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Shotgun
by Chris Curnow 10 May '03

10 May '03

Thanks for the Multifractal formula Albrecht. Try this par. Literally fast on the draw! Chris Curnow I won't post Albrecht's formula as it's a bit long and we've all got it saved in a .frm file haven't we :-) Shotgun4 { ; Missed! ; t= 0:00:31.58 @ 700 Mhz ; Chris Curnow May 2003 ; Version 2002 Patchlevel 2 reset=2002 type=formula formulafile=niekamp.frm formulaname=multifractal ismand=y function=exp/exp/sin passes=1 center-mag=-0.75006312153939250/-1.713532643335148\ 00/649.9441/1/162.500000000271143/-3.8751495068378\ 7163e-011 params=-1.3863948484756/-1.278176213865714/384.000\ 04/2500.2333/2048.00012/768.00008/2500.01536/32.01\ 536/18435/5 float=y maxiter=255 inside=maxiter outside=tdis logmap=3 symmetry=none periodicity=0 rseed=-2436 cyclerange=2/255 colors=000000841<3>421311211002111<75>uuuvvvwww<2>\ yyyzzzyyz<83>5HY4GX3GX<2>1EW0DV0CX<4>08f08h07j<2>0\ 4p04r26r<2>BEo<10>aJJcKGfKD<3>pN0<38>A41 }

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Multifractal
by Albrecht.Niekamp＠t-online.de 10 May '03

10 May '03

Hi, here are three more zooms into Julia_rules. They are so different, that itïs hard to believe they are part of the same image. And there are many many more, find them.. Fractal greetings, Al. _________________________start-par_________________________________________ Inside_a_bubble { ; Albrecht Niekamp May, 03 ; Zoom into Julia_rules ; Time 1min17sec ; Version 2002 Patchlevel 4 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=070503.par formulaname=multifractal ismand=n function=exp/exp/exp passes=t center-mag=-6.16703812316714700/+0.30950456323337450/441.5011/1/-72.5000\ 000000000711/4.75849221137636391e-012 params=-0.1740997192297128/-0.2996141087069308/384.00004/256.1106/2048.0\ 0016/768.00009/768.01536/256.01025/28974.5/12 float=y maxiter=2048 inside=maxiter outside=tdis logmap=10 periodicity=0 rseed=-2436 colors=000Ho`GmZFkXFiX<5>BYOAWMAUL9SK<4>6IC5GB5DA<3>25424312100000102302\ 5047049<5>0BL0DN0DP<2>0IV0JX0KZ0L`0Mb<3>0Rj0Sl0Tn0Up4Yr8atCgvGkxKqz<3>4_\ s0Vq0Uo<6>0Ma0L_0KY<3>0FQ0DO0DM<3>08E06C06A048046024012000100<12>R0LT0NV\ 0PX0P<3>d0Wf0Yh0Z<3>p0e<3>xOtzUxyOuwIquCns6iq0g<2>k0bi0`g0_e0Z<3>Y0SW0RU\ 0O<7>E0CC0AA09<2>304102010<11>0P30R30T40V40X3<3>0d40f50h5<3>0p6<3>WxZcze\ UyY<2>0s8<4>0i60g60e60c4<2>0Y40W30U4<5>0I20G20E20C20A1081<3>000010122153\ 2653863A84DA5EB5HB<2>7NG8PI8RJ9TKAVNAXM<3>DdTDfVEhWFjYFlYGn_Gp`Prd<3>zzz\ <2>_ulRsgHqa } The_cave { ; Albrecht Niekamp May, 03 ; Zoom into Julia_rules ; Time 6min53sec ; Version 2002 Patchlevel 4 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=070503.par formulaname=multifractal ismand=n function=exp/exp/exp passes=t center-mag=-5.42564/3.62714/4.693333/1/124.999999999999957/1.31075705844\ 807544e-014 params=-0.1740997192297128/-0.2996141087069308/384.00004/256.1106/2048.0\ 0016/768.00009/768.01536/256.01025/28974.5/12 float=y maxiter=2048 inside=maxiter outside=tdis logmap=10 periodicity=0 rseed=-2436 colors=000GkxKqz<3>4_s0Vq0Uo<6>0Ma0L_0KY<3>0FQ0DO0DM<3>08E06C06A04804602\ 4012000100<12>R0LT0NV0PX0P<3>d0Wf0Yh0Z<3>p0e<3>xOtzUxyOuwIquCns6iq0g<2>k\ 0bi0`g0_e0Z<3>Y0SW0RU0O<7>E0CC0AA09<2>304102010<11>0P30R30T40V40X3<3>0d4\ 0f50h5<3>0p6<3>WxZczeUyY<2>0s8<4>0i60g60e60c4<2>0Y40W30U4<5>0I20G20E20C2\ 0A1081<3>0000101221532653863A84DA5EB5HB<2>7NG8PI8RJ9TKAVNAXM<3>DdTDfVEhW\ FjYFlYGn_Gp`Prd<3>zzz<2>_ulRsgHqaHo`GmZFkXFiX<5>BYOAWMAUL9SK<4>6IC5GB5DA\ <3>254243121000001023025047049<5>0BL0DN0DP<2>0IV0JX0KZ0L`0Mb<6>0Up4Yr8at\ Cgv } Science_fiction { ; Albrecht Niekamp May, 03 ; Zoom into Julia_rules ; Time 1.12.15 ; ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=070503.par formulaname=multifractal ismand=n function=exp/exp/exp passes=t center-mag=-0.282785/1.43054/6.133334/1/-12.5000000000000302/1.310757058\ 44807544e-014 params=-0.1740997192297128/-0.2996141087069308/384.00004/256.1106/2048.0\ 0016/768.00009/768.01536/256.01025/28974.5/12 float=y maxiter=2048 inside=maxiter outside=tdis logmap=10 periodicity=0 rseed=-2436 colors=000025047049<5>0BL0DN0DP<2>0IV0JX0KZ0L`0Mb<3>0Rj0Sl0Tn0Up4Yr8atCg\ vGkxKqz<3>4_s0Vq0Uo<6>0Ma0L_0KY<3>0FQ0DO0DM<3>08E06C06A04804602401200010\ 0<12>R0LT0NV0PX0P<3>d0Wf0Yh0Z<3>p0e<3>xOtzUxyOuwIquCns6iq0g<2>k0bi0`g0_e\ 0Z<3>Y0SW0RU0O<7>E0CC0AA09<2>304102010<11>0P30R30T40V40X3<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<4>6IC5GB5DA<5>121000\ 001023 } -------------------------------start-frm----------------------------------- FRM:Multifractal { ;Albrecht Niekamp May, 03 ;only integers as first input, second input 5 digits to the right ;real(p2) factor1,border1 ;imag(p2) (-)maxiter1,input bas.frm1_2digits input bas.frm2_2digits ;real(p3) bailout,hyb.mandel: number of sides (Many_mods L.Allison) ;imag(p3) factor2,border2 ;real(p4) maxiter2,factor3 ;imag(p4) border3,maxiter3 ;real(p5) 1digit_shape only 5digits: shape,out1,out2,in1,in2 ; 1_mand 2_jul 3_hyb.mand 4_hyb.jul +5_reset (not shape) <0_no in/out1 ; optional basic frm2: out-nbr 1digit in-nbr 1digit 3_both +5_shape ;imag(p5) 1digit : 1_iter1reset 2_iter2reset 3_both +5_shape effect ; 2digits : many_mods multipl. shutoff +10_in/out1 +20_inout2 +30_both ; optional input2: frequency_2digits level_2digits amplitude_2digits ; d=real(p2) fac1=trunc(d) b1=(d-fac1)*100000 ; d=imag(p2) da=(d<0) if (da) d=-d endif mi1=trunc(d) d=round((d-mi1)*10000) p6=trunc(d/100)/10 d=d-1000*p6 if (da) p6=-p6 endif p7=d/10 ; d=real(p3) ba=trunc(d) mm=round((d-ba)*100000) ; d=imag(p3) fac2=trunc(d) b2=(d-fac2)*100000 ; d=real(p4) mi2=trunc(d) fac3=round((d-mi2)*100000) ; d=imag(p4) b3=trunc(d) mi3=round((d-b3)*100000) ; da=real(p5) t=(da<0) if (t) da=-da endif start=2-t dd=trunc(da) if (dd<5) start=0 endif vb=(dd==3)+(dd==4) da=round((da-dd)*100) d=trunc(dd/10000) vb=(d==3)+(d==4)+vb dd=dd-d*10000 d=trunc(dd/1000) or1=(d>5) d=d-5*or1 vv1=(d==3) vv2=(d==4) dd1=(d==2)+(d==4) dd=dd-d*1000 d=trunc(dd/100) or2=(d>5) d=d-5*or2 vv3=(d==3) vv4=(d==4) dd2=(d==2)+(d==4) dd=dd-d*100 d=trunc(dd/10) inr1=(d>5) d=d-5*inr1 v1=(d==3) v2=(d==4) d1=(d==2)+(d==4) dd=dd-d*10 d=trunc(dd) inr2=(d>5) d=d-5*inr2 v3=(d==3) v4=(d==4) d2=(d==2)+(d==4) d=trunc(da/10) ab=(d>=5) d=d-5*ab da=da-10*d bb1=(d==1) bb2=(d==2) d=da ab=(d>=5) d=d-5*ab ab1=(d==1) ab2=(d==2) ; d=imag(p5) dd=trunc(d) d=round((d-dd)*1000000) le=(d>10000) da=trunc(dd/10) so1=((da==1)+(da==3)==0) so2=((da==2)+(da==3)==0) dd=dd-10*da wo=(dd>=5) dd=dd-5*wo ir1=(dd==1)+(dd==3) ir2=(dd==2)+(dd==3) if (le) freq=round((trunc(d/10000))*10) ;frequency_lake effect by S.Gallet d=d-freq*1000 level=(trunc(d/100))/100 ;water level d=d-level*10000 ampl=d/100 ;amplitude of the wave angle=real(rotskew*pi/180) t=exp(-flip(angle)) h=1/real(magxmag) q=h/0.75*imag(magxmag) tanskew=tan(imag(rotskew*pi/180)) w=2*q*t v=2*h*(tanskew+flip(1))*t z3rd=center+(-q-h*tanskew-flip(h))*t z=pixel-z3rd s=imag(conj(w)*z)/imag(conj(w)*v) if (s<=level) da=level-s z=z+2*da*(1+ampl*sin(freq*da^0.2))*v endif z=z+z3rd endif if (ismand) if (vb) c=0.4*log(sqr(pixel^mm)) z=z*le else c=z*le+pixel*(le==0) z=0 endif else c=p1 z=z*le+pixel*(le==0) endif t=0 d3=(ismand==0) u=d3 : if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) ;frm: Albrecht Niekamp else z2=fn1(z)+c ;frm: Many_mods Linda Allison sqz2=cos(z2) z=c*(1-sqz2)/(1+sqz2) endif else if (ab) z=z*z+c+c*c-p7 ;frm: Puskás István else z2=z*z ;frm: Puskás István modified z=z2*z2+(p6+u)*z2+c-p1*(d3==0) endif bo=|z| If (wo) t=t+1 if ((t<mi1)+(bo>b1)) u=2*(fn1(t/fac1)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) else c=z*le+pixel*(le==0) endif else z=z*le+pixel*(le==0) c=p1*u endif wo=0 if (ir1) t=0 endif endif elseif (start) t=t+1 if (start==2) if (bo>b2) u=2*(fn2(t/fac2)) rs=or1 ab=bb1 if (dd1) if (rs) z=pixel endif c=p1*u vb=vv2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=1 endif elseif (t>mi2) u=2*(fn2(t/fac2)) rs=inr1 ab=ab1 if (d1) if (rs) z=pixel endif c=p1*u vb=v2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=1 if (ir2) t=0 endif endif elseif (bo>b3) u=2*(fn3(t/fac3)) ab=bb2 rs=or2 if (dd2) if (rs) z=pixel endif c=p1*u vb=vv4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=0 endif elseif (t>mi3) u=2*(fn3(t/fac3)) ab=ab2 rs=inr2 if (d2) if (rs) z=pixel endif c=p1*u vb=v4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=0 endif endif bo<=ba } -------------------------------------------end-----------------------------

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Multifractal, FNSF.PAR
by Albrecht.Niekamp＠t-online.de 09 May '03

09 May '03

Hi, John as your parfile was scrubbed, probably because no attachments are possible, I´d be happy if you could mail it to my private address. I really am thrilled to watch it, especially as I also came upon a zoom, which for me is like a view out of a spaceship window . Check the Science_fiction image posted today. Regards, Al.

