of my janitor position you may have to endure extensive emmission from\ me and my processor (1 and 2) during the weekend(tell me if it disturbe), math and your line totaly give me the will to drive work endure and caluclate... since i mostly use high end of procession those day it may be time for some real IN work tonight leaving the IR to master of the splendide cubic formation,... feel cheap? at 40$ a month i will have nothing to complain since i have so much to complain about i do not think about you.... feel follower and cheap, jar money somewhere if you can, a yes! internet seem to open to free calculatot like me since you i have lot's of free *.eu product thank's but product make me work more i have to concentrate... for food? logging travelling i based on only one sponsor.... Humm free and or freedome is a cased?!?!?!?!? aaaaa at least their object i like working and object i hate, anyway this money is a techno porno and i'am bored of it.. torrentz good point, thing start to get classified porno find under the word free was freexcafe for those who wonder where the nude been... deep like a mother hole. in navigation only if you whant your computer to become a porno star... i laught with my own... torrentz have no word line anymore she jumped on musicme........ freedome will adjuste i wish but i still use it carefully find a link rat lab and alien . ??? i really wonder by time, just hope Z get some class. this fractal a mandeloid who try to designe number 3 i left it normal color and it's based to parent, i will explore it later feel free to do so also... -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com start parameter file================================= mandel_3 { ; just out of storm reset=2004 type=formula formulafile=2012_6.frm formulaname=escapecard function=sin center-mag=-1.64e-006/2.205e-006/0.6666676 params=-1/1/1/1 inside=0 colors=00000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzzzLzzz000555<3>HHHKKKOO\ O<3>ccchhhmmmssszzz00z<3>z0z<3>z00<3>zz0<3>0z0<3>0zz<2>0GzVVz<3>zVz<3>zV\ V<3>zzV<3>VzV<3>Vzz<2>Vbzhhz<3>zhz<3>zhh<3>zzh<3>hzh<3>hzz<2>hlz00S<3>S0\ S<3>S00<3>SS0<3>0S0<3>0SS<2>07SEES<3>SES<3>SEE<3>SSE<3>ESE<3>ESS<2>EHSKK\ S<2>QKSSKSSKQSKOSKMSKK<2>SQKSSKQSKOSKMSKKSK<2>KSQKSSKQSKOSKMS00G<3>G0G<3\ >G00<3>GG0<3>0G0<3>0GG<2>04G88G<2>E8GG8GG8EG8CG8AG88<2>GE8GG8EG8CG8AG88G\ 8<2>8GE8GG8EG8CG8AGBBG<2>FBGGBGGBFGBDGBCGBB<2>GFBGGBFGBDGBCGBBGB<2>BGFBG\ GBFGBDGBCG000<6>000 } frm:escapecard{;sinpix a=real(p1),b=imag(p1/a),f=real(p2),g=imag(p2/-f) z=0.707106/1.4142,c=fn1(pixel): s=z*a+z*b+z^(-z+1+pixel) t=z*f/z+g m=z^3.001+c z=z+m+t+s |z|<10 } end parameter file==================================

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been informed of a electro probleme
by Sebastien Helie 21 Sep '12

21 Sep '12

Has i know, time parasite are comming from belgique (belgium) and are active under radio-canada television has a origine. communication had never been possible with them on the ground floor also, and i become sick and parasited the day i try to exchange dias(picture) slide of a long climbing road trip thru america and europe.. we see their (big computer) and lot's of green screen under their new... has i know Valcartier military are now informed of it and slowly get inside them.... best i know from the origine of this elecro broker (stronger than american one anyway) tank'us? -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com

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reality based on DOS compilated curve.
by Sebastien Helie 21 Sep '12

21 Sep '12

These 2 geometric file, are what i considere been my geometric base, just know that i come from deep schizoide dissorder (98-2002)and since i get my ass to mathematic my state of mind deeply ameliorate, from those 2 normal creation i became almost normal, now i'am forced to pills but i do not think i need it since i stay awoken 70 hours or so doing geometrie, i do not think the chimical can have action to controle the level of dopamine facing this self experience and experience just little state of transe(you see), i got about 60 of hem ... so i'am normal ?! no worry transes are also normal! but when they take the lead you got to considere yourself. we have a great master! FILE use hem with drop box and put egavga.bgi in the same folder it's the video driver needed by the graphic file.(*BORLAND C++made*)the lowest abandon ware and really rare i could find. , it could be our team normal star since their the automated creation do lot's of them and amplification of fractal reaction world wide not only driven under par is observed, i often worry cause mathematic cynergia can also make the mind decay... touch all those i could find to observe computer instability i hate when the screen become grey....?@i hate fractal also...best not mathematic!!!!!!!cynergia. greated?!?!?!? Accident of oct2011 still in activity... i should get better... i also have a paid videotron mail but the screen was full of spam when i tried it. Gmail seem solide but not really professional since i received a little reply i belived it ameliorate. One thing good on a machina who been sing like something build to decay?>???????????????? i lived it!!! it's hard to get out of it also. mostly proude of myself thank's for communication https://dl.dropbox.com/u/68454194/MATRITS.EXE https://dl.dropbox.com/u/68454194/MBTPSM.EXE https://dl.dropbox.com/u/68454194/EGAVGA.BGI -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com

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the chain of reality
by Sebastien Helie 21 Sep '12

21 Sep '12

Some fractal are not important but this one represent a interesting mathematic scene, two mathematic reality are on top of each other, one represent the sinus curve and behind a mandeloide, one get the mandeloide accurate the other end up in pure noise dealing with seemlike simple curve. i mannage my way out of chaos usually. In other term i tell you on audio once to get ready if you whanted to start fractal automation program known has apophysis. i deal myself with intense mind burst and high state of feeling doing fractal reserch, you probably remark and in order to stabilize the mind and the fractal reaction i usually set on multitasking normal mathematic curve....Self done has more has you can and also (interesting idea) has deep in compilation has possible (by deep i meen best should be in ASM language with a self sin table).... anyway we get cheated on a little by compilator (has intelligence #2) i think. exemple at https://dl.dropbox.com/u/68454194/page1.GIF Their is day i swear i should had been born english..god damn, but i think i get better.? -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com thechainofreality { ; 21_09_2012 reset=2004 type=formula formulafile=2012_7.frm formulaname=lizard_belief function=sin center-mag=-2.81852/0.0100167/4.901961 params=-1/0.5/2/1 float=y inside=0 colors=000<3>0WS0cZ0bY<7>8PN9NMALK<2>DGGEEEHHH<3>WWW___ccchhhmmmssszzz00\ z<3>z0z<3>z00<3>zz0<3>0z0<3>0zz<2>0GzVVz<3>zVz<3>zVV<3>zzV<3>VzV<3>Vzz<2\ >Vbzhhz<3>zhz<3>zhh<3>zzh<3>hzh<3>hzz<2>hlz00S<3>S0S<3>S00<3>SS0<3>0S0<3\ >0SS<2>07SEES<3>SES<3>SEE<3>SSE<3>ESE<3>ESS<2>EHSKKS<2>QKSSKSSKQSKOSKMSK\ K<2>SQKSSKQSKOSKMSKKSK<2>KSQKSSKQSKOSKMS00G<3>G0G<3>G00<3>GG0<3>0G0<3>0G\ G<2>04G88G<2>E8GG8GG8EG8CG8AG88<2>GE8GG8EG8CG8AG88G8<2>8GE8GG8EG8CG8AGBB\ G<2>FBGGBGGBFGBDGBCGBB<2>GFBGGBFGBDGBCGBBGB<2>BGFBGGBFGBDGBCG000<6>000 } frm:lizard_belief{;sinpix a=real(p1),b=imag(p1),e=real(p2),f=imag(p2) z=c=a+pixel*b+pixel: z=z^2+c t=a*z+b*z r=e*z+f*z z=fn1(r)^(t-1) |z|<74 }

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corrected FOTD for Sept 20
by Susan Brown 21 Sep '12

