- Fractint - mailman.xmission.com

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

1 0

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--------------------------

1 0

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 21 Nov '12

21 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-------------------

1 0

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

20 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=========================================

1 0

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