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Albrecht, when do you sleep? (James R. McKenzie)
by Albrecht.Niekamp＠t-online.de 09 May '03

09 May '03

Hi, James what a question! I definetly get enough. I´m a working man and exploring a "new country" like this is pure fun and excitement, no stress involved, whatsoever. And it is the best cure for that everyday frustration, believe me! Fractal Greetings, Al

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FOTD 09-05-03 (Smooth Sailing [8])
by Jim M. 09 May '03

09 May '03

FOTD -- May 09, 2003 (Rating 8) Fractal visionaries and enthusiasts: Another busy day means another shortened discussion. Today's image, with its spectacular curvilinear elements, rates an 8. Actually, I thought about rating it a 9, but I could not find that definite extra something that would earn the 9. I named the image "Smooth Sailing" for no reason that I can state with certainty. (I think there once was a candy bar named 'Smooth Sailing'.) Most likely, it is the smoothly curving lines that earned the title. The entire scene is located at the tip of the filament extending from the Mandeloid bud at the northeast corner of the parent, slightly past the point where the filament intersects the ring. The scene actually lies in the interior of the ring, which is surprising, as no rings appear in the image. Usually, the features surrounding midgets are a reflection of the overall area of the parent in which the midgets are located. The rather slow render time of 9 minutes can be avoided by downloading the finished image from the W.W.W. It is available at two web sites. Paul's site is found at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's is at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather was changeable here at Fractal Central on Thursday. A light shower in the morning gave way to a sunny afternoon with a temperature of 75F 24C, but at nightfall a series of thunder- showers passed just to the north. The duo of cats made the most of the sunny period and did not worry themselves while it was raining or thundering. This morning is starting foggy and misty, with more rain promised. It remains to be seen what kind of day the duo will have. For me, it's going to be another busy day. Until next FOTD, take care, and look for those alternate realities hidden within our own. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Smooth_Sailing { ; time=0:09:30.40--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+1.72175526509034800/-9.632722714904958\ 00/43170.52/1/20/2.7121696985488164e-008 params=-10/-1.1/-1/-11/0/525/0/0 float=y maxiter=1200 inside=0 logmap=170 periodicity=10 colors=000RFUSETTDTUCTVBTW9SX8SY7SZ6R_5R`4Ra3Rc2Td\ 2Uf2Vg2Wi2Xj2Yl2_m2`o2ap2br2cs2dt2eu3du4du5dv6cv7c\ v8cw9bwAbwAbwBbxCaxDaxEayF`yG`yH`yH`wJcuLftMhrOkqP\ noRpnSslUvkVxaSvSPuJNs9Kr0Iq3Ko5Lm7Ml9NjBPiDQgFRfH\ SdJUcLVaNW`QXZSYXU_WW`UYaT_bRadQceOefNggLihKfjMdkN\ blP`nQYoRWpTcqUmsVwtXzuYzwZzx`zyazzbzyczxdzwdzvezu\ eztfzsgwsgmrhcqhUpiKoj6nj5mk5mk7mf8mbAmZBmVDmREmMG\ mIHmEJmAKm6Lm2Oi4Rf5Ub6X_7_W8aT9dQAgMBjJCmFDpCEr9F\ uGJxMMwLLvKLuJLtILsHLrGLqFKpEKoEKnDKmCKlBKkAJj9Ji8\ Jh7Jg6Jg6JfCMeHPeMSdRVdXYca`cfcbkfbph`nf_mdZlbYkaX\ j_WhYVgXTfVSeTRdRQbQPaOO`MN_LLZJKXHJWFIVEHUEGTGFSI\ HUKJWMLYONZQP`SRbUTcWVeYXg_Zia`jcbledngfoihqkjsmkt\ oipqglsehucdwcawcYwcUwcQwcNwcJwcFwcBwc8wd7we7wf7wg\ 7wh7wk6wn6wq6wt6ww6wzEwzFwzFwzFwzFwzFwzGwzGwzGwzGw\ zGwzHwzHwzHwzHwzHwzNwzSwzXwzUwzUwzUwzPwz2wz6wzAwzE\ wzHwzLwzPwzTwzUwzUwzUwzUw } frm:MandelbrotMix2 {; 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 20.0 PAR-FORMULA FILE==================================

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FOTD 08-05-03 (The Devil's Fire [6])
by Jim M. 08 May '03

08 May '03

FOTD -- May 08, 2003 (Rating 6) Fractal visionaries and enthusiasts: Another unusually busy day will demand a truncated discussion. A FOTD fractal image without a midget at the center has become a rarity. To demonstrate that such images still exist, today's FOTD has no Minibrot at its center. The scene is located in the 'handle' of the fan-like element of the parent. The immediate area is non-critical, but filled with interesting detail nonetheless. I named the image "The Devil's Fire" when I had a rather apocalyptic impression while studying it. It's not that I expect the world to end soon, but rather that the image reminds me of certain frames of the 'Bald Mountain' section of Disney's 63-year-old film "Fantasia". After not-too-careful consideration, I was able to give the image a rating no higher than a 6. But the render time of 6 minutes is not too terribly long, and the completed image may be downloaded in a fraction of that time from one of the FOTD web sites. Paul's site is: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's is: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather Wednesday here at Fractal Central was fair enough, with lots of sun and a temperature of 79F 26C. A light shower fell in the early evening, but by that time the duo had completed their day's fun in the yard. Needless to say, their moods were better than average. Today, it is already raining. I expect the duo's mood will suffer. As for me, I've got some work to finish, some grass to trim, a fractal to find, and a bit of high-class philosophizing to do. Until next FOTD, which will appear in 24 hours, plus or minus an insignificant hour or two, take care, and prepare for imminent enlightenment. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Devil's_Fire { ; time=0:06:12.34--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+0.53696554835343270/+0.001047316541995\ 04/65042.98/1/135/-1.06789917186933536e-010 params=-10/-1.1/-1/-11/0/525/0/0 float=y maxiter=1200 inside=0 periodicity=10 colors=000yIbyGeyFgyEiyDkyCmyBoyAqy9suBlqDemEZiGSe\ ILaJEBl9BfVB`oDcnEenFhnHjmImmJomHrmFumEwm6VlXRgvOc\ gIfTCiE6l00o9IbHZRNXVSVYYUabSdgQgmPkrNnwMqmWkcdfUm\ aLvXEng7frGcjPabXZVeXNmVG`UMPUSCUY0Ub9KjIAqKAoMAmO\ AkQAjSAhUAfWAdYAcJkUF`MBQFGSGLUGQVHVXH_ZId_IiaJnbJ\ R7rPDqNJqLPpKVpI`oGfoElnDrnDsdDsWDsNDsEFnDHiDJdCK_\ CMVC00ZQLBRGBTHJUIQ00ZXKdYLkZLrUPq00ZLVoGZnCam7dl0\ 0Z6hk00ZBjjDkjIfkNal0AZXSnaNobQobSo00ZcXoc_odaoddo\ 00Zgdijbdm`ZoZUzXOzVJzTDzR8z_5zh3zp1zq3zr5zs7zt8zu\ AzvCzwEzwFzwGzwHzmgzmfzmgzwKzmczmhzmePMiRNhTOjVPkX\ PkYQl_RlaSmcSmeTmgUmiVmjVmkTmlRmmPmmOmnQloSjpUipWg\ qYfr_dsacscate`ugZwiYzkUwmRroOrqLzsIzuFzwCzw9zu6zt\ 6zt6zs6zs6zr6zr6zq6zq6zp6zp6zo6zo6zn6zn6zm6zm6zl6z\ l6zk6zk6zj6zj6zi6zi6zi6zg7zf8ze9zcAzbBzaCz`DzZEzYF\ zXGzWHzUIzUJzUKzULzUMzUNzUOBUPBUQBURCUSCUTCUUDUVDU\ WDUXEUYEUZEUZCUYRQRbNVnKZ } frm:MandelbrotMix2 {; 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 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] Multifractal
by Jim M. 07 May '03

07 May '03

At 06:13 PM 5/6/03 -0700, John W. wrote: >I, too, have been "wowed" by Albrecht Niekamp's >new formula. I *have* to show off a zoom I made >into Mandela2. I've called it FnSF because it >reminded me of *all* the covers of the old >"Fantasy and Science Fiction" magazine I used to >devour back in the '50's. I 'devoured' FnSF in the 50's also. And those covers, which were apparently inspired by surrealistic art, especially the art of Yves Tanguy, were what led me toward the field of art and design. And yes, Albrecht's new formula is a winner. Too bad that, with a FOTD to produce on a daily basis, I have almost no spare time in which to investigate the images it creates. Jim M.

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FOTD 07-05-03 (Enter the Rings [7])
by Jim M. 07 May '03

07 May '03

FOTD -- May 07, 2003 (Rating 8) Fractal visionaries and enthusiasts: I'm quite rushed today, so this one will have to be short. With today's image we enter the ring territory of the parent fractal for May, thus the name "Enter the Rings". Today's scene is located in a tiny cut-off area of chaos in the interior of the ring that lies at the tip of the filament extending from the second-largest fragmentary bud at the top of the fan-like element of the parent. (It's kind of hard to write descriptions of fractals. They are pictures, and a single picture is worth a thousand words.) I like today's image enough to rate it at an exceptional 8. But even this rating leaves considerable room for improvement. Will we find a fractal with a rating of 9, or maybe even a 10, before the month ends? Only time will tell. And speaking of time, today's image uses 5-1/2 minutes of it when it renders from the attached parameter file. Less time is expended when the finished image is downloaded from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> It did not rain here at Fractal Central on Tuesday, but neither did the sun shine, and the temperature did not rise above 62F 17C. The dynamic fractal cats took most of the inconvenience in stride however, needing only a small treat of sliced turkey to maintain their good spirits. Today is starting sunny, but showers are forecast for later. Who knows what kind of day the duo will have. My day will be busy, regardless. Until the next FOTD appears in 24 hours, take care, and strike while the fractal is hot. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Enter_the_Rings { ; time=0:05:34.77--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=mandelbrotmix2 function=recip passes=1 center-mag=+4.40285707549754500/-2.951900882629842\ 00/8635917/1/-162.5/2.24149607753326707e-006 params=-10/-1.1/-1/-11/0/525/0/0 float=y maxiter=1200 inside=0 logmap=94 periodicity=10 colors=000UwzUvzUuzUtzUszUrzUqzUpzUozUnzUmzVlxWkvX\ jtYirZgqZfo_em_dk`bj`aha`faZdaZcZW`WWZVUXQTVTSTKRR\ TQPEONBNL8MJ5LHJRPWWWhaczjjxffvbbt__rWWpTSoRPoOLnM\ ImJElGAkE7jB3j90eE4`J8WOCRSFMXJHaNCfR8jUCkXFkZJkaM\ kcQkfTkhXkk_kmcchgWckPZoHUs9Pw2Kv7MvCOuHPuMRtRTtWU\ t`WseYsjZro`rtbrxcpsano_lkYjfWibUgZSeVQcQOaMM`IKZD\ IX9GV5EU1CX3E_5Ga6Hd8JfAKiBMkDNnFPpGQqHPrIPrJOsKOs\ LOtMNtNNuOMuPMvQMvRLwSLwTLhVQVXVGZ_2_d1_jUbhuefsfe\ qgdphcnhbmiakj`ij_hkZflYelXcmWbnV`nUZoTYpSWpRVqQTr\ PRrOQsN9yDOtMNtLLuKKvJIvIGwHFxGDxFCyEAzDbIN`KM_MMZ\ OLYQLXRKVTKUVJTXJSZJR_IPaIOcHNeHMgGLhGJjFIlFHnFGpE\ FqEDsDCuDBwCAyCa_H_aGZbGXdGWeGUfFThFRiFQjFOlENmEMn\ EKpEJqDHrDGtDEuDDvCBxCAyCWhoUimTjkSkiRlgQmePmdOnbN\ o`MpZLqXKqWJrUIsSHtQGuOFvMEvLDwJCxHByFAzD8zZ9zW9zT\ 9zQ9zN9zK9zH9zERziPzfOzdNzaLz_KzXJzVIzTGzQFzOEzLCz\ JBzGAzE2zG3zF4zF4zE5zE6zE } frm:MandelbrotMix2 {; 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 20.0 PAR-FORMULA FILE==================================

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Multifractal
by John Wilson 07 May '03

07 May '03

I, too, have been "wowed" by Albrecht Niekamp's new formula. I *have* to show off a zoom I made into Mandela2. I've called it FnSF because it reminded me of *all* the covers of the old "Fantasy and Science Fiction" magazine I used to devour back in the '50's. John W.

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Multifractal
by Albrecht.Niekamp＠t-online.de 06 May '03