21 Sep '12

FOTD -- September 20, 2012 (Rating 6) Fractal visionaries and enthusiasts: This FOTD is posted a second time because the original posting included the wrong formula in the parameter file. Please delete the first posting. We have another rush in progress here at Fractal Central today. And when time is lacking, the accuracy of the image sometimes suffers. The name of today's image, "Busy Busier Busiest", explains the lowly rating of a modest 6 points. The image las a lot of color action, that's for sure, but like so many current movies, it has too much action and not enough plot. Even the addition of the 'tdis' rendering fails to bring life to the moribund image. The only thing worth noting in the image is the central minibrot, shaped suspiciously like a peanut. The formula behind the scene is Z^(1.7)+C, which I iterated 69 levels up the hyperladder with the 'ident' function applied. This mixture creates a parent fractal that somehow reminds me of a mermaid. A very prominent cut-off minibrot lies south of the main body, with today's image located in a valley of this minibrot. The too-long calculation time of 7 minutes merely adds to the disappointment. But at least with this time aspect, relief may be found on the FOTD web sites. View the completed image online at: <http://www.crosscanpuzzles.com/Archives.html> A high-definition rendering is at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back FOTD's are at: <http://www.Nahee.com/FOTD/ <http://www.nahee.com/FOTD/>> After the early morning fog cleared off here at Fractal Central today, the rest of the day was near ideal, with mostly sunny skies and a temperature of 70F 21C. The fractal cats enjoyed the outside conditions from the inside, but when an unwanted cat wandered by, the dynamic duo leaped to the window and growled their warnings at the intruder. Except for a slightly heated lunch time exchange of opinions about politics and culture, the humans had a quiet day. The next FOTD will be posted in due time. Until whenever, take care, and if only one of the thousands of claims about alien abduction is true, then aliens from space actually are visiting earth. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= BusyBusierBusiest { ; time=0:07:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=+0.5231137961416107/-1.34126660456844/\ 1.53e+008/1/125/0 params=1.7/0/69/0 float=y maxiter=12000 inside=0 outside=tdis periodicity=6 colors=000_ldakbbkadk`fkZgkYikXmmZjkWhiUegRceP`cNZ\ aKW_IUYFRWDQX8PVBOUDNTFMRILQKKPMJNPIMRHLTGJWFIYEH_\ DFbCEdCDfEFcGGaIH_KIXMJVOKTQMQSNOUOMWPJYQH_RFlJH`S\ DP`ADh7Fi9HzBJzDKzFMzHOzIQzKRzMTjOVjQXkRYkT_kVakXc\ kZac2dk__eeVgnW`kXUiYOgZHec5d`8cZBcXDcUGbSJbQLbNOa\ LRaDOXGR_JTaLWcOYeR`gTbiWekZgn`jpclrfothqvktxmvzmt\ xzrzzzzzzzzzzfzodznzKlzdjzKiz`gzKezsozhiZYdaNZdCUf\ 2Pg9OgGOgNNgTNh_MhfMhmLkwKhsLepLblL_iMXeMUbMRZMOWN\ LSNIPNAD9DIGGMNJRUMV_P_fScm_jwVgsRdoNakJ_hFXdBU`7S\ Y9SXASXBSXCSWDSWESWFSWGSVHSVISVJSUKSULSUQMWMSUIYSE\ bQAhO5kOmlN6mNmnN7nNmoN8pN8pMmqMmrMmrMAsMmtM9wJmtM\ ArPBpRBnUClWCjZDh`DfcEdeEbhBdhDbiE`jFZkHXlIVmJTnLR\ oMPpSRuPPsNOqLMpJLnHJmFIkCGiAFh8Df6Ce4Ac29b9TZFkWF\ lVFlVFmUFmUGnTGnTGoSGoSGpRGpRMeLSWGYMAcC5aD8`DB_EE\ ZEHYFKWFMVGPUGSTGVSHYQH_PIbOauObtOcsPerPfqPgpPhoQj\ nQkmQllQmlSljUliVlhXlfZle } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 20-09-12 (Busy Busier Busiest [6])
by Jim Muth 20 Sep '12

20 Sep '12

FOTD -- September 20, 2012 (Rating 6) Fractal visionaries and enthusiasts: We have another rush in progress here at Fractal Central today. And when time is lacking, the quality of the image sometimes suffers. The name of today's image, "Busy Busier Busiest", explains the lowly rating of a modest 6 points. The image las a lot of color action, that's for sure, but like so many current movies, it has too much action and not enough plot. Even the addition of the 'tdis' rendering fails to bring life to the moribund image. The only thing worth noting in the image is the central minibrot, shaped suspiciously like a peanut. The formula behind the scene is Z^(1.7)+C, which I iterated 69 levels up the hyperladder with the 'ident' function applied. This mixture creates a parent fractal that somehow reminds me of a mermaid. A very prominent cut-off minibrot lies south of the main body, with today's image located in a valley of this minibrot. The too-long calculation time of 7 minutes merely adds to the disappointment. But at least with this time aspect, relief may be found on the FOTD web sites. View the completed image online at: <http://www.crosscanpuzzles.com/Archives.html> A high-definition rendering is at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back FOTD's are at: <http://www.Nahee.com/FOTD/> After the early morning fog cleared off here at Fractal Central today, the rest of the day was near ideal, with mostly sunny skies and a temperature of 70F 21C. The fractal cats enjoyed the outside conditions from the inside, but when an unwanted cat wandered by, the dynamic duo leaped to the window and growled their warnings at the intruder. Except for a slightly heated lunch time exchange of opinions about politics and culture, the humans had a quiet day. The next FOTD will be posted in due time. Until whenever, take care, and if only one of the thousands of claims about alien abduction is true, then aliens from space actually are visiting earth. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= BusyBusierBusiest { ; time=0:07:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=+0.5231137961416107/-1.34126660456844/\ 1.53e+008/1/125/0 params=1.7/0/69/0 float=y maxiter=12000 inside=0 outside=tdis periodicity=6 colors=000_ldakbbkadk`fkZgkYikXmmZjkWhiUegRceP`cNZ\ aKW_IUYFRWDQX8PVBOUDNTFMRILQKKPMJNPIMRHLTGJWFIYEH_\ DFbCEdCDfEFcGGaIH_KIXMJVOKTQMQSNOUOMWPJYQH_RFlJH`S\ DP`ADh7Fi9HzBJzDKzFMzHOzIQzKRzMTjOVjQXkRYkT_kVakXc\ kZac2dk__eeVgnW`kXUiYOgZHec5d`8cZBcXDcUGbSJbQLbNOa\ LRaDOXGR_JTaLWcOYeR`gTbiWekZgn`jpclrfothqvktxmvzmt\ xzrzzzzzzzzzzfzodznzKlzdjzKiz`gzKezsozhiZYdaNZdCUf\ 2Pg9OgGOgNNgTNh_MhfMhmLkwKhsLepLblL_iMXeMUbMRZMOWN\ LSNIPNAD9DIGGMNJRUMV_P_fScm_jwVgsRdoNakJ_hFXdBU`7S\ Y9SXASXBSXCSWDSWESWFSWGSVHSVISVJSUKSULSUQMWMSUIYSE\ bQAhO5kOmlN6mNmnN7nNmoN8pN8pMmqMmrMmrMAsMmtM9wJmtM\ ArPBpRBnUClWCjZDh`DfcEdeEbhBdhDbiE`jFZkHXlIVmJTnLR\ oMPpSRuPPsNOqLMpJLnHJmFIkCGiAFh8Df6Ce4Ac29b9TZFkWF\ lVFlVFmUFmUGnTGnTGoSGoSGpRGpRMeLSWGYMAcC5aD8`DB_EE\ ZEHYFKWFMVGPUGSTGVSHYQH_PIbOauObtOcsPerPfqPgpPhoQj\ nQkmQllQmlSljUliVlhXlfZle } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD Sept 19
by Susan Brown 20 Sep '12