06 May '03

Hi, now that itïs ready i find the time to do some exploring. These zooms into Julia_rules are worth waiting, I think. Fractal greetings, Al. _________________________start-par_________________________________________ The_valley { ; Albrecht Niekamp May, 03 ; Zoom into Julia_mountains ; Time 2.57.36 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=n function=exp/exp/exp passes=t center-mag=-0.88333481282099860/-0.40169492625939180/2203.42/1/-137.4999\ 99999998522/-1.18278303817831443e-012 params=-0.1740997192297128/-0.2996141087069308/384.00004/256.1106/2048.0\ 0016/768.00009/768.01536/256.01025/28424.5/12 float=y maxiter=2048 inside=maxiter outside=tdis logmap=10 periodicity=0 rseed=-2436 colors=0000j5<2>0p6<3>WxZczeUyY<2>0s8<4>0i60g60e60c4<2>0Y40W30U4<5>0I20G\ 20E20C20A1081<3>0000101221532653863A84DA5EB5HB<2>7NG8PI8RJ9TKAVNAXM<3>Dd\ TDfVEhWFjYFlYGn_Gp`Prd<3>zzz<2>_ulRsgHqaHo`GmZFkXFiX<5>BYOAWMAUL9SK<4>6I\ C5GB5DA<3>254243121000001023025047049<5>0BL0DN0DP<2>0IV0JX0KZ0L`0Mb<3>0R\ j0Sl0Tn0Up4Yr8atCgvGkxKqz<3>4_s0Vq0Uo<6>0Ma0L_0KY<3>0FQ0DO0DM<3>08E06C06\ A048046024012000100<12>R0LT0NV0PX0P<3>d0Wf0Yh0Z<3>p0e<3>xOtzUxyOuwIquCns\ 6iq0g<2>k0bi0`g0_e0Z<3>Y0SW0RU0O<7>E0CC0AA09<2>304102010<9>0L20N20P30R30\ T40V40X3<5>0h5 } The_center { ; Albrecht Niekamp May, 03 ; Zoom into Julia_rules ; Time 0.16.23 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=n function=exp/exp/exp passes=t center-mag=-0.05053709997832860/-0.00922749254324538/26.88172/1/-47.5/3.\ 88578058618804789e-016 params=-0.1740997192297128/-0.2996141087069308/384.00004/256.1106/2048.0\ 0016/768.00009/768.01536/256.01025/28974.51/12 float=y maxiter=2048 inside=maxiter outside=tdis logmap=10 periodicity=0 rseed=-2436 colors=000049<5>0BL0DN0DP<2>0IV0JX0KZ0L`0Mb<3>0Rj0Sl0Tn0Up4Yr8atCgvGkxKq\ z<3>4_s0Vq0Uo<6>0Ma0L_0KY<3>0FQ0DO0DM<3>08E06C06A048046024012000100<12>R\ 0LT0NV0PX0P<3>d0Wf0Yh0Z<3>p0e<3>xOtzUxyOuwIquCns6iq0g<2>k0bi0`g0_e0Z<3>Y\ 0SW0RU0O<7>E0CC0AA09<2>304102010<9>0L20N20P30R30T40V40X3<3>0d40f50h5<3>0\ p6<3>WxZczeUyY<2>0s8<4>0i60g60e60c4<2>0Y40W30U4<5>0I20G20E20C20A1081<3>0\ 000101221532653863A84DA5EB5HB<2>7NG8PI8RJ9TKAVNAXM<3>DdTDfVEhWFjYFlYGn_G\ p`Prd<3>zzz<2>_ulRsgHqaHo`GmZFkXFiX<5>BYOAWMAUL9SK<4>6IC5GB5DA<3>2542431\ 21000001023025047 } Spacecapsule { ; Albrecht Niekamp May, 03 ; Zoom into Julia_rules ; Time 0.13.42 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=n function=exp/exp/exp passes=t center-mag=-0.06805984151223035/-0.04559319636224127/182.8429/1.2051/57.\ 5000000000000497/-5.05012698326368081e-014 params=-0.1740997192297128/-0.2996141087069308/384.00004/256.1106/2048.0\ 0016/768.00009/768.01536/256.01025/28974.51/12 float=y maxiter=2048 inside=maxiter outside=tdis logmap=10 periodicity=0 rseed=-2436 colors=000049<5>0BL0DN0DP<2>0IV0JX0KZ0L`0Mb<3>0Rj0Sl0Tn0Up4Yr8atCgvGkxKq\ z<3>4_s0Vq0Uo<6>0Ma0L_0KY<3>0FQ0DO0DM<3>08E06C06A048046024012000100<12>R\ 0LT0NV0PX0P<3>d0Wf0Yh0Z<3>p0e<3>xOtzUxyOuwIquCns6iq0g<2>k0bi0`g0_e0Z<3>Y\ 0SW0RU0O<7>E0CC0AA09<2>304102010<9>0L20N20P30R30T40V40X3<3>0d40f50h5<3>0\ p6<3>WxZczeUyY<2>0s8<4>0i60g60e60c4<2>0Y40W30U4<5>0I20G20E20C20A1081<3>0\ 000101221532653863A84DA5EB5HB<2>7NG8PI8RJ9TKAVNAXM<3>DdTDfVEhWFjYFlYGn_G\ p`Prd<3>zzz<2>_ulRsgHqaHo`GmZFkXFiX<5>BYOAWMAUL9SK<4>6IC5GB5DA<3>2542431\ 21000001023025047 } Mandelweb { ; Albrecht Niekamp May, 03 ; Zoom into Julia_rules ; Time 0.10.47 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=n function=exp/exp/exp passes=t center-mag=-0.04702177726320782/-0.01948403974853397/3953.194/1/67.49999\ 99999997442/3.56610574403504188e-013 params=-0.1740997192297128/-0.2996141087069308/384.00004/256.1106/2048.0\ 0016/768.00009/768.01536/256.01025/28974.51/12 float=y maxiter=2048 inside=maxiter outside=tdis logmap=10 periodicity=0 rseed=-2436 colors=000049<5>0BL0DN0DP<2>0IV0JX0KZ0L`0Mb<3>0Rj0Sl0Tn0Up4Yr8atCgvGkxKq\ z<3>4_s0Vq0Uo<6>0Ma0L_0KY<3>0FQ0DO0DM<3>08E06C06A048046024012000100<12>R\ 0LT0NV0PX0P<3>d0Wf0Yh0Z<3>p0e<3>xOtzUxyOuwIquCns6iq0g<2>k0bi0`g0_e0Z<3>Y\ 0SW0RU0O<7>E0CC0AA09<2>304102010<9>0L20N20P30R30T40V40X3<3>0d40f50h5<3>0\ p6<3>WxZczeUyY<2>0s8<4>0i60g60e60c4<2>0Y40W30U4<5>0I20G20E20C20A1081<3>0\ 000101221532653863A84DA5EB5HB<2>7NG8PI8RJ9TKAVNAXM<3>DdTDfVEhWFjYFlYGn_G\ p`Prd<3>zzz<2>_ulRsgHqaHo`GmZFkXFiX<5>BYOAWMAUL9SK<4>6IC5GB5DA<3>2542431\ 21000001023025047 } Julia_mountains { ; Albrecht Niekamp May, 03 ; Zoom into Julia_rules ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=n function=exp/exp/exp passes=t center-mag=-0.88112912875275460/-0.40222637253519330/537.6344/1/42.49999\ 99999996732/7.76441411165507134e-013 params=-0.1740997192297128/-0.2996141087069308/384.00004/256.1106/2048.0\ 0016/768.00009/768.01536/256.01025/28974.5/12 float=y maxiter=2048 inside=maxiter outside=tdis logmap=10 periodicity=0 rseed=-2436 colors=0000R30T40V40X3<3>0d40f50h5<3>0p6<3>WxZczeUyY<2>0s8<4>0i60g60e60c\ 4<2>0Y40W30U4<5>0I20G20E20C20A1081<3>0000101221532653863A84DA5EB5HB<2>7N\ G8PI8RJ9TKAVNAXM<3>DdTDfVEhWFjYFlYGn_Gp`Prd<3>zzz<2>_ulRsgHqaHo`GmZFkXFi\ X<5>BYOAWMAUL9SK<4>6IC5GB5DA<3>254243121000001023025047049<5>0BL0DN0DP<2\ >0IV0JX0KZ0L`0Mb<3>0Rj0Sl0Tn0Up4Yr8atCgvGkxKqz<3>4_s0Vq0Uo<6>0Ma0L_0KY<3\ >0FQ0DO0DM<3>08E06C06A048046024012000100<12>R0LT0NV0PX0P<3>d0Wf0Yh0Z<3>p\ 0e<3>xOtzUxyOuwIquCns6iq0g<2>k0bi0`g0_e0Z<3>Y0SW0RU0O<7>E0CC0AA09<2>3041\ 02010<11>0P3 } -------------------------------start-frm----------------------------------- FRM:Multifractal { ;Albrecht Niekamp May, 03 ;only integers as first input, second input 5 digits to the right ;real(p2) factor1,border1 ;imag(p2) (-)maxiter1,input bas.frm1_2digits input bas.frm2_2digits ;real(p3) bailout,hyb.mandel: number of sides (Many_mods L.Allison) ;imag(p3) factor2,border2 ;real(p4) maxiter2,factor3 ;imag(p4) border3,maxiter3 ;real(p5) 1digit_shape only 5digits: shape,out1,out2,in1,in2 ; 1_mand 2_jul 3_hyb.mand 4_hyb.jul +5_reset (not shape) <0_no in/out1 ; optional basic frm2: out-nbr 1digit in-nbr 1digit 3_both +5_shape ;imag(p5) 1digit : 1_iter1reset 2_iter2reset 3_both +5_shape effect ; 2digits : many_mods multipl. shutoff +10_in/out1 +20_inout2 +30_both ; optional input2: frequency_2digits level_2digits amplitude_2digits ; d=real(p2) fac1=trunc(d) b1=(d-fac1)*100000 ; d=imag(p2) da=(d<0) if (da) d=-d endif mi1=trunc(d) d=round((d-mi1)*10000) p6=trunc(d/100)/10 d=d-1000*p6 if (da) p6=-p6 endif p7=d/10 ; d=real(p3) ba=trunc(d) mm=round((d-ba)*100000) ; d=imag(p3) fac2=trunc(d) b2=(d-fac2)*100000 ; d=real(p4) mi2=trunc(d) fac3=round((d-mi2)*100000) ; d=imag(p4) b3=trunc(d) mi3=round((d-b3)*100000) ; da=real(p5) t=(da<0) if (t) da=-da endif start=2-t dd=trunc(da) if (dd<5) start=0 endif vb=(dd==3)+(dd==4) da=round((da-dd)*100) d=trunc(dd/10000) vb=(d==3)+(d==4)+vb dd=dd-d*10000 d=trunc(dd/1000) or1=(d>5) d=d-5*or1 vv1=(d==3) vv2=(d==4) dd1=(d==2)+(d==4) dd=dd-d*1000 d=trunc(dd/100) or2=(d>5) d=d-5*or2 vv3=(d==3) vv4=(d==4) dd2=(d==2)+(d==4) dd=dd-d*100 d=trunc(dd/10) inr1=(d>5) d=d-5*inr1 v1=(d==3) v2=(d==4) d1=(d==2)+(d==4) dd=dd-d*10 d=trunc(dd) inr2=(d>5) d=d-5*inr2 v3=(d==3) v4=(d==4) d2=(d==2)+(d==4) d=trunc(da/10) ab=(d>=5) d=d-5*ab da=da-10*d bb1=(d==1) bb2=(d==2) d=da ab=(d>=5) d=d-5*ab ab1=(d==1) ab2=(d==2) ; d=imag(p5) dd=trunc(d) d=round((d-dd)*1000000) le=(d>10000) da=trunc(dd/10) so1=((da==1)+(da==3)==0) so2=((da==2)+(da==3)==0) dd=dd-10*da wo=(dd>=5) dd=dd-5*wo ir1=(dd==1)+(dd==3) ir2=(dd==2)+(dd==3) if (le) freq=round((trunc(d/10000))*10) ;frequency_lake effect by S.Gallet d=d-freq*1000 level=(trunc(d/100))/100 ;water level d=d-level*10000 ampl=d/100 ;amplitude of the wave angle=real(rotskew*pi/180) t=exp(-flip(angle)) h=1/real(magxmag) q=h/0.75*imag(magxmag) tanskew=tan(imag(rotskew*pi/180)) w=2*q*t v=2*h*(tanskew+flip(1))*t z3rd=center+(-q-h*tanskew-flip(h))*t z=pixel-z3rd s=imag(conj(w)*z)/imag(conj(w)*v) if (s<=level) da=level-s z=z+2*da*(1+ampl*sin(freq*da^0.2))*v endif z=z+z3rd endif if (ismand) if (vb) c=0.4*log(sqr(pixel^mm)) z=z*le else c=z*le+pixel*(le==0) z=0 endif else c=p1 z=z*le+pixel*(le==0) endif t=0 d3=(ismand==0) u=d3 : if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) ;frm: Albrecht Niekamp else z2=fn1(z)+c ;frm: Many_mods Linda Allison sqz2=cos(z2) z=c*(1-sqz2)/(1+sqz2) endif else if (ab) z=z*z+c+c*c-p7 ;frm: Puskás István else z2=z*z ;frm: Puskás István modified z=z2*z2+(p6+u)*z2+c-p1*(d3==0) endif bo=|z| If (wo) t=t+1 if ((t<mi1)+(bo>b1)) u=2*(fn1(t/fac1)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) else c=z*le+pixel*(le==0) endif else z=z*le+pixel*(le==0) c=p1*u endif wo=0 if (ir1) t=0 endif endif elseif (start) t=t+1 if (start==2) if (bo>b2) u=2*(fn2(t/fac2)) rs=or1 ab=bb1 if (dd1) if (rs) z=pixel endif c=p1*u vb=vv2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=1 endif elseif (t>mi2) u=2*(fn2(t/fac2)) rs=inr1 ab=ab1 if (d1) if (rs) z=pixel endif c=p1*u vb=v2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=1 if (ir2) t=0 endif endif elseif (bo>b3) u=2*(fn3(t/fac3)) ab=bb2 rs=or2 if (dd2) if (rs) z=pixel endif c=p1*u vb=vv4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=0 endif elseif (t>mi3) u=2*(fn3(t/fac3)) ab=ab2 rs=inr2 if (d2) if (rs) z=pixel endif c=p1*u vb=v4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=0 endif endif bo<=ba } -------------------------------------------end-----------------------------

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Re: Albrecht Niekamp Multifractal
by JackOTradez 06 May '03

06 May '03

Those Al-Niekamp Multifractal images are incredible! It is a long formula and Im trying to figure it out so I can animate them. I am trying to do "The Gate" image now. But a zoom into the Mandala was easy. If interested it is: http://www.sonic.net/~jot/mandalaz.zip Stay Amazed! JoTz

1 0

FOTD 06-05-03 (A Golden Oldie [7])
by Jim M. 06 May '03

06 May '03

FOTD -- May 06, 2003 (Rating 7) Fractal visionaries and enthusiasts: Returning to the parent fractal for May, which appeared on May 3, we notice that the upper edge of the 'fan' is dotted with bits and pieces of small Mandeloids and Mandeloid buds. Today's scene pictures a midget located in the most prominent valley of the largest of these partially-obscured Mandeloids. I named the image "A Golden Oldie". I forget whether it was the color that inspired the name, or if I gave it the name because it gives me a feeling of olde tymes. Most likely it was a com- bination of these things. As the month progresses, I shall use nothing but the convention- al equal-iteration-band method to render and color the images. There will be no 'evaporated' or 'tdis' images. This limitation will not result in boring images however. The parent fractal has nearly (and in fact, actual) unlimited variety. When the time to rate the image arrived, I decided on an above- average 7. I'm not exactly sure I like the mixture of green and orange in the golden parts of the image. But it's still a strik- ingly different scene, well worth the 7. The parameter file renders the image in 16 minutes on my machine. The completed GIF image will download from the FOTD web sites in a fraction of that time. The URL of Paul's site is: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's site can be accessed at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The cats' good luck ended on Monday, as steady light rain moved in on schedule shortly after lunch time. The temperature of 48F 9C was no help at all. Confined as the duo were to the indoors, their moods quickly soured, they grew testy, and a treat of tuna was necessary to partially restore their good spirits. For some reason, Tippy tried to pick a fight with Thomas in the evening, but Thomas, being the peaceful cat that he is, backed down grace- fully, and they both ended the day as good friends. Today is cloudy and threatening rain again. A totally peaceful day among the dynamic duo might be too much to hope for, but we shall see how it goes. Until tomorrow, when we'll return to the parent fractal for May, take care, and who knows what we don't know about fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Golden_Oldie { ; time=0:16:35:74--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=mandelbrotmix2 function=recip passes=1 center-mag=+5.32247257841096700/-2.024785183651587\ 00/744559.3/1/-115/-2.37486178181200991e-007 params=-10/-1.1/-1/-11/0/525/0/0 float=y maxiter=1800 inside=0 logmap=285 periodicity=10 colors=000OKULKUJKUHKUFKUCKUAKU7KV5KV0KV2KV3KW4KW5\ KW6KW7KX8KXAKYBKYCKZDKZEK_FK_GK`IK`JKaKLaLMaMNbNOc\ OPcOOcPNdQMdRLeRKeSLeTMfUNfUOfVPgWWgXYhX_hYchZdi_e\ i_ii`ijaljbmkbokcqkdsleulfukewldvlcvlbumaum`tm_smZ\ snYrnXrnWqnVpoUpoTooSooRnpQmpPmpOlqNlqMkqLjqKjrJir\ IirHhrGgsFgsEfsChvDfsEeqEdoFcmFbkGaiH`gH_eIYcIXaJW\ _JVYKUVLTTLSRMRPMPNNOLONJOMHPLFPKDQJBIB3QI9YOFdVLl\ `RwiXugWsfWqdWocWmbWk`Vi_VgZVeXVcWVaVV_TUYSUWRUUPU\ SOUQNUROTSPTTQTURTVSSWTSXUSYVSZVS_WR`XRaYRbZRc_Qd`\ QeaQfbQgbQhcPidPjePkfPogOshOwiOzjOzjOwiNshMohLlgKh\ gJefJcfIceHceGcdFcdFbcEabD`bCZaBYaAX`AW`9V_8U_7TZ6\ OY1QZ4SZ6UZ9W_BX_DZ_G``Ib`Kc`Ne`PhaRkaUnaWqbYtb`wb\ bzbdwZbrW`mS_hPYcLXZIVUCVPEUKFUFGVAHWAIX9KY9LZ8M_8\ N`7Oa6Qb6Rc5Sd5Te4Uf4Wg3Xh3Yi2Zj2_k3_l4`m4an5bo6cp\ 6dq7er8fs8gt9hu9ivAjwBkxBlyCmzDnzDozEpzEqzFrzGszGt\ zHuzIvzIwzJxzJyzVzzWzzJzz } frm:MandelbrotMix2 {; 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 20.0 PAR-FORMULA FILE==================================

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Multifractal
by Albrecht.Niekamp＠t-online.de 05 May '03

05 May '03

Hi, no comments needed. Check it out. Fractals are fun! Al -----------------------------start-par------------------------------------ Julia_rules { ; Time 1.17.02 p4 2giga 1600/1200 ; Albrecht Niekamp May, 03 ; ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=n function=exp/exp/exp passes=t center-mag=-8.88178e-016/6.66134e-016/1.344086/1/-47.5/-1.23373533611470\ 521e-014 params=-0.1740997192297128/-0.2996141087069308/384.00004/256.1106/2048.0\ 0016/768.00009/768.01536/256.01025/28424.5/12 float=y maxiter=2048 inside=maxiter outside=tdis logmap=10 periodicity=0 rseed=-2436 colors=000049<5>0BL0DN0DP<2>0IV0JX0KZ0L`0Mb<3>0Rj0Sl0Tn0Up4Yr8atCgvGkxKq\ z<3>4_s0Vq0Uo<6>0Ma0L_0KY<3>0FQ0DO0DM<3>08E06C06A048046024012000100<12>R\ 0LT0NV0PX0P<3>d0Wf0Yh0Z<3>p0e<3>xOtzUxyOuwIquCns6iq0g<2>k0bi0`g0_e0Z<3>Y\ 0SW0RU0O<7>E0CC0AA09<2>304102010<9>0L20N20P30R30T40V40X3<3>0d40f50h5<3>0\ p6<3>WxZczeUyY<2>0s8<4>0i60g60e60c4<2>0Y40W30U4<5>0I20G20E20C20A1081<3>0\ 000101221532653863A84DA5EB5HB<2>7NG8PI8RJ9TKAVNAXM<3>DdTDfVEhWFjYFlYGn_G\ p`Prd<3>zzz<2>_ulRsgHqaHo`GmZFkXFiX<5>BYOAWMAUL9SK<4>6IC5GB5DA<3>2542431\ 21000001023025047 } -------------------------------start-frm----------------------------------- FRM:Multifractal { ;Albrecht Niekamp May, 03 ;only integers as first input, second input 5 digits to the right ;real(p2) factor1,border1 ;imag(p2) (-)maxiter1,input bas.frm1_2digits input bas.frm2_2digits ;real(p3) bailout,hyb.mandel: number of sides (Many_mods L.Allison) ;imag(p3) factor2,border2 ;real(p4) maxiter2,factor3 ;imag(p4) border3,maxiter3 ;real(p5) 1digit_shape only 5digits: shape,out1,out2,in1,in2 ; 1_mand 2_jul 3_hyb.mand 4_hyb.jul +5_reset (not shape) <0_no in/out1 ; optional basic frm2: out-nbr 1digit in-nbr 1digit 3_both +5_shape ;imag(p5) 1digit : 1_iter1reset 2_iter2reset 3_both +5_shape effect ; 2digits : many_mods multipl. shutoff +10_in/out1 +20_inout2 +30_both ; optional input2: frequency_2digits level_2digits amplitude_2digits ; d=real(p2) fac1=trunc(d) b1=(d-fac1)*100000 ; d=imag(p2) da=(d<0) if (da) d=-d endif mi1=trunc(d) d=round((d-mi1)*10000) p6=trunc(d/100)/10 d=d-1000*p6 if (da) p6=-p6 endif p7=d/10 ; d=real(p3) ba=trunc(d) mm=round((d-ba)*100000) ; d=imag(p3) fac2=trunc(d) b2=(d-fac2)*100000 ; d=real(p4) mi2=trunc(d) fac3=round((d-mi2)*100000) ; d=imag(p4) b3=trunc(d) mi3=round((d-b3)*100000) ; da=real(p5) t=(da<0) if (t) da=-da endif start=2-t dd=trunc(da) if (dd<5) start=0 endif vb=(dd==3)+(dd==4) da=round((da-dd)*100) d=trunc(dd/10000) vb=(d==3)+(d==4)+vb dd=dd-d*10000 d=trunc(dd/1000) or1=(d>5) d=d-5*or1 vv1=(d==3) vv2=(d==4) dd1=(d==2)+(d==4) dd=dd-d*1000 d=trunc(dd/100) or2=(d>5) d=d-5*or2 vv3=(d==3) vv4=(d==4) dd2=(d==2)+(d==4) dd=dd-d*100 d=trunc(dd/10) inr1=(d>5) d=d-5*inr1 v1=(d==3) v2=(d==4) d1=(d==2)+(d==4) dd=dd-d*10 d=trunc(dd) inr2=(d>5) d=d-5*inr2 v3=(d==3) v4=(d==4) d2=(d==2)+(d==4) d=trunc(da/10) ab=(d>=5) d=d-5*ab da=da-10*d bb1=(d==1) bb2=(d==2) d=da ab=(d>=5) d=d-5*ab ab1=(d==1) ab2=(d==2) ; d=imag(p5) dd=trunc(d) d=round((d-dd)*1000000) le=(d>10000) da=trunc(dd/10) so1=((da==1)+(da==3)==0) so2=((da==2)+(da==3)==0) dd=dd-10*da wo=(dd>=5) dd=dd-5*wo ir1=(dd==1)+(dd==3) ir2=(dd==2)+(dd==3) if (le) freq=round((trunc(d/10000))*10) ;frequency_lake effect by S.Gallet d=d-freq*1000 level=(trunc(d/100))/100 ;water level d=d-level*10000 ampl=d/100 ;amplitude of the wave angle=real(rotskew*pi/180) t=exp(-flip(angle)) h=1/real(magxmag) q=h/0.75*imag(magxmag) tanskew=tan(imag(rotskew*pi/180)) w=2*q*t v=2*h*(tanskew+flip(1))*t z3rd=center+(-q-h*tanskew-flip(h))*t z=pixel-z3rd s=imag(conj(w)*z)/imag(conj(w)*v) if (s<=level) da=level-s z=z+2*da*(1+ampl*sin(freq*da^0.2))*v endif z=z+z3rd endif if (ismand) if (vb) c=0.4*log(sqr(pixel^mm)) z=z*le else c=z*le+pixel*(le==0) z=0 endif else c=p1 z=z*le+pixel*(le==0) endif t=0 d3=(ismand==0) u=d3 : if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) ;frm: Albrecht Niekamp else z2=fn1(z)+c ;frm: Many_mods Linda Allison sqz2=cos(z2) z=c*(1-sqz2)/(1+sqz2) endif else if (ab) z=z*z+c+c*c-p7 ;frm: Puskás István else z2=z*z ;frm: Puskás István modified z=z2*z2+(p6+u)*z2+c-p1*(d3==0) endif bo=|z| If (wo) t=t+1 if ((t<mi1)+(bo>b1)) u=2*(fn1(t/fac1)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) else c=z*le+pixel*(le==0) endif else z=z*le+pixel*(le==0) c=p1*u endif wo=0 if (ir1) t=0 endif endif elseif (start) t=t+1 if (start==2) if (bo>b2) u=2*(fn2(t/fac2)) rs=or1 ab=bb1 if (dd1) if (rs) z=pixel endif c=p1*u vb=vv2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=1 endif elseif (t>mi2) u=2*(fn2(t/fac2)) rs=inr1 ab=ab1 if (d1) if (rs) z=pixel endif c=p1*u vb=v2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=1 if (ir2) t=0 endif endif elseif (bo>b3) u=2*(fn3(t/fac3)) ab=bb2 rs=or2 if (dd2) if (rs) z=pixel endif c=p1*u vb=vv4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=0 endif elseif (t>mi3) u=2*(fn3(t/fac3)) ab=ab2 rs=inr2 if (d2) if (rs) z=pixel endif c=p1*u vb=v4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=0 endif endif bo<=ba } -------------------------------------------end-----------------------------

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FOTD 05-05-03 (Starry Mandelbrot [8])
by Jim M. 05 May '03

05 May '03

FOTD -- May 05, 2003 (Rating 8) Fractal visionaries and enthusiasts: Yesterday's FOTD image took us to the place where the right edge of the large fan-like element of the parent fractal merges into the 'East Valley' area of an obvious Mandel-like feature. Today's image takes us to the place where the left edge of the symmetrical fan-like element merges into a less-Mandel appearing feature. The 'fan' itself is filled with tiny holes, which are disconnected from the main body of the parent fractal but are rich with fractal detail nonetheless. Since the area in which today's scene lies is disconnected, the midget at the center is disconnected also. This isolation gives the midget, with its surroundings, the appearance of a star in a dark sky. The obvious 8-pointed star-like feature completes the effect of stellar glory and justifies the name "Starry Mandelbrot". I am quite satisfied with the appearance of today's image, and feel the rating of a much-above-average 8 is fully justified. Unfortunately, as is so often the case, something worth having must be waited for, and the 1/2-hour render time of today's image on my machine must be considered a wait, even when reduced to a fraction of that amount on a faster machine. Now, I suppose it is only fair to admit that I am no expert, at least in the field of math and fractals. (Despite the occasional dissension of critics, I am an expert in philosophy however, ;-) but my modesty prevents me from discussing it here.) In these fractal discussions, I often make statements that I think are true, but the fact that I think these things are true does not necessarily make them actually true. So the things I write in these discussions (other than my well-pondered philosophy) should be taken as entertainment rather than proven fact. Those with much patience can see today's image in 1/2 hour by running the attached parameter file. Those with better ways to fill their time will pick up the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Well, I survived Sunday's trip to the antique emporium. In fact, I actually found a picture that I liked at a price I liked even better. The dynamic duo meanwhile remained on guard, pro- tecting Fractal Central from intruders. If any wrongdoer had dared to break in, the draft behind the dynamic duo as they dashed for cover would have knocked the intruder flat. The weather was cloudy and 64F 18C, but the rain held off again. This was irrelevant however, since the dynamic ones were alone by themselves indoors most of the day. Today is starting cloudy again, and the forecast is for rain by afternoon. I hope the duo stays happy. Until next time, which will be here in the wink of a fractal, take care, and be kind to your fractal -- it could be somebody's mother. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Starry_Mandelbrot { ; time=0:29:37.98--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=mandelbrotmix2 function=recip passes=1 center-mag=+1.25085078864374300/+3.023813723474635\ 00/4.386769e+009/1/-82.5/0.00713534581712483434 params=-10/-1.1/-1/-11/0/525/0/0 float=y maxiter=2700 inside=0 logmap=479 periodicity=10 colors=000307407406405404403503502501cn_cnZdoYdoXd\ pXepWeqVfqUfrTfrTgGacAc`5eb7Wc9MdBCeD3`F4WH4RJ4ML4\ HN5CP57R53T5LSGbSQsS_oSbkSdgSfcSh_SjWSlSSnUVjWXfY_\ b_aZadVcfReiNgkJinFkpBlr8ms7ns7os7ps7qs7rt6st6st6t\ t6ut6vu5wu5xu5yu5zu5zu5wo8ujAreCp_EmVGkQIw26r78nC9\ jGBfLCbQEZUFVZHRbITcLVcOXcRZcU`cXbc_ccaef`gh_ikZjm\ YlpXnrWotWnoUnjTneSm`QmWPmSOnRRpQUqPXgpfikbjgZkcWm\ _SnWOoRLpNHrJDsFAtB6u73pA8kDDfGIaINXLSTOXORaJTfEWk\ 9Zp4au0czH`zYYznVzoXrpYkqZdr_Ys`RtaKubDvc6oa8o`9kZ\ BhYCfXEaVFYUHVSIRRKOQLKONHNOEMPFOMGRJITGKVDNXAQZ7T\ a8Wd9ZfAaiBdkCgmDjoEmqEmsDmvDmwCmxCmyBmzBPnAQoAQpA\ Qp9Qq9Rr9Rs8Rt8Rt8_fEhTJqFOz1Tr2Uk3Ud4UX5UQ6UJ7UC8\ UKAVSCVZEVfGWnIWuJWmN1kP4iR6gT8eUAcWCaYE_ZGZ`IXbLV\ cNTePRgRPhTNjVLlXKmZJiWIeUHaSHaQGcOFeMFgKEiIDkGDmE\ EoEEqEEsEEuEEvEEwEFxEFyEFzEFzEFzEFzEDzICzLBzOAzR8z\ U7zX6z_5zb3zehzOfzTdzXbz` } frm:MandelbrotMix2 {; 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 20.0 PAR-FORMULA FILE==================================