20 Sep '12

FOTD -- September 19, 2012 (Rating 7) Fractal visionaries and enthusiasts: Today's scene is a trip into the parent fractal that results when three negative parts of Z^(-2.3) are combined with one negative part of Z^(-5.6) on each iteration before (1/C) is added. This parent roughly resembles a diamond filled with debris. The southeast point of the diamond has strong Mandelbrot features including a pseudo-main bay and a very prominent straight main spike pointing southeast, which terminates as a filament in the shape of a large broken circle. Today's scene is located near the evaporating southwest edge of the shore line of the 'main bay'. A good part of the image is actually 'inside' stuff made visible by the 'zmag' inside fill. The black inside of the large central minibrot is hand colored. Luckily, none of the inside- the-minibrot color registers also appear outside the minibrot. The name "Reciprocal of Infinity" is a phrase that came to mind as I studied the image. The actual reciprocal of infinity is zero, though there might be different orders of zero (are they technically called infinitesimals?) for the different orders of infinity. I lack the knowledge to recognize the difference. With a rating of a 7, the worth of the image falls right in the middle of the FOTD range. The calculation time of 4-1/4 minutes is a slight drag, but headache relief is always available on the web sites. To avoid a calculation headache check the finished image at: <http://www.crosscanpuzzles.com/Archives.html> A high-definition rendering is at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> All the FOTD back images are online at: <http://www.Nahee.com/FOTD/ <http://www.nahee.com/FOTD/>> After yesterday's washout, when over 3-inches or 8-cm of rain fell, today seemed quite pleasant. The sky cleared just after sunrise, leading to a partly cloudy invigorating day with a high temperature of 68F 21C. The fractal cats, fully invigorated, got into a lively tussle over something only they were aware of. Little Cassie came out on top, while oversized Nicholas sulked away his defeat. The humans passed the mid-week doing totally human things such as finishing the unexpectedly heavy work. The next FOTD will certainly be posted, but I am not saying exactly when. Until whenever, take care, and don't forget to add rice to the list of foods that are hazardous to one's health. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Recip_of_Infinity { ; time=0:04:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip center-mag=+0.4271053768113824/-1.341152341307607/\ 41582/1/-105/0 params=-3/-2.3/-1/-5.6/0/0/0/0 float=y maxiter=1500 inside=zmag periodicity=6 colors=000SimOhkKhiGggCgeBdbBa`BZZBXXBUUBRSBOQBMOZ\ X9US8PN8LI8GE7C97747307BXxDUoERfGOYHLPSVSbdVmnYww`\ qrbkndeif_ehVaiXUbZMX`ERa7LUETNL`GSh9Zp2dw9hvGluMp\ uTttZxt`weavRbvCYnKTgSP`_SbVUdRWfN`jUdm_hpe0000000\ 00UUUmZZUUUhbaeXWbRR_LLXFG_DIbBKe9Mg7Nj5Pm3Rp1Tr0U\ fEOVRIH4NH4RJ4VL5ZN6bP7fR8lT7nV7rWDqWJqWPpWUpW_pWe\ oWhoWkoXnlXqiXqfXqcXq`XqYXqVXqTe_BhaAjb9mc8od7qe6t\ f5vg4xh4wZ5vQ6vH6rGCoFIlEOiDUfC_cCd`KaZSZW_WUgTSoQ\ RiUQdYP_aOVeNQiMLmMGpXSefbWb`XZZXWYXSWXOUXLTXORSQP\ OSOKVMGXKCZJ8kKZxLxZVr9dmCejFfgHfdKgbMg_PhXRhVNfZJ\ daGbeC`h8Zl5XoCVpJTqQRrWPsbNtiLuoKvjGkeC``8RW4GS06\ tS`oUYkVWgWTcXRZZPV_MR`KNaIQcOSdUUeZWgdYhj_ioWgpSe\ qOdqKbrHarSPgbDXm1Nl6PkARjESjIUiNWhRXgVZgZ_a_TX_MS\ _FN_9WgLdnXlugciiVYjMNkDBl50m76n9BnAHnCMnESnFXnHbn\ IgnMhmPimTilWjl_kkbkkfljiljdfb``VWVNSQFTRCUSAVT8WU\ 6XV4YV2RN4LF5F76907PXd0x3 } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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mandel into the noise
by Sebastien Helie 19 Sep '12

19 Sep '12

Having hard time finding formula vector with descent object those last day. Anyway to add to the story here a minibrot who find himself deepdown into a noise channel... -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com start parameter file====================================== into_the_noise { ; 18_09_2012 reset=2004 type=formula formulafile=2012_7.frm formulaname=seth center-mag=+0.77293646694583450/+0.09975384023301036/121.5315 params=-1.707106/1 float=y bailout=1000 inside=0 periodicity=0 colors=000<3>000000000<2>000000222444<6>VVVZZZbbb0ffjjjnnnrrr0vvzzzywzxs\ zwmzvkz<3>qWy000R9ymKylGyzz0j8yhlxd4x`4xX3aT3y<3>D2y91y51y00z44x88vCNzGG\ r<2>TTl0zi``g<3>qq_uuYzzV<3>VzV<3>Vzz<2>Vbzhhz<3>zhz<3>zhh<3>zzhuzh<6>wd\ pwaqwZr<3>yMxzIyzFz<8>sJQrJLrKH<3>nM0<3>wS0zU0zU0<7>vS3uS4uS4<3>rQ6<2>zU\ 0<9>cPDaPEZOFXOHVNISMKSOKSQKSSK<2>MSKKSKKSMKSOKSQKSS<2>KMS00G<3>G0G<3>G0\ 0<3>GG0<3>0G0<3>0GG<2>04G88G<2>E8GG8GG8EG8CG8AG88<2>GE8GG8EG8CG8AG88G8<2\ >8GE8GG8EG8CG8AGBBG<2>FBGGBGGBFGBDGBCGBB<2>GFBGGBFGBDGBCGBBGB<2>BGFBGGBF\ GBDGBCG000<5>000kkk } frm:seth{;sinpix a=real(p1),b=imag(p1) z=c=pixel: t=a*z+b*z+1/z r=t^2+c z=r |z|<74 } end parameter file=======================================

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FOTD 17-09-12 (Alien Landscape [7])
by Jim Muth 19 Sep '12

19 Sep '12

FOTD -- September 17, 2012 (Rating 7) Fractal visionaries and enthusiasts: Today, as I promised yesterday, we move beyond the field of rectangles into the field of landscapes on other planets, where we find the curious scene illustrated in today's image. The gravity on this alien planet must be extremely weak, since the fractal rock formations appear barely able to support them- selves. At the same time, the planet appears to have gravity enough to hold a thin atmosphere, which gives the dark purplish tinge to the background sky. The generating formula, Mandnewt12, is the last in my ancient series of MandNewt formulas, the purpose of which I have long since forgotten. These formulas seem to generate images that combine Mandelbrot features with features found in fractals generated by Newton's method of extracting roots. At the present time, the formulas serve to create fractals that are a total surprise, which is why I sometimes turn to them when I wish to be surprised. Since many images created by these formulas consist only of 'inside' stuff, they do not come to life until an active inside fill is applied. In today's image the 'atan' fill does the job. The parameters were found by the evolver feature of Fractint and then rounded off to make things simpler. However I did set the p3 parameters to unity by hand. The calculation time of a mere 25 seconds will bring relief to those who have more to do than can be squeezed into the time available. The web sites can eliminate even this brief delay. The official FOTD web site may be accessed at: <http://www.crosscanpuzzles.com/Archives.html> The finished image is posted there to be viewed for free by all interested fractalists. A high-definition rendering is available, also for free, at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are available online at: <http://www.Nahee.com/FOTD/> And all of them are free. Today began foggy and chilly here at Fractal Central, with a temperature of 48F +9C. The fog cleared by mid-morning, leading to a partly sunny afternoon with a high temperature of 73F 23C. Rain was due to arrive after dark, but as of FOTD post time, had not yet appeared. The fractal cats had a day of roughhousing, apparently forgetting that they had talked with the doctor when they were kittens. The humans made it through another day without anything happen- ing that was worth reporting. The next FOTD will be posted when the neat come home. Jumbo was a bull elephant; Ferdinand was a bull neat. Don't call him a bull cow; it makes no sense and he might be deeply offended! Until whenever, take care, and keep iterating. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Alien_Landscape { ; time=0:00:25.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=mandnewt.frm formulaname=MandNewt12 center-mag=1.49823/-0.03563\ 47/65.396/1/-102.5/0 params=-2.06/4.81/-3.31/-0.91\ /1/1 float=y maxiter=95 inside=atan periodicity=0 colors=000G2rH2tI2vJ2xK2z02z02z02z02z02z02z02z02z0\ 2z02zLWyLVyLUyLTyLRwLQwLPwLNwLMwLLwJJvJJtJJsIIpIIn\ HHmzzzzvzzrztmzmhzedzZZzTTtMMmHHeBDZBBUA9QA8N97M95\ L85I84H74G74D63D63B529528416845D74IA3PF2TJ1WP0ZU0R\ Z0Vb0Yf0ek0mp0tt0zs0zp0zn0zm1tk3mh4ef6`e8WbAVaDUTF\ TRHRPJQNMPLPNJRMHULGW1L03M05N07P09Q0BT0DU0GV0IW0LY\ 0H0qH0vI0yI0zJ0tM1mN6dPAYQGQTLIURDVW6Yb0Y`2ZY5ZV8`\ TAaPDaMHbJLdHNeFReDVf9Zh7ah5ej3jj5jh6hh8hh9ffBffDe\ fFefHdeIdeLbeMbdPadQadT`bU`bWZaUZZRZYPZVMZUJZTHZQF\ ZPD`MA`L8`J6`H4`G2`D0`D0`A0aB0aF0`I0ZM0YQ0WU0VV0YW\ 2`Y7bYBeZHh`NkaUnbWmdZkdahebffeehhdhkajn`kqZmsYmvV\ nyUpsWqnZshatddtZfvUjwQmyLpkNh`QaPRUFUN5WH5WG5WG5W\ F4WD4WD4WD4WB4WA4WA4W94W83W83W73W63W63W53W43W32W32\ W22W12W12W02W02W02W01W01W01W01W00W02W05W17W4AW8DWB\ GWGJWJMWPQYTTYYWYa`YfbYkfYqjYvnYznYynYwnZtnZqnZnnZ\ mp`jp`fp`ep`bp``paYpaWpaU } frm:MandNewt12 {; Jim Muth z=g=pixel, a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), e=real(p3), f=imag(p3): h=z^a+(g-1)*(z-b) j=c*z^d+g z=z-e*h/(f*j), .0000000000000000000000000000005 <= |h| } END PARAMETER FILE=========================================