1 0

Multifractal
by Albrecht.Niekamp＠t-online.de 05 May '03

05 May '03

Hi, Lee sorry, its like you said, I forgot to rename those two which have been added later. Here they are again and a new one. There is a minor modification in the main loop of the formula, but it only slightly improves the performance. Fractal Greetings, Al. -------------------------start-par-------------------------------------- Speedtest { ; Time 1min10sec p4 2giga 1600/1200 ; Albrecht Niekamp May, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=n function=exp/exp/exp passes=t center-mag=0.117455/3.33067e-016/2.552858/1/90/3.88578058618804789e-016 params=-0.173894466994232/-0.3000579851680044/384.00001/256.1133/2048.00\ 008/768.0256000000001/768.01536/2560.01025/4/35.324051 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=0000200000101221532653863A84DA5EB5HB<2>7NG8PI8RJ9TKAVNAXM<3>DdTDf\ VEhWFjYFlYGn_Gp`Prd<3>zzz<2>_ulRsgHqaHo`GmZFkXFiX<5>BYOAWMAUL9SK<4>6IC5G\ B5DA<3>254243121000001023025047049<5>0BL0DN0DP<3>0JX0KZ0L`0Mb0Nd<3>0Sl0T\ n0Up4Yr8atCgvGkxKqz<3>4_s0Vq0Uo<6>0Ma0L_0KY<3>0FQ0DO0DM<3>08E06C06A04804\ 6024012000100<12>R0LT0NV0PX0P<3>d0Wf0Yh0Z<3>p0e<3>xOtzUxyOuwIquCns6iq0g<\ 2>k0bi0`g0_e0Z<3>Y0SW0RU0O<8>C0AA09807506304102010<9>0L20N20P30R30T40V40\ X3<3>0d40f50h5<3>0p6<3>WxZczeUyY<2>0s8<4>0i60g60e60c4<2>0Y40W30U4<5>0I20\ G20E20C20A1081061040 } Mandala2 { ; 5*many_mods ; Albrecht Niekamp May,03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=y function=exp/exp/exp passes=t center-mag=4.44089e-016/-2.22045e-016/0.5706667 params=-0.1738944669942329/-0.3000579851680044/384.00001/256.0076/256038\ 4.00008/1536.0256/768.01536/5120.01024/38888/2 float=y maxiter=3072 inside=maxiter outside=tdis logmap=yes periodicity=0 rseed=-2436 colors=200U00<9>A00<4>000<25>iiijjjlll<3>sss<25>BBB999777<2>222000012<24\ >0bo0cq0es<3>0kz<25>09C08A068<2>022000211<24>oiQqjRslS<3>zsX<25>CB7A9687\ 5<3>000400<23>o00q00s00<3>z00<15>W00 } Mandala2_deep_zoom { ;Albrecht Niekamp May, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=y function=exp/sin/exp passes=t center-mag=-0.09443402126328944/+0.06768140116763766/266.6667 params=-0.1738944669942329/-0.3000579851680044/384.00001/256.0076/512038\ 4.00015/1536.0256/768.01536/5120.01024/37314/0 float=y maxiter=3072 inside=maxiter outside=tdis logmap=yes periodicity=0 rseed=-2436 colors=200BBB<3>444222000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<22\ >keOmgPoiQqjRslSunT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C0\ 0A00800<3>000<23>eeegggiiijjjlllnnn<2>sss<24>DDD } ---------------------------start-frm--------------------------------------- FRM:Multifractal { ;Albrecht Niekamp May, 04 ;only integers as first input, second input 5 digits to the right ;real(p2) factor1,border1 ;imag(p2) (-)maxiter1,input bas.frm1_2digits input bas.frm2_2digits ;real(p3) bailout,hyb.mandel: number of sides (Many_mods L.Allison) ;imag(p3) factor2,border2 ;real(p4) maxiter2,factor3 ;imag(p4) border3,maxiter3 ;real(p5) 1digit_shape only 5digits: shape,out1,out2,in1,in2 ; 1_mand 2_jul 3_hyb.mand 4_hyb.jul +5_reset (not shape) <0_no in/out1 ; optional basic frm2: out-nbr 1digit in-nbr 1digit 3_both +5_shape ;imag(p5) 1digit : 1_iter1reset 2_iter2reset 3_both +5_shape effect ; 2digits : many_mods multipl. shutoff +10_in/out1 +20_inout2 +30_both ; optional input2: frequency_2digits level_2digits amplitude_2digits ; d=real(p2) fac1=trunc(d) b1=(d-fac1)*100000 ; d=imag(p2) da=(d<0) if (da) d=-d endif mi1=trunc(d) d=round((d-mi1)*10000) p6=trunc(d/100)/10 d=d-1000*p6 if (da) p6=-p6 endif p7=d/10 ; d=real(p3) ba=trunc(d) mm=round((d-ba)*100000) ; d=imag(p3) fac2=trunc(d) b2=(d-fac2)*100000 ; d=real(p4) mi2=trunc(d) fac3=round((d-mi2)*100000) ; d=imag(p4) b3=trunc(d) mi3=round((d-b3)*100000) ; da=real(p5) t=(da<0) if (t) da=-da endif start=2-t dd=trunc(da) if (dd<5) start=0 endif vb=(dd==3)+(dd==4) da=round((da-dd)*100) d=trunc(dd/10000) vb=(d==3)+(d==4)+vb dd=dd-d*10000 d=trunc(dd/1000) or1=(d>5) d=d-5*or1 vv1=(d==3) vv2=(d==4) dd1=(d==2)+(d==4) dd=dd-d*1000 d=trunc(dd/100) or2=(d>5) d=d-5*or2 vv3=(d==3) vv4=(d==4) dd2=(d==2)+(d==4) dd=dd-d*100 d=trunc(dd/10) inr1=(d>5) d=d-5*inr1 v1=(d==3) v2=(d==4) d1=(d==2)+(d==4) dd=dd-d*10 d=trunc(dd) inr2=(d>5) d=d-5*inr2 v3=(d==3) v4=(d==4) d2=(d==2)+(d==4) d=trunc(da/10) ab=(d>=5) d=d-5*ab da=da-10*d bb1=(d==1) bb2=(d==2) d=da ab=(d>=5) d=d-5*ab ab1=(d==1) ab2=(d==2) ; d=imag(p5) dd=trunc(d) d=round((d-dd)*1000000) le=(d>10000) da=trunc(dd/10) so1=((da==1)+(da==3)==0) so2=((da==2)+(da==3)==0) dd=dd-10*da wo=(dd>=5) dd=dd-5*wo ir1=(dd==1)+(dd==3) ir2=(dd==2)+(dd==3) if (le) freq=round((trunc(d/10000))*10) ;frequency_lake effect by S.Gallet d=d-freq*1000 level=(trunc(d/100))/100 ;water level d=d-level*10000 ampl=d/100 ;amplitude of the wave angle=real(rotskew*pi/180) t=exp(-flip(angle)) h=1/real(magxmag) q=h/0.75*imag(magxmag) tanskew=tan(imag(rotskew*pi/180)) w=2*q*t v=2*h*(tanskew+flip(1))*t z3rd=center+(-q-h*tanskew-flip(h))*t z=pixel-z3rd s=imag(conj(w)*z)/imag(conj(w)*v) if (s<=level) da=level-s z=z+2*da*(1+ampl*sin(freq*da^0.2))*v endif z=z+z3rd endif if (ismand) if (vb) c=0.4*log(sqr(pixel^mm)) z=z*le else c=z*le+pixel*(le==0) z=0 endif else c=p1 z=z*le+pixel*(le==0) endif t=0 d3=(ismand==0) u=d3 : if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) ;frm: Albrecht Niekamp else z2=fn1(z)+c ;frm: Many_mods Linda Allison sqz2=cos(z2) z=c*(1-sqz2)/(1+sqz2) endif else if (ab) z=z*z+c+c*c-p7 ;frm: Pusk s Istv n else z2=z*z ;frm: Pusk s Istv n modified z=z2*z2+(p6+u)*z2+c-p1*(d3==0) endif bo=|z| If (wo) t=t+1 if ((t<mi1)+(bo>b1)) u=2*(fn1(t/fac1)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) else c=z*le+pixel*(le==0) endif else z=z*le+pixel*(le==0) c=p1*u endif wo=0 if (ir1) t=0 endif endif elseif (start) t=t+1 if (start==2) if (bo>b2) u=2*(fn2(t/fac2)) rs=or1 ab=bb1 if (dd1) if (rs) z=pixel endif c=p1*u vb=vv2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=1 endif elseif (t>mi2) u=2*(fn2(t/fac2)) rs=inr1 ab=ab1 if (d1) if (rs) z=pixel endif c=p1*u vb=v2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=1 if (ir2) t=0 endif endif elseif (bo>b3) u=2*(fn3(t/fac3)) ab=bb2 rs=or2 if (dd2) if (rs) z=pixel endif c=p1*u vb=vv4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=0 endif elseif (t>mi3) u=2*(fn3(t/fac3)) ab=ab2 rs=inr2 if (d2) if (rs) z=pixel endif c=p1*u vb=v4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=0 endif endif bo<=ba } -----------------------end-frm---------------------------------------

2 1

FOTD 04-05-03 (Sargasso Seaweed [7])
by Jim M. 04 May '03

04 May '03

FOTD -- May 04, 2003 (Rating 7) Fractal visionaries and enthusiasts: As I said in yesterday's FOTD, during the month of May I will restrict my fractal explorations to a single fractal -- the fractal that appeared as the FOTD for May 3, which was yesterday. I am doing this because in my continuing haste to find ever more fractals, I rarely stay with a single fractal long enough to become familiar with its various parts. And this parent fractal that I have chosen for May is one of the most varied I have yet found. Today we take our first venture into the parent fractal for May, which will serve as the parent of the FOTD images that will appear during the rest of the month. Today's image is located in the area where the edge of the large fan-like element merges into the 'East Valley' area of the obvious Mandel-shape on the right. I have named the image "Sargasso Seaweed". I gave it this name because something about it reminds me of rafts of seaweed lazily floating on a nearly calm ocean. But I could easily have given the image a name such as "Holey Iterations", since it has more holes than one can shake a golf course at. These holes are not Mandelbrot midgets, nor are they Julia sets. In fact, I don't know what they are, except just plain 'holes'. Such holes often appear in images created with the MandelbrotMix series of formulae. They also appear in certain parts of some fractals created with the MandelbrotBC1 formula, which draws the more remote levels of the fractals that contain a fractional power of Z. Today's image undergoes some curious changes when the bailout radius, which is the imag(p3) parameter, is raised to a sufficiently high value. These changes are the beginning of fractal 'evaporation'. They appear suddenly and unexpectedly. Finding the exact point of the beginning of fractal breakup is a challenging task, though in some cases, worth the effort. I used the MandelbrotMix2 formula to create the parent fractal for May, as well as all images that will appear during this month. This formula works exactly like the MandelbrotMix4 formula except that it has two additional changeable parameters, which can be used to change the starting point of Z. After studying today's image for all of 5 minutes, I decided that it was worth a rating of an above-average 7. The render time of 20 minutes, at least on my machine, is a bit slow, but relief can be found on the internet in the form of the completed image, which is or soon will be posted to the FOTD web sites. Paul's site is at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's is at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> On Saturday, good luck once again prevailed here at Fractal Central. There was little sun, but the rain held off and the temperature reached 63F 17C, producing conditions that any fractal cat would find enjoyable. Being fractal in nature, the dynamic cat duo thoroughly enjoyed their afternoon in the yard. At one time, the cat from two doors down made a brief appearance in the brush at the bottom of the yard. I think he was just trying to be friendly, but Tippy once again chased the other cat back down where Tippy feels he belongs. Today is once again threatening rain. Hopefully, the good luck will continue, and the rain will hold off. But there is no guarantee. Somehow, I got myself dragged into spending today looking at old junk at one of the local antique emporiums, so the duo will have to remain indoors until we return late this afternoon. Until next time, take care, and be ever more alert to signs of fractals in the world around you. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Sargasso_Sea-Weed { ; time=0:20:33.41--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+1.26815170075631500/-3.043295039151435\ 00/127119.9/1/70/1.31606140499340718e-008 params=-10/-1.1/-1/-11/0/525/0/0 float=y maxiter=1500 inside=0 logmap=196 periodicity=10 colors=000h09g06f03e00d70cG0bI0aJ0`F0XA0V60T11Q03P\ 09L1S44JO6YA9TQAaICdQFiOGoHJpTLyQMuOLpFJn6IQLAOY4M\ j0Jx0Ip1Yj9mmDfoI`rMTsQOuVIx_Ayc4zg0zl0zp0zr0zs0yu\ 0xu0vv0ux0sx0py0oz0mz0lz0jz0iz0gz0cz0_z4VyAQvIMuPI\ sVDpa9oi4moFpjPrf_sa`uYavTbxPcvQdvSevSbvTSvTOxSLyS\ IzSFzSCzS9zSdzS1zSbzS0zS0xS0zS0tS0zQ0qP1rO6lMXgLFf\ JT`IO`GSVFPYFOXFL`FJcFIfFFjFDmF`pF9uFgxF6zFFY6MXFT\ XM`VTgV`oTgvTozTvzIxzOfzSPzX7z`0y_0uY0pX4mV9iTDdSI\ `QMYQP_JX`Daa6ic0od0uX0pO0lF1g73cD1aJ0aO0aT0aY0ac0\ ag0`m0`r0`x0`z0`z0`z0`z0cz0dz0fz1iz4jz7lzAmzDpzGrz\ JszMuzPxzSyzVzzYzz_uz`mzafzc_zcSzdLzfDzg6zi0zi0yf0\ yc0xa1x_4xX7vVAvSDuPGuOJuLMsIPsGTrDXrA_r9ap6dp3go1\ jo0mo0pm0sm0vr0zm0yj0xg0vd0ua0s_0rX0rOaFVaMacTia`g\ c_gcYgcYgcXgcVgdVgdTgdSfdSfdQfdPffPfgOfjMfmMfpLfsL\ auO_vQXxTSyXPz_MzaIzdFzgCzj7zm4zp1zs0zv0zy0zz0zz0z\ z0zz1zz4zz9zzDzzGzzLzzLzz } frm:MandelbrotMix2 {; 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 20.0 PAR-FORMULA FILE==================================