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FOTD 18-09-12 (Ring Around the World [7])
by Jim Muth 18 Sep '12

18 Sep '12

FOTD -- September 18, 2012 (Rating 7) Fractal visionaries and enthusiasts: Today's image is a scene on one of the five tiny stems of the Z^(6.003)+C Mandeloid. The stem in question differs from the other four because it lies directly on the negative X-axis, where the fractal break-up begins. The other stems are virtu- ally identical to those of the Z^(6)+C Mandeloid. The area I checked lies just east of the large minibrot, the area where the strange rectangles of the Z^(2.003)+C Mandeloid are found. In today's Z^(6.003)+C Mandeloid there are no rectangles, but rather an area of partly-merged, moth-eaten minibrots connected by a complex network of cobweb-like fila- ments. Today's image shows one of these networks. The rating of a 7 seems about right. Perhaps if I had put more effort into the coloring I might have raised the rating a half- point or so, but when I first saw the image I found too little potential in it. The name "Ring Around the World" does not refer to a dream of universal comradeship, which will forever remain a dream, it refers to the circular spider filament surrounding the central 'whatever it is' open area. The calculation time of 4-1/2 minutes is true when the image is calculated with the passes set to 1. This time may be cut by rendering the scene with the passes set to 'g'. Doing this will cause some of the thinner filaments to drop out however. View the image without such calculation worries on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> A high-definition version is online at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are available at: <http://www.Nahee.com/FOTD/> Dark clouds, gusty winds and torrential rain showers totally spoiled things here at Fractal Central. The temperature of 72F 22C was fair enough for outdoor activity, but not with the rain falling. The fractal cats, weather prognosticators that they are, knew that the foul day was coming, and when it arrived they shrugged it off with a thrash of their tails. The humans, (at least we still were when we last checked), had too much indoor stuff to finish to be concerned with a rainy day. Unless I am mistaken, the next FOTD will be posted in a day or so. Until whenever, take care, and remember those 1960's protests? Go out today and protest about whatever you wish. The 1960's are gone and not coming back. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= RingAroundTheWorld { ; time=0:04:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotN passes=1 center-mag=-1.132053240991767/+0.00000000304411211\ /3.178357e+009 params=6.003/0/0/0/0/0 float=y maxiter=1750 inside=0 periodicity=6 colors=000gkQijOliMniKfXMZLNS9OUDRWGTXKWZNY_Q_VRbR\ SeNShJTkFTn27y46n65d74V93LA3B95D96E88F89G7BH7CJ6EK\ 6FL5GM5IN4JP4LQ3MR3OS2PT2QU9URFXOM_MSbJZeGdhEkkBqn\ 9pjCogFndImaLlZOlWRlYSl_Sl`TlbTldUleUlgVlhVljWllWl\ mXloXlqYlrYltZluZjtXitWgsVfsUdsTcrRazQ`zzmzzczzXqz\ SlzOgzKczFZFBUD7QC6SC5UD4VD6TF8SGAQICPJENLGMMIKOKJ\ PMHROGSQIQRJPSKOTMNUNMVOLWQJXRIYSHZUG_VF`WEaXDZWGW\ VIUULRTNPSPMRzKQzHPzFOmCNcAMb8HT7DK59A45188KCBbGDu\ KCsNCqQCpUBnXBm_BkcAifAhiAfm9ep9cs9bqDcoGdmKekNfiR\ ggUheYic`iadj_gkYklWnmUrnSuoRxoWkh`_aeOViCPhFPhHPg\ JPgLPgNPfPPfRPeTPeVPeXPdZPd`PdbPeaSe`Ue_We_YeZ_eYa\ eXceXeeWgeVieUkeUmeToeSqeSshUnkWimYdp__saVucQxeLzf\ Gp_DfUBXN9NH6DA4442332221221110000NirMgpLfoLemKdlK\ ckJbiI`hI_gHZe06B86BA7BD7BF8BH9AK9AMAAPAARBATBAXHB\ `MCcRDgWEj`FneGqjHuoIxtJBASFBUIBVLBWOBYRBZUB_XBa_C\ bbCceCehCfkCgnCiqCjtCkqFi } frm:MandelbrotN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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FOTD 16-09-12 (On a Higher Plane [9.5])
by Jim Muth 17 Sep '12

17 Sep '12

FOTD -- September 16, 2012 (Rating 9.5) Fractal visionaries and enthusiasts: There was no FOTD on September 15 because FL and I took a short trip to a nearby primeval forest and spent time by a waterfall -- a very enjoyable thing that we actually did without a 'smart' cell phone giving us constant access to the internet. (I wonder how people got along back in the ancient 20th Century without one of those smart devices to keep them connected?) The FOTD for September 14 was supposed to be the last of the current rectangle series, but that evening, while I was going through some early formulas, searching for the image in which I originally discovered the Z^(2.003)+C rectangle, I turned up today's image, which I feel fully deserves the honor of being re-declared an FOTD. The image has already appeared in a slightly modified form, as an early FOTD, but it has lost none of its impact since then. Do not be scared off by the following description of today's image. It contains none of the offensive gore we see so much of in violent movies and games. At first glance the image looks like a man with his head missing and a trapezoid, which is actually the distorted rectangle, floating above his neck. A close look will reveal two vague wings like angels are supposed to have, extending from the trapezoid and flapping in the air. Since it is difficult to remain physically alive with one's head missing, I assume the wings are carrying the man's soul, (whatever a soul might be), to wherever souls go when a person passes on. The formula is an early effort to draw oblique slices through the Julibrot. It is not new, but it has been used so rarely that it should be considered a new one. With some effort, I could have calculated the same image with a present-day working formula, but laziness set in and I let it go as it is. The name "On a Higher Plane" refers to one of those higher spiritual planes of the new-age culture, which cause skeptics knees to start knocking in apprehension. Since the astronomers have failed to find heaven even with their most powerful instru- ments, it must lie on one of these planes of higher vibration. The rating of a 9.5 indicates that I consider the image to be one of the all-time best. It does indeed have a bit of artistic worth, as those familiar with the strange paintings of the surrealist artist Rene Magritte will recognize. The calculation time of 1-1/4 minutes is a true bargain, so snap it up before it is gone. The finished image is available in totally absolute glory on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> and in even more glory at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are posted at: <http://www.Nahee.com/FOTD/> and some of those images go pretty far back. Things are beginning to take on a feeling of Autumn here at Fractal Central. The day dawned with a temperature of 50F 10C, and by afternoon it warmed to a high of only 72F 22C. The brilliant sun did its best to warm the air further, but its angle is getting so low that it is fast losing strength. The fractal cats enjoy the lower sun angle however. They spent the afternoon on their shelf in the southwest window, where the sun now shines in more strongly every afternoon. The humans spent the day doing human things such as watching the news and discussing politics. The next FOTD, again guaranteed to hold no rectangles, will be posted when it is ready (most likely in 24 hours). Until whenever it does appear, take care, and will mankind's growing fascination with computer-driven technology be his salvation or downfall? (Or are we all being brainwashed into zombies by the space aliens from Sirius-C? ) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= On_a_Higher_Plane { ; time=0:01:25.00 SF5 at 2000MHZ reset=1960 type=formula formulafile=may-98.par formulaname=mult2-003-XY-ZW function=flip/ident center-mag=+0.00652543223009536/0/92.95638/0.6626/\ -90/0 params=89.79892/94.33779/0.000177/0.073865/\ -1.743502/0 float=y maxiter=1200 inside=bof61 logmap=49 periodicity=6 passes=1 colors=00055AC6RD7TD8VE9XEAZCBWDC`DDaCEaCFbCGcAF_B\ IeAJfAJg9Kh9Ki9Fj9Kk9Kl8Km8Kn7Ko7Gl6Lp6Lq6Lr5Ls5Lt\ 4Ip4Lv4Lw3Lx3Ky2Kz2Jv3Lz3Lz4Mz4Mz4Mz4Lz5Nz5Nz5Nz5O\ z6Oz6Ny6Py7Py7Py7Qy7Qy8Qy8Qy8Ry9Ry9Ry9Sy9SyASyATyA\ TyATyBTyBUyBUyCUyCVxCVxCVxDWxDWxDWxEWxEXxEXxEXxFYx\ FYxFYxFZxGZxGZxGZxH_xH_xH_xH`wI`wI`wIawJawJawJawJb\ wKbwKbwKcwKcwLcwLdwLdwMdwMdwMewMewNewNfwNfvOfvOgvO\ gvOgvPgvPhvPhvPhvQivQivQivOixPiwPiwQivRivRiuSiuTit\ TitUisVirVirWiqXiqYipYipZio_in_in`imaimailbilcikci\ kdijeiieiifihgihgighigiifiifjiekidkidlicmicnibnibo\ iapi`pi`qi_ri_riZsiZtiYtiYuiXviWxjXwjXwiXviXviXuiX\ uhXthXthXsgXsgXrgXrgXqfXqfXpfXpeXoeXoeXneXndWmdWmd\ WlcWlcWkcWjcWjbWibWibWhaWhaWgaWgaWf`Wf`We`We_Wd_Wd\ _Wc_WcZWbZWbZWaYWaYW`YW`YW_XW_XWZXWZWWYWWXWWXWWWVW\ WVWVVWVUVUUVUUVTUVTTVSTVSTVRSVRSVQSVQSVPRVPRVORVOQ\ VNQVNQVMQVMPVLPVLPVMPUMPT } frm:mult2-003-XY-ZW {; draws 6 planes and many rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real((p1)+10^(-100))*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3: z=z^2.003+c, |z| <= 36 } END PARAMETER FILE=========================================