1 0

Multifractal
by Albrecht.Niekamp＠t-online.de 03 May '03

03 May '03

Hi, is this post-fractint? Kinda pick up the pieces and make something new of it? I hope not. It was supposed to be an update to Mandelmania but it turned out to become something different, more a tool then a formula. A tool to be used without leaving fractint, which lets you compose your image,- or the first approach to it. It mixes 4 fractals with seperate inside/ outside options.Two basic formulas which are ismand compatible and two hybrid mandel and julia variations. Of course a huge number of inputs is needed, but I have tried to make them as easy and comfortable as even possible. The p1 values are used as Julia seed and shared to define the default mandel, I call it shape. If you need both, start with the Julia values, see what basic image you get and define it further with the P6 input,(real P2) after the dot. The first 2 digits are used, they even can be negative, a "minus" will be applied to this value only. The other two digits are used to define the 2nd shape. This one has many variations of mirrored mandels that can be combined to one special shape. Use the evolver, max mutation for example 0.003. Both are written by Puskás István. The default one is modified to enforce Julia compatability and to use the "warp"effect for further modification. The inputs are sorted as shape/ in/out1 and in/out2 factor,border, maxiter. Border1 can be fractional, a border value of 1.4567 would appear as (factor1).000014567. The primary input Real P5 consists of five digits, shape, out1, out2, in1, in2. You type the number of the fractal to be used and add five to reset it, not the shape of course. A "minus" will shut off in/out1. Number 3 is Many_mods (mandel) by Linda Allison with a modification by Sylvie Gallet. I like this because it creates beautiful structures and its very complex. The circular form can be changed if you take a mandel as basic shape. It mixes very well with the hybrid Julia, (Nr.4),own write, which also gains complexity with the warpeffect, as it shares iteration. This one can be replaced by a different frm, if it dosnt need an additional input. The other ones are "built in" so some rewriting would be necessary in order to replace them. If you want the shape only, no in/out options, just type one number. Do not forget to set ismand according to your selection. The secondary input consists of 2 digits.You type the number out1/out2 and in1/in2 (or zero) to use the second basic formula, 3 if you want to use it for both, add five to use it as shape. This input is optional. Resetting generally adjusts the concerned part to the screen instead of the surroundings, it also helps avoid chaotic spots due to overcomplexity. Many-mods gains complexity, the number of "sides", (real P3,2nd input) is doubled if called as in/out option and again if twice f.e "(bailout).00008". This also creates the multiplication in "cockpit", I think. Imag P5 is optional, one or two digts, 1 for resetting the internal counter after shape (1) or after in/out1 (2), 3 if both. Add five or only 5 to use the warpeffect on the shape. This sometimes helps if you dont get an inside image and lets you see the difference. Counter resetting starts the calculation of the warp effect from zero. If you dont reset it and use the same factor for all options, the effect will increase with iteration. If you want to shut off the many_mods multiplication add 10 for in/out1, add 20 for in/out2 or 30 to shut it off completely. The Lake input ,2nd input, is radically simplified (sorry, Sylvie), you just type one six digits number, 2 digits for each value. 324151 means a frequency of 320, a level of 41% and an amplitude of 0.51. Any valid input activates the lake effect. The functions are used for the calculation of the warp effect, possibly a new factor must be found if changed. Fn1 is shared with many_mods, so if you dont warp the shape it is free to use. I did not use fn4 or fn5 for the 2nd function as at least 2 lines are needed to scroll the text. If you dont want the outside options set the values higher then bailout, or vv maxiter higher then maxiter on the x-screen. It was not possible to include twoway border values and separate bailout values, P6 is needed. Its a good idea to have a hardcopy available when doing the inputs, also some basic pars ready to modify. There is one problem: Many_mods is n o t compatible with the lake effect, as they both define "c", applying the effect to "z" does not do the job and the image is partly distorted. P l e a s e tell me, if you see a solution, maybe only Sylvie can help. If you have questions or bugs to report, please dont hesitate and -- please post your images. Writing this was like a trip into a new country, and when you finally detect, that it´s much more complex then it´s parts, well- that´s it. Fractal Greetings, Al. ---------------------------------------start-par-------------------------- - The_flying_mandel { Albrecht Niekamp Apr, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=y function=exp/exp/exp passes=t center-mag=-0.426332/0.037594/0.8912656/1/-90/3.88578058618804789e-016 params=-0.2724234748374889/0.09260841700491348/384.00001/256.1113/2048.0\ 0008/768.00004/1025.01536/2560.01536/18115.11/0 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200022000<4>A85CA6EC7GE8IF9KHA<13>keOmgPoiQqjRslSunT<2>zsX<25>CB7\ A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<23>eeegggiiijjjlll\ nnn<2>sss<25>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<29>034 } The_gate { ; Albrecht Niekamp Apr, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=y function=exp/exp/exp passes=t center-mag=0.512575/-0.480315/2.675131/1/-90/3.88578058618804789e-016 params=0.5125888851588488/-0.4719992675557726/384.00001/256.3601/2048.00\ 008/768.0256000000001/768.01536/2560.01025/11113.11/1.324051 float=y maxiter=3072 inside=maxiter outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=200000<23>eeegggiiijjjlllnnn<2>sss<25>BBB999777<2>222000012<24>0b\ o0cq0es<3>0kz<25>09C08A068<2>022000211<22>keOmgPoiQqjRslSunT<2>zsX<25>CB\ 7A96875<3>000400<23>o00q00s00<3>z00<30>200 } Hades { ; Albrecht Niekamp Apr, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=y function=exp/exp/exp passes=t center-mag=-1.09933852316632100/+1.00410963532720300/204.7945/1/-169.999\ 999999999545/4.83828255237739313e-013 params=-0.1738944669942329/-0.3000579851680044/384.00001/256.1113/3072.0\ 0016/768.0001600000001/768.01536/32.01025/34231/5 float=y maxiter=3072 inside=maxiter outside=tdis logmap=yes periodicity=0 rseed=-2436 colors=20009C<19>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<22>keOmgPoiQqj\ RslSunT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>00\ 0<23>eeegggiiijjjlllnnn<2>sss<25>BBB999777<2>222000012<3>07A } Cockpit { ; Albrecht Niekamp Apr, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=y function=exp/exp/exp passes=t center-mag=-1.16761/0.932037/6.553424/1/-47.5/-3.77822773067748585e-014 params=-0.1738944669942329/-0.3000579851680044/384.00001/256.1113/3072.0\ 0016/768.0001600000001/768.01536/32.01025/34231/5 float=y maxiter=3072 inside=maxiter outside=tdis logmap=yes periodicity=0 rseed=-2436 colors=000XXX<10>oooqqqsss<2>xxxzzzyyy<25>CCCAAA888<2>222000000<56>00000\ 0000<2>000111332<23>ldTnfUpgV<3>xn_<27>A86875654443222000<52>000000000<2\ >000111333<15>VVV } No_admission { ; Albrecht Niekamp Apr, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=y function=exp/exp/sin passes=t center-mag=0.222172/-0.0164743/3.404629/1/-90/-1.23373533611470521e-014 params=0.3009095217749565/-0.00961206396679584/384.00001/256.3601/2048.0\ 0008/768.0256000000001/768.01536/64.01025/11193/0 float=y maxiter=3072 inside=maxiter outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=200000<25>iiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0cq0es<3\ >0kz<25>09C08A068<2>022000211<24>oiQqjRslS<3>zsX<25>CB7A96875<3>000400<2\ 3>o00q00s00<3>z00<30>200 } Mandala { ; Albrecht Niekamp Apr, 03 ; ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=postpar.par formulaname=multifractal ismand=y function=exp/exp/exp passes=t center-mag=0.128196/0.0103203/1.14051/1/-90/3.88578058618804789e-016 params=0.1044648579363384/-0.01168858912930693/384.00004/256.00768/2048.\ 00005/768.00008/384.01536/384.01025/18939/5 float=y maxiter=2048 inside=maxiter outside=tdis logmap=5 periodicity=0 rseed=-2436 colors=200000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<22>keOmgPoiQqj\ RslSunT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>00\ 0<23>eeegggiiijjjlllnnn<2>sss<25>BBB999777555444222 } Speedtest { ; Time 1min10sec p4 2giga 1600/1200 ; Albrecht Niekamp May, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifrac_239 ismand=n function=exp/exp/exp passes=t center-mag=0.117455/3.33067e-016/2.552858/1/90/3.88578058618804789e-016 params=-0.173894466994232/-0.3000579851680044/384.00001/256.1133/2048.00\ 008/768.0256000000001/768.01536/2560.01025/4/35.324051 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=0000200000101221532653863A84DA5EB5HB<2>7NG8PI8RJ9TKAVNAXM<3>DdTDf\ VEhWFjYFlYGn_Gp`Prd<3>zzz<2>_ulRsgHqaHo`GmZFkXFiX<5>BYOAWMAUL9SK<4>6IC5G\ B5DA<3>254243121000001023025047049<5>0BL0DN0DP<3>0JX0KZ0L`0Mb0Nd<3>0Sl0T\ n0Up4Yr8atCgvGkxKqz<3>4_s0Vq0Uo<6>0Ma0L_0KY<3>0FQ0DO0DM<3>08E06C06A04804\ 6024012000100<12>R0LT0NV0PX0P<3>d0Wf0Yh0Z<3>p0e<3>xOtzUxyOuwIquCns6iq0g<\ 2>k0bi0`g0_e0Z<3>Y0SW0RU0O<8>C0AA09807506304102010<9>0L20N20P30R30T40V40\ X3<3>0d40f50h5<3>0p6<3>WxZczeUyY<2>0s8<4>0i60g60e60c4<2>0Y40W30U4<5>0I20\ G20E20C20A1081061040 } Thousand_Julias { ; Time 22m35s p4_2giga_1600/1200 ; Albrecht Niekamp Apr, 03 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=y function=exp/exp/exp passes=t center-mag=-1.16373570930467300/+1.00897822713355100/131.0685/1/132.5000\ 00000000682/-1.31000071901254955e-012 params=-0.1738944669942329/-0.3000579851680044/384.00001/256.1113/3072.0\ 0016/768.0001600000001/768.01536/32.01025/34231/5 float=y maxiter=3072 inside=maxiter outside=tdis logmap=5 periodicity=0 rseed=-2436 colors=2000Ub<13>09B089067<2>021000210<22>keNmgOoiPqjQslRunS<2>zsW<25>CB\ 6A95874653442220000400<23>o00q00s00<3>z00<25>C00A00800<3>000<2>554776998\ BBACCB<16>eedggfiihjjillknnm<2>ssr<25>BBA998776<2>221000011<24>0bn0cp0er\ <3>0ky<10>0Wd } Thousand_mandels { ; Albrecht Niekamp Apr, 03 ; ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=y function=exp/exp/sin passes=t center-mag=-0.175549/-0.304679/1.39428/1/-90/-1.23373533611470521e-014 params=-0.173894466994232/-0.3000579851600044/384.00004/2500.2333/2048.0\ 0012/768.00008/2500.01536/32.01536/18435/5 float=y maxiter=2048 inside=maxiter outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=200211<24>oiQqjRslS<3>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z0\ 0<25>C00A00800<3>000<25>iiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0\ cq0es<2>0jy0kz0jy<30>000 } Thousand_mandels2 { ; a bit chaotic, but... ; Albrecht Niekamp Apr, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=y function=exp/exp/sin passes=t center-mag=-0.57996076807419270/-1.17390745582887600/27.8856/1/-152.5000\ 00000000142/1.65777114258247593e-013 params=-0.173894466994232/-0.3000579851600044/384.00004/2500.2333/2048.0\ 0012/768.00008/2500.01536/32.01536/18435/5 float=y maxiter=2048 inside=maxiter outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=20007A<20>0bo0cq0es<2>0jy0kz0jy<24>09C08A068<2>022000211<24>oiQqj\ RslS<3>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<2\ 5>iiijjjlll<3>sss<25>BBB999777<2>222000012<2>068 } Mandala2 { ; 5*many_mods ; Albrecht Niekamp May,03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifrac_239 ismand=y function=exp/exp/exp passes=t center-mag=4.44089e-016/-2.22045e-016/0.5706667 params=-0.1738944669942329/-0.3000579851680044/384.00001/256.0076/256038\ 4.00008/1536.0256/768.01536/5120.01024/38888/2 float=y maxiter=3072 inside=maxiter outside=tdis logmap=yes periodicity=0 rseed=-2436 colors=200U00<9>A00<4>000<25>iiijjjlll<3>sss<25>BBB999777<2>222000012<24\ >0bo0cq0es<3>0kz<25>09C08A068<2>022000211<24>oiQqjRslS<3>zsX<25>CB7A9687\ 5<3>000400<23>o00q00s00<3>z00<15>W00 } ---------------------------start-frm--------------------------------------- FRM:Multifractal { ; Albrecht Niekamp Apr, 03 ;only integers as first input, second input 5 digits to the right ;real(p2) factor1,border1 ;imag(p2) (-)maxiter1,input bas.frm1_2digits input bas.frm2_2digits ;real(p3) bailout,hyb.mandel: number of sides (Many_mods L.Allison) ;imag(p3) factor2,border2 ;real(p4) maxiter2,factor3 ;imag(p4) border3,maxiter3 ;real(p5) 1digit_shape only 5digits: shape,out1,out2,in1,in2 ; 1_mand 2_jul 3_hyb.mand 4_hyb.jul +5_reset (not shape) <0_no in/out1 ; optional basic frm2: out-nbr 1digit in-nbr 1digit 3_both +5_shape ;imag(p5) 1digit : 1_iter1reset 2_iter2reset 3_both +5_shape effect ; 2digits : many_mods multipl. shutoff +10_in/out1 +20_inout2 +30_both ; optional input2: frequency_2digits level_2digits amplitude_2digits ; d=real(p2) fac1=trunc(d) b1=(d-fac1)*100000 ; d=imag(p2) da=(d<0) if (da) d=-d endif mi1=trunc(d) d=round((d-mi1)*10000) p6=trunc(d/100)/10 d=d-1000*p6 if (da) p6=-p6 endif p7=d/10 ; d=real(p3) ba=trunc(d) mm=round((d-ba)*100000) ; d=imag(p3) fac2=trunc(d) b2=(d-fac2)*100000 ; d=real(p4) mi2=trunc(d) fac3=round((d-mi2)*100000) ; d=imag(p4) b3=trunc(d) mi3=round((d-b3)*100000) ; da=real(p5) t=(da<0) if (t) da=-da endif start=2-t dd=trunc(da) if (dd<5) start=0 endif vb=(dd==3)+(dd==4) da=round((da-dd)*100) d=trunc(dd/10000) vb=(d==3)+(d==4)+vb dd=dd-d*10000 d=trunc(dd/1000) or1=(d>5) d=d-5*or1 vv1=(d==3) vv2=(d==4) dd1=(d==2)+(d==4) dd=dd-d*1000 d=trunc(dd/100) or2=(d>5) d=d-5*or2 vv3=(d==3) vv4=(d==4) dd2=(d==2)+(d==4) dd=dd-d*100 d=trunc(dd/10) inr1=(d>5) d=d-5*inr1 v1=(d==3) v2=(d==4) d1=(d==2)+(d==4) dd=dd-d*10 d=trunc(dd) inr2=(d>5) d=d-5*inr2 v3=(d==3) v4=(d==4) d2=(d==2)+(d==4) d=trunc(da/10) ab=(d>=5) d=d-5*ab da=da-10*d bb1=(d==1) bb2=(d==2) d=da ab=(d>=5) d=d-5*ab ab1=(d==1) ab2=(d==2) ; d=imag(p5) dd=trunc(d) d=round((d-dd)*1000000) le=(d>10000) da=trunc(dd/10) so1=((da==1)+(da==3)==0) so2=((da==2)+(da==3)==0) dd=dd-10*da wo=(dd>=5) dd=dd-5*wo ir1=(dd==1)+(dd==3) ir2=(dd==2)+(dd==3) if (le) freq=round((trunc(d/10000))*10) ;frequency_lake effect by S.Gallet d=d-freq*1000 level=(trunc(d/100))/100 ;water level d=d-level*10000 ampl=d/100 ;amplitude of the wave angle=real(rotskew*pi/180) t=exp(-flip(angle)) h=1/real(magxmag) q=h/0.75*imag(magxmag) tanskew=tan(imag(rotskew*pi/180)) w=2*q*t v=2*h*(tanskew+flip(1))*t z3rd=center+(-q-h*tanskew-flip(h))*t z=pixel-z3rd s=imag(conj(w)*z)/imag(conj(w)*v) if (s<=level) da=level-s z=z+2*da*(1+ampl*sin(freq*da^0.2))*v endif z=z+z3rd endif if (ismand) if (vb) c=0.4*log(sqr(pixel^mm)) z=z*le else c=z*le+pixel*(le==0) z=0 endif else c=p1 z=z*le+pixel*(le==0) endif t=0 d3=(ismand==0) u=d3 : if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) ;frm: Albrecht Niekamp else z2=fn1(z)+c ;frm: Many_mods Linda Allison sqz2=cos(z2) z=c*(1-sqz2)/(1+sqz2) endif else if (ab) z=z*z+c+c*c-p7 ;frm: Pusk s Istv n else z2=z*z ;frm: Pusk s Istv n modified z=z2*z2+(p6+u)*z2+c-p1*(d3==0) endif bo=|z| If (wo) t=t+1 if ((t<mi1)+(bo>b1)) u=2*(fn1(t/fac1)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) else c=z*le+pixel*(le==0) endif else z=z*le+pixel*(le==0) c=p1*u endif wo=0 if (ir1) t=0 endif endif elseif (start) t=t+1 if (start==2) if (bo>b2) u=2*(fn2(t/fac2)) rs=or1 ab=bb1 if (dd1) if (rs) z=pixel endif c=p1*u vb=vv2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=1 endif elseif (t>mi2) u=2*(fn2(t/fac2)) rs=inr1 ab=ab1 if (d1) if (rs) z=pixel endif c=p1*u vb=v2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=1 if (ir2) t=0 endif endif elseif (start==1) if (bo>b3) u=2*(fn3(t/fac3)) ab=bb2 rs=or2 if (dd2) if (rs) z=pixel endif c=p1*u vb=vv4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=0 endif elseif (t>mi3) u=2*(fn3(t/fac3)) ab=ab2 rs=inr2 if (d2) if (rs) z=pixel endif c=p1*u vb=v4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=0 endif endif endif bo<=ba }