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rectangle_swirl
by Sebastien Helie 15 Sep '12

15 Sep '12

The reaction really soften since a few day. probably cause of apophysis extensive usage. I also encounter the rectangle thru my reserch, here the parent show a part of rectangle with a ellipsoide above it, in union. the resulted fractal is in a debris Field surronding the ellipsoide. pretty an ritch enought to be posted with a 6.5 -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com start parameter file=========================== rectangle_swirl { ; 15_09_2012 reset=2004 type=formula formulafile=2012_6_1.frm formulaname=retro_virus1 center-mag=-1.64464712041402300/-1.44959021993491700/6633.707/1/90/-1.23\ 373533611470521e-014 params=4/-4 float=y inside=0 colors=00000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzzzLzzz000555<3>HHHKKKOO\ O<3>ccchhhmmmssszzz00z<3>z0z<3>z00<3>zz0<3>0z0<3>0zz<2>0GzVVz<3>zVz<3>zV\ VzbVzjV<8>mX`kVajUb<2>ePdcNecPe<7>ddfdffdhf<3>epg<3>QkgLjfHhf<3>0ce<8>0X\ L0WJ0WH<3>0S7<2>0SS<2>07SEES<8>66_55`44a<2>11d00e11d<8>IDVKETMFSOHRQIQSK\ OSKMSKK<2>SQKSSKQSKOSKMSKKSK<2>KSQKSSKQSKOSKMS00G<3>G0G<3>G00<3>GG0<3>0G\ 0<3>0GG<2>04G88G<2>E8GG8GG8EG8CG8AG88<2>GE8GG8EG8CG8AG88G8<2>8GE8GG8EG8C\ G8AGBBG<2>FBGGBGGBFGBDGBCGBB<2>GFBGGBFGBDGBCGBBGB<2>BGFBGGBFGBDGBCG000<6\ >000 } frm:retro_virus1{;sinpix a=real(p1^(-1*0.707106)),b=imag(p1/2) z=1.4142^0.70106,c=pixel: m=z^a+c z=b*m/c*z |z|<1974 } end parameter file=================================

1 0

leave a chance
by Sebastien Helie 15 Sep '12

15 Sep '12

Since my internet get infected by baby mixing themself with geometrie, i decided to leave them room, a fractint frame who express 3 baby in formation. I leave room but i do not think it could be made serial. probably a uncommon possibility, something attract hem?<! zooming in it also express a few more potential position baby can take, so i may just start to think the reaction was normal.. hoping it will stabilize. i hate seeing mix of faces and geometrie. for the reason that full personage also apear every know and then. thru apophysis... simple parent. -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com two_and3_child { ; 15_09_2012 reset=2004 type=formula formulafile=2012_6_1.frm formulaname=retro_virus center-mag=-0.866444/0.400501/1.718213/1/-90/3.88578058618804789e-016 params=2/0 float=y maxiter=15000 inside=0 logmap=226 periodicity=6 mathtolerance=0.05/1 colors=cX00000e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzzzLzzz000555<3>HHHKKKOO\ O<3>ccchhhmmmssszzz00z<3>z0z<3>z00<3>zz0<3>0z0<3>0zz<2>0GzVVz<3>zVz<3>zV\ V<3>zzV<3>VzV<3>Vzz<2>Vbzhhz<3>zhz<3>zhh<3>zzh<3>hzh<3>hzz<2>hlz00S<3>S0\ S<3>S00<3>SS0<3>0S0<3>0SS<2>07SEES<3>SES<3>SEE<3>SSE<3>ESE<3>ESS<2>EHSKK\ S<2>QKSSKSSKQSKOSKMSKK<2>SQKSSKQSKOSKMSKKSK<2>KSQKSSKQSKOSKMS00G<3>G0G<3\ >G00<3>GG0<3>0G0<3>0GG<2>04G88G<2>E8GG8GG8EG8CG8AG88<2>GE8GG8EG8CG8AG88G\ 8<2>8GE8GG8EG8CG8AGBBG<2>FBGGBGGBFGBDGBCGBB<2>GFBGGBFGBDGBCGBBGB<2>BGFBG\ GBFGBDGBCG000<6>000 } frm:retro_virus{;sinpix a=real(p1),b=imag(p1) z=1.4142^0.70106,c=pixel: z=z^a+c |z|<1974 }

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FOTD 14-09-12 (Ultimate Rectangle [8])
by Jim Muth 14 Sep '12