2 1

FOTD 03-05-03 (The May Parent [NA])
by Jim M. 03 May '03

03 May '03

FOTD -- May 03, 2003 (Rating NA) Fractal visionaries and enthusiasts: The Mandelbrot set is sometimes called the most complex object in the world of mathematics. And it truly is a complex object. But there are other fractal objects created by other fractal formulae, which are more complex than even the M-set. Of course, since the M-set is infinitely complex, these other objects would appear to demand a higher order of infinity. Today's image could be one of these 'higher' fractals. It is titled "The May Parent". I give it this name because, for the rest of the month of May, I shall use it as the source of my FOTD images. This limitation in no way implies a shortage of images or a reduction in their quality, though on occasion I will go beyond my normal style of image with a midget at the center. The formula mixes one negative part of Z^(-11) with ten negative parts of Z^(-1.1), then adds 1/C before being calculated with a bailout radius of 625. In some places, the oversized resulting fractal is filled with holes like a swiss cheese. In other places, it appears to hold the usual Mandel-stuff. In yet other places, it is filled with rings, while a prominent fan-shaped element fills the center. The variety is endless, and the fractal has midgets hiding almost everywhere. I gave today's image no rating, since it is not really a finished product, but rather the source of the next 28 FOTD images. The render time of a little over one-minute should give little difficulty, but for extra convenience, the completed GIF image is posted to the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The rain that was expected here at Fractal Central on Friday never arrived. Instead of the rain, we had a mostly sunny day with a temperature of 81F 27C. The fractal cats thoroughly enjoyed the unexpectedly pleasant day, and spent several hours romping in the yard. Today is starting cloudy and quite a bit cooler -- once again threatening rain. Will good fortune prevail, giving the fractal duo another good day? Only time will tell. My day will turn good when the work is finished, so until next time, take care, and see you in 24 hours with the next image. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_May_Parent { ; time=0:01:11.96--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=3.56788/-0.692098/0.1341384/1/135/-3.77\ 822773067748585e-014 params=-10/-1.1/-1/-11/0/525/\ 0/0 float=y maxiter=400 inside=0 logmap=yes periodicity=10 colors=000CHgEIfGJgIJgKKcLLhNMePMiR\ NhTOjVPkXPkYQl_RlaSmcSmeTmgUmiVmjVmkTmlRmmPmmOmnQl\ oSjpUipWgqYfr_dsacscate`ugZwiYzkUwmRroOrqLmsImuFhw\ CFw9Au69t69t69s69s68r68r68q68q67p67p67o67o66n66n66\ m66m65l65l65k65k64j64j64i64i64i65g75f85e96cA6bB6aC\ 7`D7ZE7YF8XG8WH8UI9UJ9UK9ULAUMAUNAUOBUPBUQBURCUSCU\ TCUUDUVDUWDUXEUYEUZEUZCUYAUX9UY9UY9UY9UY8UZ8UZ8UZ8\ UZ7U_7U_7U_7U_7T_FScMSfURi`RleYeidZmkTqrMuyGowMjvS\ etY`scVqiQpoLnuGmzHmxImwJmvJmuKmtLmrMmqMmpNmoOmnOm\ mVm8Wx9Xw9YwAYwAZwB_wB`wC`wCawDbwDcwDcwEdwEewFfwFf\ wGgwGhwHiwHiwHgwJewKcwMawN_wOYwQWwRUwSSwUQwVOwXNwY\ LwZJw`HwaFwbDwdBwe9wg7wh5wi3wk1wl0wm6whBwcGwZLwURw\ PWwK`wFewAjw5mw6ow7qw8sw8uw9wwAywAvwFtwJqwOowSmwXj\ w`hweewicwnawrIw8NwBRwEVwGZwJcwLgwOkwQowTswVtwUuwU\ vwUvwUrwWnwYkw_gw`dwb`wdYwfUwgQwiNwkJwmGwnCwp9wr5w\ t2wu8whEwWKwJPw7Ow9OwAOwBOwCOwDOwFOwGNwH } frm:MandelbrotMix2 {; 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 20.0 PAR-FORMULA FILE==================================

1 0

FOTD 01-05-03 (Fractal Epicycles [8])
by Jim M. 03 May '03

03 May '03

FOTD -- May 01, 2003 (Rating 8) Fractal visionaries and enthusiasts: This is the day, the day fractal fans have been waiting for with bated, but not abated, breath -- the day the FOTD resumes its one-a-day schedule. And we start with a fractal that earns a lofty rating of 8. I named the image "Fractal Epicycles" for no good reason. I simply liked the sound of the title. An epicycle is not an epihertz. It is not an electronic wave at all. It is a revolution around a moving point. Before men under- stood the true nature of the solar system, the retrograde loops the planets trace in the sky when they are near opposition were assumed to be a result of the planets circling a point that in turn circled the earth. As we discovered later, this is not so, and epicycles fell from favor, eventually going the way of the luminiferous aether. Today's image is a zoom into the curiously symmetrical image posted by Lee Skinner about 5 days ago. I lowered the bailout radius to 30, but left the other parameters unchanged. In fractals generated from formulae that contain negative powers of Z, the value given the bailout makes a huge difference in the final appearance of the image. Increasing the bailout causes the elements to shrivel and break into separate pieces which eventually shrink to nothing, leaving an image that consists entirely of 'inside stuff'. But even when the elements have 'evaporated' the ghost of the original image can still be raised by setting the inside fill to something like bof61. This ghost is sometimes the best version of the scene, though in today's image it is too chaotic and far too slow. Decreasing the bailout has the opposite effect. The elements increase in size until one expands to fill the entire screen, resulting in an image of a single featureless color. Using an outside coloring method other than the standard equal-iteration- bands occasionally results in an interesting variation, though this is the exception rather than the rule. Today's image renders in a relatively modest 7-1/2 minutes on my aging and overworked P200 machine, the one with the noisy exhaust fan that needs a pep talk to make it start turning. The finished GIF image is available on the two FOTD web sites, which have been slow lately, but will become more active now that the daily FOTD is back. The URL of Paul's site is: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's site is found at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather here at Fractal Central on Wednesday was fractal in nature, as it always is. The warm sun and temperature of 75F 24C brought out the best in the fractal duo, who passed most of the afternoon in the yard and on the porch, watching for intruding cats. At one time, the cat that lives three doors down the hill thought of walking through the duo's yard. His thoughts were quickly laid to rest when Tippy leaped to the attack position. Thomas observed the goings on with interest, presumably ready to run to help, (or more likely, for help), if things got too far out of control. Today is starting far less pleasantly, with lots of clouds, and rain threatening. On such days, the duo usually stays indoors, while I try to finish the work that needs to be done. And right now, I have enough to be done to keep me busy most of the day, so until next time, which will arrive in 24 hours, take care, and if an infinity of other me's exist somewhere out there, what practical difference does it make? After all, I will never meet them (or me). Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Epicycles { ; time=0:07:39.13--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.60678114611431010/+0.052890451621420\ 53/1894179/1/137.5/1.24117062995365846e-007 params=-3.7/-1/-1.6/-2/-0.4/-70 float=y maxiter=4500 inside=0 logmap=120 periodicity=10 colors=000PKsfRshTsKKrKKpIAoKKsFKnFGmDHkCIjAJi9Kh8\ Lg6Mf5Ne3Od2Pc1Pb7OaCN`IM_NLZTKYYJXcIWhHVnGUsFTxES\ yJPyOMyTKyYHzbEzgCKz9zzzzz4mpztUAqhDncGk_JhWMeSPbN\ S000000000000000000000000000000000000000000000000d\ A`zmUlC`lGZlKXzzVmTSmXQnaOneMniKkdMh`NeWObSQ_NRXJS\ YGbZEldPmjZnohnpijqjgqkdrk`slYsmVtnRunOuoLvpHwqEwq\ BrpDnoFjnHfmJamKYlMUkOQjQLjRHiTDhV9gX5gYCfbIfgOelU\ eqXfl_fhbgceg_hhWkhRniNqiItjEujAwiByhCzgDzfEzeFzdG\ wcHrcImbJhaKf`Le_McZNbYO`XP_XQ_VO_TN_RM_PK_NJ_LIXN\ HVOGSPFQRENSDLUDIZCGcBDhABm99m9CrBEcDGSFIPPKNUMLZO\ IcQGhSEmUBrW9wY7z_4za2zc0z`2ZY4XV5VS7TP9RMAPJCNGEL\ DFJAHH7IFBJGFKGJLGNMHRMHVNHZOHbPIfQIjSInUJrWJvYJz_\ JzaSzc_zegzgozimzkkzmizogzqfzsdzubzw`zx_zy`zzZzzXz\ zVzzTzzRzzPzzNzzLzzJzzHzzFzzDzzBzzGzzKzzPzzTzzYzza\ zzYzzVzzRzzOzzLzzTzzVzzXzz_zzazzczzfzzhzzjzzlzznzz\ ozzqzzrzzszzszzszzszzszzs } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 02-05-03 (A Networking Fractal [6])
by Jim M. 02 May '03