14 Sep '12

FOTD -- September 14, 2012 (Rating 8) Fractal visionaries and enthusiasts: As the name implies, today's rectangle is the ultimate, at least of the current string of images if not of quality. It lies in the Elliptic orientation, which is determined by the real(c), imag(z) axes, and is located in the interior of the original Julia rectangle. In my opinion however, it *is* the best of the current rectangle lot, well worth the rating of an 8. To bring the rectangle to recognizable proportions, I stretched and skewed the image about as far as possible. At this degree of distortion, (the skewing is over 89.9), strange things sometimes start to happen with the program, though so far I have noticed none in today's scene. The coloring is a bit quirky, but this merely adds to the overall effect. The calculation time of 1-3/4 minutes is fast enough to keep boredom at bay, but there is still the minor chore of setting up and running the included parameter file. So enjoy life without the calculation. Check the finished image at: <http://www.crosscanpuzzles.com/Archives.html> and the high-definition versions at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are online at: <http://www.Nahee.com/FOTD/> Near perfect conditions continued today here at Fractal Central, with low humidity and a temperature of 79F 26C. The only flaw was an increase in clouds. The fractal cats spent the day looking for trouble they might get into. Cassie finally found it when she got herself locked in a closet, where she stayed over an hour before she was found and released. She never cries when locked somewhere. Nicholas' problem is his tendency to eat strange stuff such as plastic, but he was well behaved, at least for today. The humans had another typical day, agreeing on some things, disagreeing on others. The next FOTD will be posted in about two days. It will be something other than a rectangle. Until then, take care, and why does religion, which preaches goodness, bring about so much evil? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Ultimate_Rectangle { ; time=0:01:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=+0.000484087\ 85092349/+0.00218988416650909/8.820301e+010/0.0070\ 22/-70.7667429766036236/89.9210014763847312 params=90/90/0/0/-1.7435/0/0.000175/0.073883/2.003\ /0 float=y maxiter=15000 inside=0 logmap=226 periodicity=6 mathtolerance=0.05/1 colors=000E9EEADDBDCCDBD9BF8DGAGHDJIDLJGOKJQMNSORU\ RVWTZYWa__dacgcfmyGUoFMgBFbA7XA0RB2UB4YC6aC8eC9`B7\ WB6RB5MB4HB3CB27B13B0DL5NVAWdEenJnwNltLqeSihYbkcVn\ jUnBUsAUwAcuCcvDcwFcxGmyImzJmzLmzMzzOzzPzzRzzSzzUz\ zVzzXzzYzzZzzZzzZzzZzz_zz_zz_zz_zz_zzRzzIzz9zz0Y`o\ Z`oZ`oZ`o_`o_`o__o`_n`_n`_na_na_na_nbZnbZncZncZncZ\ ndZndZndZneYneYneYnfYnfYmfYmgYmgXmhXmhXmhXmiXmiXmi\ XmjXmjWmjWmkWmkWmkWmlWmlWmmXnlWmlWmkWlkVljVkjVkiUj\ iUjhUihTigThgThfSgfSgfSgeRfeRfdRedQecQdcQdbPcbPcaP\ baOb`Oa`Oa_N`_N`_N`ZN_ZM_YMZYMZXLYXLYWLXWKXVKWVKWU\ JVUJVTJUTIUTIUSITSHTRHSRHSQGRQGRPGQPFQOFPOFPNEONEO\ MENMDNMDNLDMLDMKCLKCLJCKJBKIBJIBJHAcHAcGAcG9cF9cF9\ cF8cE8cE8cD7cD7cC7cC6cB6cB6cA5cA5U95U94U84U84U73U8\ 4U84U84U94U95U95U95UA5UA5UA6UA6KB6KB6KB7KB7KC7KC7K\ C7KD8KD8KD8KD8KE8KE9KE9KE9KF9AFAAFAAFAAGAAGAAGBAHB\ AHBAHBAHBAICAICAICAICAJDA } frm:SliceJulibrot4 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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FOTD 13-09-12 (Shot Tower [7])
by Jim Muth 14 Sep '12

14 Sep '12

FOTD -- September 13, 2012 (Rating 7) Fractal visionaries and enthusiasts: There was no FOTD for yesterday, September 12. It was an unfortunate break due to an unexpected rush job that arrived at FC. Yesterday's fractal lack is hopefully made up for by today's image, which shows what happens to our strange open rectangle when it is viewed in its Parabolic orientation. The rectangle, or at least three sides of it, lies at the apex of the tall brownish central tower. This tower consists entirely of inside stuff made visible by the FMOD inside fill. When the rectangle is made visible in this way, we can see that its effects extend artificially well beyond its assumed bounds. I named the image "Shot Tower". It reminds me of a historic shot tower in Downtown Baltimore that fascinated me when I was an impressionable and very curious youngster. The rating of a 7 might be more than the image is actually worth. After all, a fractal rectangle can be stretched only so far. But the calculation time of only one brief minute is a bargain price for any image. Perfect weather prevailed here at Fractal Central today, with wispy clouds and a temperature of 82F 28C. The fractal cats had an unusually lazy day, sleeping from 10am until after 3pm. The humans had a few words to say about politics, but for a change we pretty much agreed. The next FOTD will be posted when it is ready. To find when that might be, keep checking. Until when- ever, take care, and the U.S. says it wants to defend freedom. Does this include the freedom of nations that do not wish to be 'defended' to expel U.S. military forces from their territory? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Shot_Tower { ; time=0:01:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=-0.000548662\ 20215659/-0.00012616493069158/655.6835/0.02004/90/0 params=0/90/0/0/-1.7435/0/0.000175/0.073883/2.003/0 float=y maxiter=326 inside=fmod periodicity=6 colors=000UUcVUcVVcWVbWWbXWbXXbXXbXXbKgl7rv8pu9ouA\ ntBmtC03D04E05F06G07H08I09J0AK0BL0CL0DM0EN0FO0GP1H\ Q2IR3JS4KT5LU6MV7NW8OX9PYAQZBR_CS`DTaEUbFVcGWdHXeI\ YfHXgGXhFXiEWjDWkCVlBVlAWmCWmDXnEYnFYoHZoI_pJ_pK`q\ MaqN`rO`rP`sR_sS_sT_tUZtVZuXZuYYvZYv_YwaXwbXxcXxdW\ yfWygWzhVziVzjVyiUxhUwhTwgTvfSufSteStdRsdRrcQqcQqb\ QpaPoaPn`On_Om_NlZNkYNkYMjXMiXLhWLhVLgVKfUKeTJeTJd\ SIcSIbRIbQHaQH`PG_OG_OGZNFYMFXMEXLEWLDVKDUJDUJCTIC\ SHBRHBRGBQFAPFAOE9OE9ND8MC8LC8LB7KA7JA6I96I96HA7HA\ 8HB9HBAHBAHCBHCCHCDHDEGDEGDFGEGGEHGEIGFIGFJGFKGGLG\ GMFGMFHNFHOFHPFIQFIQFIRFJSFJTEIUFJTFJSFKSFKRFLQGLQ\ GLPGMPGMOGNNHNNHNMHOMHOLHPKIPKIQJIQJIQIIRHJRHJSGJS\ FJSFJTEKTEKUDKUCKVCKVBLVBLWALW9LX9LX8MW7LX8LX8LX8L\ X8LX9LX9KX9KX9KXAKXAKXAKXAJXBJXBJXBJXBJXCJXCIXCIXC\ IXDIXDIXDIXDHXEHXEHXEHXEHXFHXFGXFGXFGXGGXGGXGGXGFX\ HFXHFXHFXHFXIFXIEXIEXIEXJ } frm:SliceJulibrot4 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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baby bad_bad.
by Sebastien Helie 13 Sep '12

13 Sep '12

observe a baby introduction thu pixel+geometrie apophysis.... send a warning....most will become food for nature. no relational geometrie the world of hot medusa,shrime and geometre. Baby just know nothing, it's a impulsion with no memory.... it fare from being the place to learn. and fractint handle embryo, and image of adulte. https://dl.dropbox.com/u/68454194/bad_bad.mp3 -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com

1 0

2 Z..
by Sebastien Helie 13 Sep '12

13 Sep '12

For those who absolutely have no clue here is two Z exemple.... https://dl.dropbox.com/u/68454194/2.bmp grapheq question: for now has i know their is two version one for mac one for PC any inquiry can join tupper(a)peda.com he the one in charge of the compilation... i encounter him also personaly felt a little funky thru internet but really descent into the public. He do not know all about (his) product, like most math system but do a real effort he does flirt with chinese a lot so nothing is impossible. feel free to ask and of force hem to deal with linux??????????????????? -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com

2 3

Re: [Fractint] collection of pedagogery software grapheq hard curve
by jimmckenzie＠earthlink.net 13 Sep '12

13 Sep '12

OK. Is there a Linux version not a Window$ version that can run in an emulator a native Linux Version? -----Original Message----- >From: david <gnome(a)hawaii.rr.com> >Sent: Sep 12, 2012 3:14 PM >To: Fractint and General Fractals Discussion <fractint(a)mailman.xmission.com> >Subject: Re: [Fractint] collection of pedagogery software grapheq hard curve > >A GrafEq data file: > >http://www.file-extensions.org/gqs-file-extension > >Something proprietary. > >On 09/12/2012 07:04 AM, jimmckenzie(a)earthlink.net wrote: >> What kind of file is this? >> >> -----Original Message----- >> From: Sebastien Helie >> Sent: Sep 12, 2012 12:30 PM >> To: Fractint and General Fractals Discussion >> Subject: [Fractint] collection of pedagogery software grapheq hard >> curve >> >> b nut lucky!!! >> stone caress. https://dl.dropbox.com/u/68454194/Stone_caress.gqs > > >-- >David >gnome(a)hawaii.rr.com >authenticity, honesty, community >http://clanjones.org/david/ >http://dancing-treefrog.deviantart.com/ > >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint

3 2

z movie lover
by Sebastien Helie 13 Sep '12

13 Sep '12

like to watch movie on your computer http://www.videolan.org/vlc/ is here compatible with most stange xvid codec... having a computer dedicated to sucking Z torrent is a smart idea little dangerous for your brain but has long has you do not have probleme with hard booting i cannot see what is the probleme about been a little fuzzed? danger raise when you torrent with a active development operational..... viscious and sometime delicious. -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com

1 0

play hell bank!
by Sebastien Helie 12 Sep '12

12 Sep '12

-- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com

1 0

Re: [Fractint] collection of pedagogery software grapheq hard curve
by jimmckenzie＠earthlink.net 12 Sep '12

12 Sep '12

3 2

evil me
by Sebastien Helie 12 Sep '12

12 Sep '12

The dude interlink everybody and then take crasy torrent risk? sadely i may have start another polemique. Someone spit on me in the street... i freeze and laught inside... just know your evil ... but fuck my game is a real god damn game i just wont watch lot's of movies... next will be love story... Le grand meaunle.. i whant it in my collection.collection half sorry can spit on me! -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com

1 0

collection of pedagogery software grapheq hard curve
by Sebastien Helie 12 Sep '12

12 Sep '12

b nut lucky!!! stone caress. https://dl.dropbox.com/u/68454194/Stone_caress.gqs -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com

1 0

you may have to forget
by Sebastien Helie 12 Sep '12

12 Sep '12

sorry but this file is required by fractint... been emmited by a tim ghost... come in handy.. https://dl.dropbox.com/u/68454194/f_f_f.jpeg -- a nail most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com

1 0

santa clause is a pusher
by Sebastien Helie 12 Sep '12

12 Sep '12

OK my little experience not a failure but do affect my fractal result, less energising but a great gain in range for the reason that the fractal product now stand until number 4 usually beteweem -1 -- 1 Not to considere image really but i'am really proud of yesterday drive and so i publish what it does....the result really suspect that computer is a little tired also and had a great 1/x^2 type of apophysis reaction offline after torrentz suck. will exchange sometime. torrentz really dangerous!! but exciting! my game. get dirty if you feel ready?! some people may think i do little too much it's thru but when i sleep even train have probleme to take me on/ so that it folk some will see how to shrink the univers.? love earth. or hate here, have a feeling at least she got different mood. -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com start parameter file================================= pusher { ; 12_09_2012 reset=2004 type=formula formulafile=2012_7.frm formulaname=606_2 center-mag=0.325407/0.0200334/2.73224 params=2/3 float=y inside=0 potential=256/200/4 colors=00000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzzzLzzz000555<3>HHHKKKOO\ O<3>ccchhhmmmssszzz00z<3>z0z<3>z00<3>zz0<3>0z0<3>0zz<2>0GzVVz<3>zVz<3>zV\ V<3>zzV<3>VzV<3>Vzz<2>Vbzhhz<3>zhz<3>zhh<3>zzh<3>hzh<3>hzz<2>hlz00S<3>S0\ S<3>S00<3>SS0<3>0S0<3>0SS<2>07SEES<3>SES<3>SEE<3>SSE<3>ESE<3>ESS<2>EHSKK\ S<2>QKSSKSSKQSKOSKMSKK<2>SQKSSKQSKOSKMSKKSK<2>KSQKSSKQSKOSKMS00G<3>G0G<3\ >G00<3>GG0<3>0G0<3>0GG<2>04G88G<2>E8GG8GG8EG8CG8AG88<2>GE8GG8EG8CG8AG88G\ 8<2>8GE8GG8EG8CG8AGBBG<2>FBGGBGGBFGBDGBCGBB<2>GFBGGBFGBDGBCGBBGB<2>BGFBG\ GBFGBDGBCG000<6>000 } frm:606_2{;sinpix a=real(p1^2),b=imag(p1^(-1)) z=1.14142^0.707106,c=pixel: m=z^a+0.707106+c/b z=2*m+3*c |z|<1974 } end parameter file======================================

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discuss has much has you whant but
by Sebastien Helie 12 Sep '12

12 Sep '12

math + fractal = pure energy. -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com

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anybody
by Sebastien Helie 12 Sep '12

12 Sep '12

if anybody experience traumatism under dosbox fractint restart you numerisation withz^2+c... grow a different line! -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com

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fresh like a rosa addendum
by Sebastien Helie 11 Sep '12

11 Sep '12

i call the file muir on the mirror google site!\ for the rest dos box still react on other par.. -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com

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curiosity
by Sebastien Helie 11 Sep '12

11 Sep '12

curiosity happen, download dune movie from torrent and did a formula at the same time... deep worm effect came in then i try to do my formulation to have only black reaction. and computer glitch!. had to pull on the cable. switch to my laptop had a reaction, then switch the par to the dosbox... and black screen again try it some will have some don't but the image is on the balanced google site... from Jim crabe pretty enought to be top posted... at jack -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com fresh_like_a_rosa { ; hard work to drive muir... reset=2004 type=formula formulafile=2012_6_1.frm formulaname=euphoria center-mag=6.45752/-0.00841051/1.392602/1/90/3.88578058618804789e-016 params=-0.1/-2 float=y inside=0 potential=256/200/4 colors=000z0z<8>T5zQ5zM6z<3>69y<6>UVsXYr_`q<2>iinmmmsss<8>wwwwwwxxx<2>yy\ yzzzxyz<7>hkzfizdgz<3>W`z<5>GmzDozBqz<3>0zz<8>3Vz4Rz4Nz<3>68z<6>R`zUezXi\ z<3>hzz<2>hlz00S<3>S0S<3>S00<3>SS0<3>0S0<3>0SS<2>07S<3>06L05J05H<2>03C<8\ >`28e18i17<3>z05<8>e05c05`05<3>R16S05<8>L06K07K07<3>G08G04G00<3>GG0CG08G\ 0<8>JR`LSeMTi<2>QXuSZzRYw<7>HOZFNWEMT<2>AIK8GG8EG8CG8AGBBG<2>FBGGBGGBFGB\ DGBCGBB<2>GFBGGBFGBDGBCGBBGB<2>BGFBGGBFGBDGBCG000<6>000 } frm:euphoria{;sinpix a=real(0.707106+p1/2),b=imag(1.4142+p1) z=2.26*1.1416+pixel,c=pixel: T=z^a+((z/b/16)*2+c) S=2*t*(-1) M=z*0.5+0.707106*c Z=(t+s+m)^z+pixel |z|<1974 }

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FOTD 11-09-12 (Gateway to the Future [8])
by Jim Muth 11 Sep '12

11 Sep '12

FOTD -- September 11, 2012 (Rating 8) Fractal visionaries and enthusiasts: Today's image shows our strange rectangle at an angle in the fourth dimension impossible to imagine. All I can say about the angle of the slice is that it is closest to the Rectangular orientation. At this strange angle, the rectangle is no longer rectangular. It has stretched into a tall trapezoid with what resembles a marshy pathway leading up to it. I named the image "Gateway to the Future", leaving it to the viewer to decide what might lie beyond. It might be total technological breakdown followed by a collapse of civilization, or it might be the elimination of military weapons and the coming together of all the peoples of earth into one peaceful and harmonious family. But to me it remains a mystery. Even though today's image shows just another aspect of the same rectangle and uses the same color palette, it is a very unique aspect, well worth the rating of an 8 that I have given it. The calculation time of 3-1/2 minutes is a fair price to pay for the image. Bargain hunters may save some time by checking one of the web sites. The basic finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> Fancier hi-def renderings are online at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are available at: <http://www.Nahee.com/FOTD/> Another early hint of Autumn made itself felt here at Fractal Central today, when the sun rose with the temperature at 48F +9C. The rest of the day brought sun with only a few wispy clouds and a temperature of 75F 24C. To the humans, it appeared that the fractal cats spent the day considering the coming winter. The cats more likely spent the day considering getting an extra treat. The next FOTD will be posted when the proper time has passed. Until then, take care, be happy with your fractals, and don't worry about what might lie beyond the gateway. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= GatewayToTheFuture { ; time=0:03:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=+0.000000688\ 48264664/+0.00213981581517682/111.3773/58.786/180 params=82/85/0/90/-1.7435/0/0.000175/0.073883/\ 2.003/0 float=y maxiter=54000 inside=0 logmap=68 periodicity=6 colors=000KGiKIkKKmKMoIOqGPsEQuBQwDRvERuGSuHStJTuK\ TvLTwNUxOUyQVzRVzSVzUWzVWzXXzYXz_Yz`YzaYzc_zd`zfbz\ gcziezhezhdzgbzgazg_zfZzfZzeXzeWzeVzdUzdSzdRzcRzcQ\ zbPzbQzbSzaUzaWzaYxc_ve`tgaribpkcnmdmjehgfdeg_bhW`\ iSYjN_kJblEemAho6kqMnsaquVtwPwyJzzDwwKtuQqsknqWkoi\ hmwekubis_gqXeo_crRanI_k9`g0if1gd1eb2d`2bZ3aY3_W4Z\ U4XS5VQ5UP6SN6RL7PJ9RH7SI6NJ4JK0EL3KL5QL7QL9RLBRLD\ SLFSLHTLJULIVKHWJGZIFaHEdGEgFFfIGfKHfMHeOIeQJeSJeU\ KdXLdZLd`MdbNcdNcfOchPbkPbmQboRbqRasSauTawTayDczCc\ zCczCczCczBczBczBczBczAczmZzmZzmZzmZzmZzmZzmZzmZzm\ ZzmZzmYzmXzmWzmVzmUzmUzhPNkPOnPPpPPmOMmOKmNImNFmMD\ mMBmL8mL6mK4mK2mJ6mI9mHDmGGmFKmENmERmDUmCYmB`mAdm9\ gm6km9jmBimDimGhmIhzKgzMgzPfzRfzTezVezYdz_czaczdbz\ fbzhazjazm`zo`zq_zuZzs_zq_zo`zn`zl`zjaziazgbzebzdb\ zbcz`czZdzYdzWdzUezTezRfzPfzSfzRgzQizPjzNkzMmzLnzK\ ozIqzHrzGszDsK8aKAcKCeKEg } frm:SliceJulibrot4 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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mister virus addendum
by Sebastien Helie 11 Sep '12

11 Sep '12

space random do not toutch fractint at all affect apophysis color map editor text editor and personal dos based math pixel system received also full of audio file name #... i had to clean my disk from them comming in everywhere sadely i cannot read any of hem.??????????? -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com

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mister virus.
by Sebastien Helie 11 Sep '12

11 Sep '12

Warning all file i exchange will now have to be virus check. i get infected by a strange random number generator who seem to affect only particular program. and this even on my personal dev_op... some program are just not toutch by, like the internet browser. infect mostly text editor doing matrix green thru them i think it's a natural reaction but for you hyper clean computer fanatique? just scan and tell me if you see something. inject some nice effect on some of my math pixel progame, feel like activity. -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com time_string { ; 17_06_2012 reset=2004 type=formula formulafile=2012_7.frm formulaname=slefcrit2 center-mag=-0.63250539879026850/-0.01908761818425509/3132.353 params=2.5/2/3/1 float=y inside=0 colors=000<3>003004004<3>008009008<6>005004004<3>001000221<6>JMCLPENSG<3\ >YcM_fOXcQ<4>IMXFIYCF_<3>00e<8>``_eeZiiY<3>zzV<3>VzV<3>Vzz<2>Vbzhhz<3>zh\ z<3>zhh<3>zzh<3>hzh<3>hzz<2>hlz00S70S<8>3`_3d`2ha<2>1td0ye1vd3sb5pa<3>Jf\ eNdeQaf<3>dSjhQklNl<2>wFo<6>fHdcHcaHa<3>SJWPKUMKSOKSQKSSKS<2>SKMSKKSMKSO\ KSQKSSK<2>MSKKSKKSMKSOKSQKSS<2>KMS00G<3>G0G<3>G00<3>GG0<3>0G0<3>0GG<2>04\ G88G<2>E8GG8GG8EG8CG8AG88<2>GE8GG8EG8CG8AG88G8<2>8GE8GG8EG8CG8AGBBG<2>FB\ GGBGGBFGBDGBCGBB<2>GFBGGBFGBDGBCGBBGB<2>BGFBGGBFGBDGBCG000<6>000 } frm:slefcrit2{;sinix c=pixel,a=real(p1),b=imag(p1^(-1)),d=real(e^p2),f=imag(p2) h=1/f,g=1/d,j=1/(f-b),z=(a+b+g+j)^(-1): z=z^2+c+pixel, |z|<74 }

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audio a issu
by Sebastien Helie 10 Sep '12

10 Sep '12

to convert audacity record to mp3 file exist a plug in but it's a real maze. send you a dropbox version that i find who work just fine altought i probably have to add a pitch adjustment to the micro https://dl.dropbox.com/u/68454194/lame3.99.5.zip lame mp3 translator in a good seat?! anyway soon i'am going to send music track like it will be some fractal at the base of some musical trend i just find hard the position of piloting the computer and the music keyboard at the same time for now i play right and not high on one or the other. dual may take some trainning. i never train enought -- most attached file or result are positively balance at https://sites.google.com/site/sinpix12823/fractint site closed and navigation in function https://sites.google.com/site/sinpix12823fractal/ join me at sinpix12823(a)gmail.com

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FOTD 10-09-12 (Rectangular Rectangle [7])
by Jim Muth 10 Sep '12

10 Sep '12

FOTD -- September 10, 2012 (Rating 7) Fractal visionaries and enthusiasts: Today we check the Rectangular aspect of the strange rectangle. Not surprisingly, it much resembles the Oblate aspect, though it is now rotated 90 degrees. The name "Rectangular Rectangle" is a statement of fact. The rating of an average 7 indicates that the current rectangle theme is starting to grow stale. We still have a few more aspects to check however before we move on. The calculation time of 4-3/4 minutes is rather slow; visiting one of the web sites is quick however. The finished image is posted for convenience at: <http://www.crosscanpuzzles.com/Archives.html> A high-definition rendering is at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are online at: <http://www.Nahee.com/FOTD/> An early sample of autumn arrived at Fractal Central today, when the temperature reached a high of only 72F 27C and scattered lumpy gray clouds filled the sky. The fractal cats took to their window shelf just after noon. They seemed satisfied, but I felt they would have preferred more sun. The fractal humans had an uneventful day...boring to read about but relaxing to experience. The next FOTD, most likely another of those rectangles, will be posted soon. In this case, 'soon' does mean about 24 hours. Until then, take care, and, IMO, the DNA molecule is far too complex to have evolved by accident in a mere 4,000,000,000 years. At the same time, IMO of course, to assume that DNA was intelligently designed stretches credulity beyond the limit. So, once again IMO, there must be a third possibility. Whatever that might be is the question. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= RectanglarRectangl { ; time=0:04:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=0/-0.0052445\ 6022229875/102.1781/58.786/180 params=90/0/0/90/\ -1.7435/0/0.000175/0.073883/2.003/0 float=y maxiter=72000 inside=0 logmap=66 periodicity=6 colors=000KGiKIkKKmKMoIOqGPsEQuBQwDRvERuGSuHStJTuK\ TvLTwNUxOUyQVzRVzSVzUWzVWzXXzYXz_Yz`YzaYzc_zd`zfbz\ gcziezhezhdzgbzgazg_zfZzfZzeXzeWzeVzdUzdSzdRzcRzcQ\ zbPzbQzbSzaUzaWzaYxc_ve`tgaribpkcnmdmjehgfdeg_bhW`\ iSYjN_kJblEemAho6kqMnsaquVtwPwyJzzDwwKtuQqsknqWkoi\ hmwekubis_gqXeo_crRanI_k9`g0if1gd1eb2d`2bZ3aY3_W4Z\ U4XS5VQ5UP6SN6RL7PJ9RH7SI6NJ4JK0EL3KL5QL7QL9RLBRLD\ SLFSLHTLJULIVKHWJGZIFaHEdGEgFFfIGfKHfMHeOIeQJeSJeU\ KdXLdZLd`MdbNcdNcfOchPbkPbmQboRbqRasSauTawTayDczCc\ zCczCczCczBczBczBczBczAczmZzmZzmZzmZzmZzmZzmZzmZzm\ ZzmZzmYzmXzmWzmVzmUzmUzhPNkPOnPPpPPmOMmOKmNImNFmMD\ mMBmL8mL6mK4mK2mJ6mI9mHDmGGmFKmENmERmDUmCYmB`mAdm9\ gm6km9jmBimDimGhmIhzKgzMgzPfzRfzTezVezYdz_czaczdbz\ fbzhazjazm`zo`zq_zuZzs_zq_zo`zn`zl`zjaziazgbzebzdb\ zbcz`czZdzYdzWdzUezTezRfzPfzSfzRgzQizPjzNkzMmzLnzK\ ozIqzHrzGszDsK8aKAcKCeKEg } frm:SliceJulibrot4 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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