02 May '03

FOTD -- May 02, 2003 (Rating 6) Fractal visionaries and enthusiasts: Today's image is a picture of just another midget, though a rather unusual one. The filaments surrounding the small central midget are some of the most intricately interconnected I have yet seen. They form a network almost as convoluted as the internet, and have inspired the name "A Networking Midget". The rather dull coloring held the rating to a 6. The parent fractal is an oversized thing created by combining negative portions of Z^(-0.9) and Z^(-9.5), then adding 1/C. Basically, it consists of a few irregular holes surrounded by an immense network of filaments. The filaments are filled with nodes, almost like a fractal internet. Today's scene is located on a filament deep in one of these star-like nodes. The ability to find fractals seems to work like skill at sports or music. One must constantly practice to keep in shape. During the past 2 months or so, while the FOTD has been on a once-per-week basis, my ability to find fractals seems to have suffered. Oh, I still know where to look, but the intuition that a good scene lies deep in a certain area of the parent seems to have vanished. I am sure that, as I continue to search for fractals every day, the intuition part of fractaling will soon return, but until it does, it is curious to be searching blindly, with my 'sixth sense' shut down. And I also noticed a letter from a disappointed FOTD fan yesterday. This fan saw the opening of the discussion, which read something like, "this is the moment fractal fans have been waiting for", and assumed I was announcing the release of the FOTD CD. Actually, the CD is basically finished. All the images and all the discussions are found and gathered. The only thing yet to be done is to change the names of the images so that the names correspond to the dates on which they appeared. If I could be satisfied with cryptic image names that can be matched with their discussions only with some effort, then the disk would be totally finished. I am working on the task of determining the dates and changing the names whenever I find the time. That truly glorious moment of CD completion is indeed within sight. Keep tuned. The big moment will soon arrive. Today's image requires 4 minutes to render from the attached parameter file. Time can be saved by downloading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The threatening rain never arrived on Thursday, and as a result, the Fractal Central watchcats had another splendid day on the porch and in the yard. The warm sun and temperature of 79F 26C was just what they needed to put them in a good mood. They got a bit skittish early in the afternoon when someone started hammering in the yard two doors up the hill, but soon realized there was no danger, and resumed their naps. Today is once again threatening rain. Hopefully, it will hold off until the duo finish their outdoor recreation. As for me, I've got a bit of work to accomplish, so until tomorrow, take care, and keep a stiff upper fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_NetworkingMidget { ; time=0:04:09.75--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-7.915378033606101/-31.14709243995971/7\ 911.543/1/40/1.15404776568350798e-008 params=-2.2/-0.9/-6.6/-9.5/0/0 float=y maxiter=750 inside=0 logmap=75 periodicity=10 colors=000KCJLCJLCKLBKMBKMBKMBKMBLMBLLALLALLAMLAMK\ AMLAMK9MK9NL9NL9NL9NL9NMAPNBROBTPCVQDXRDZXKcYPhZUm\ _Zr`cwacxbczcazd_zeYzeWzfUxgQwgMuhIshGqiFoiEmjDkjC\ ikCgkBflAel9dm8cm8an7`n6_o5Zo5Ym8YlAYkDXiFXhIXgKXe\ NWdPWcSWaUW`XWZZVYaVXcVVfVUhUTkURmUQpUPrUQpYQn`Rmc\ RkfSjiShlSgoWfiZfdbf_efVifQleLpeGseBwe6ze1P9AQCBQE\ BQGBQICQKCRNCRPCRRDRTDRVDSYES_ESaEScESeFThFTjFTlGT\ nGTpGTrG_jqWlpSmoPnnLomIplEqkBrkAoiAmhAkf9he9fc9db\ 9a`8__8YY8VX8TV7RU7OS7MR6KP6HO6FM6DL5AJ58I56G54F88\ GABHCEIEHJGKKJNLLQMNTNPWORZPUaQWdRYgS_jTamUZhXWcZU\ ZaRVcOQeMLhJGjHClGFiGIfGKcGNaGPZGSWGUUGXRGZOGaMGcJ\ GfGGhELgDPgCTgBYfBafAef9if9jeAjdBjcBkbCkaDk`Dk_ElZ\ ElYFlXGlWGmWHmVHmUImTJnSJnTKnUKnWLoYMo_MoaNocNmeOk\ gOiiOhkOfmPdoPbqPasP_uPYwQXyQVzQTzQRzRQzROzRMzRLzR\ MzSNzSNzSOzTOzTPzTPzUQzUQzURzVRzVSzVTzWTzWUzWUzXVz\ XVzXWzYWzYXzYXzZYzZYzZKzJ } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Re: Fractint Digest, Vol 2, Issue 3
by JackOTradez 28 Apr '03

28 Apr '03

Re: Dinosaurs, Black Holes and Server Errors. 1) I also have not received the Fractint Email for several weeks; I thought I had been kicked out of the group, although I would have no reason why. I guess I missed the Mandelmania, Lee H. Skinner Images people are talking about now that look like dinosaurs or velociraptors. Can someone point me to them so I can check out? 2) I have investigated the "Black Hole" formula recently posted. I have seen many such patterns before - they are common if you zoom deep into the extreme left end of the Mandelbrot, the "needle point". (demonstrated by my Universe-2 viddie). There are many regions where you can zoom into intersecting lines forever and never encounter a mini-brot. A clue in the posted formula image is that the two flanking mini-brots are pointing towards each other. If there was a mini-brot in the center, it would be pointing in one direction, thus disrupting the symmetry. That's not good. Stated another way, since nothing CAN be at the center, nothing IS. It is an example of a recurrent phenomenon in Fractals I call "infinite regression". (The spiral regressions make for nice zoom viddies). Also, and I am not totally sure of this, but in the examples where there is a symmetrical LAKE in the center, if a sufficiently high iteration maximum is used, the lake will resolve (disappear). Finally, I zoomed deep into it and at about E+9 it all came undone. THAT I have never encountered before! I may be a Jack O(f many) TradeZ but I confess I have no explanation for this one ... BTW - I would rate the "JellyBeans" FOTD higher than the given 6 - it is one of the better images I have seen in a while. (How does that Muth dude find these things? ...) Stay Amazed! JoTz

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Re: [Fractint] FOTD 26-04-03 (Jelly-Bean Fantasy [6])
by Jim M. 27 Apr '03

27 Apr '03

At 12:45 PM 4/27/03 -0600, Lee Skinner wrote: >A strange and rare new kind of fractal symmetry object has been found! Lee: You are correct. It is a new symmetry. What you have found is a collision of two quadratic midgets. In this case, only the stems are in contact. They bump together head-on and shoot out sideways. Try gradually reducing the value of the real(p1) parameter to -3.69. The midgets will move in from the edges of the frame and start to merge, while billowing outwards sideways. As you continue reducing the value, it will make clearer what is happening here. BTW, there are some really interesting smaller midgets lurking invisibly around the edges of the frame. Jim M. >(The following refers to a zoom into the parent image of this FOTD.) > >The following par illustrates a new kind of symmetry object that I've >never seen before. Like a spiral, it goes on forever. If you zoom >into the symmetry point at the center, you will NEVER reach a mandelbrot >midget (or a dry lake). > >(But Fractint will display some weird artifacts if you zoom deeper than >5.E+8.) > >Note the two midgets on the x-axis near the left and right edges, and >how they point towards each other. This I have seen several times >before, but there has always been a symmetrical lake at the center. >This time, there is no lake - just this point singularity! In all the >MandelbrotMix images I've seen before, I've never encountered anything >like this! > >BlackHole { ; A new type of symmetry object > ; t= 0:11:20.47 on a P4 2Gh at > ; 1600x1200 Image Copyright 2003 > ; by Lee H. Skinner ver=2002 > ; Version 2002 Patchlevel 5 > reset=2002 type=formula formulafile=fractint.frm > formulaname=mandelbrotmix4 function=recip passes=1 > center-mag=-0.64674455879419490/+0.00022406378688037/\ > 140.8758 params=-3.7/-1/-1.6/-2/-0.4/240 float=y > maxiter=8500 inside=0 logmap=35 symmetry=none > periodicity=10 > colors=000ZE9<10>PJDOKDNKEMLELLEKMF<26>Q_FR_FR`FR`FRa\ > F<16>ZdRZeS_eT_eU`eU`eV_eV<12>cjqckrcktdlvdlxemz<5>os\ > zptzruz<3>yyz<4>suurutqtrosqnrpmro<3>gojfniemhcluckfn\ > mtakhchWahlZZZ<2>idamgcnigoklpmpqpu<3>mkoljnjhl<3>ddh\ > ccgaaf<2>YZcWXaWW_<3>SPSSOQRMO<3>NGGLEEKCC<16>gPIiQJj\ > RJ<3>qVMsWNuXOwZP<7>xnVxpWyrX<3>zz`<14>zNFzKDzHC<3>y7\ > 5y54y32z00<29>_E9 > } > >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint >

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FOTD 26-04-03 (Jelly-Bean Fantasy [6])
by Jim M. 27 Apr '03

27 Apr '03

FOTD -- April 26, 2003 (Rating 6) Fractal visionaries and enthusiasts: During the past day or so I have been pondering the parallel universes that, as weird as it may seem, must now be assumed to exist. As a result of the scientific investigations of the past 50 years or so, we have come to realize that an infinity of infinities of these other universes must exist. Not only does every possible universe exist, an infinity of every possible universe exists. Right now, if this phrase has any meaning, there are an infinity of other versions of myself typing these same words. There are an infinity of other myselves that have made the same single mis-spelling in one word of the discussion. And there are an infinity of myselves that have found exactly the same fractal for today's FOTD. So I guess fractals are not quite as unique as I once supposed. Today's fractal, by the way, reminds me of a bowl of jelly- beans. I named it "Jelly-Bean Fantasy" accordingly. It is part of the parent fractal that results when various portions of 1/Z and Z^(-2) are combined, and 1/C is added before the whole thing is iterated with an escape radius of 340. Using whole-number powers of Z prevents distracting discontinui- ties from forming, though, as is the case with most fractals with negative exponents, different elements tend to overlap. The rating of 6 is reasonably honest. I could have done better if I had tried harder. But a 6 is still above average, so this rating will remain. The 23 minutes spent waiting for the image to render from the parameter file could most likely be spent in more productive endeavors. To save time, I recommend picking up the finished image from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather has been changeable during the past week here at Fractal Central. The cats' moods have been changeable as well. As a single example, Friday was warm and sunny; today is starting rainy and chilly. This is the way it goes in this part of the world at this time of year. The dynamic duo appears sullen, as they always are when it is raining, but they will survive the inconvenience -- at least they always have in the past. As for myself, I'm using the bad weather to catch up on some tasks that have needed to be done around the place for some time. The daily FOTD will resume on schedule this Thursday, May 1. The FOTD CD will be ready as soon as I get all the image file-names changed. Until Next time, which will arrive in five glorious days, take care, and what would you think if you actually met an alternate version of yourself? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Jelly-Bean_Fantasy { ; time=0:23:06.60--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.94249648630458650/-0.211984547670434\ 70/3398605/1/115.000001038892464/-1.11471021949083\ 315e-006 params=-3.7/-1/-1.6/-2/-0.4/240 float=y maxiter=8500 inside=0 logmap=335 periodicity=10 colors=000VJ0H20G00G00G00aO0E00C00i00E00G00G00G02H\ 35H57J99JCCJGELJGLMJMOLMRMMVQOZROaVOdXQfZQiaRmcRpd\ RshTwiTykVznVzpVzrXzuXzwXzyZzwZzw_zw_zwazwazwazucz\ uczudzudzudyufysfwshushsshrsipsiprknrkmrkkrmirmhrn\ frnfppdppcppapr_prZpsZnsXnsVnuTnuRnwQnwQmwOmyMmyLm\ zJmzHmzHmsGpmGrfGs_GuTGwMGzGGz9Gz2Gz0Gz2Jy9MrEQiLT\ cQXVX_OacGhf9mi0sm0zm0yn0wn0wn0un0un0sp3sp9rpCppGp\ pJnrMnrQmrVmrZkraksdishhskhspfssfuwduzduzcuzcuzarz\ apzanz_mz_kz_hy_fwZduZcsZarX_pXXmXVkXTiVRhVQfVOdTL\ cTJaTH_TGZREXRCVR9RQ7QQ5OQ3MQ2LO0JO0HO0GM0EM0CM0AH\ 07M09R09V0A_0Ac0Ch0Cm2Ep5Eu7GyAGzCHzHCzEHzCMzARz9X\ z7az5fz3kz2pz0uz5rz9nzCmzHizLfzOdzTazVZzXXzZTz_Qza\ OzcQzdRzfTzhVziXziZzk_zkazmczmdznfznhzpizpkzrmzrnz\ spzsrzuszuuzwwzwyzyzzyzzzzzzzzzszzhzzZzzOzzJzzGzzC\ zz7zz3zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0yz0yz0yz0wz\ 0wz0wz0uz0uz0uz0sz0sz0sz0 } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Mandelmania, Lee H. Skinner Images
by Albrecht.Niekamp＠t-online.de 26 Apr '03

26 Apr '03

Hi Lee, a big thank you for those images. They are fantastic and they are a new experience to me as I never have seen images made by my formulas except my own. I definetely hope there will be more. For me the best one is the last one. "Velociraptor", a kind of dinosaurer I think, is really is a suitable name for those structures. Presently I`m working on a big thing and I can understand Jim´s problems with his cd, as everytime I think its done, I come onto new things that make it better or more complete. Hopefully it will be ready for the next digest. Fractal greetings, Al.

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FOTD 19-04-03 (Feelers [7])
by Jim M. 19 Apr '03

19 Apr '03

FOTD -- April 19, 2003 (Rating 7) Fractal visionaries and enthusiasts: The Easter season here and a dinner is planned for Sunday. As a result, I find myself with lots of work to accomplish, both fractal and otherwise. With so many other things to do, I have made little progress on the much promised but little seen FOTD CD since my last report one week ago. But fear not, the critter will soon be on the market, later than Windows95, but better late than never. In recent months I have uncovered a whole new infinite world to be explored -- the world of evaporated fractals made visible by the < bof61 > inside fill. And with a whole new world waiting to be discovered, the best thing to do is to start exploring. Today's evaporated scene is part of the evaporated left-overs of the fractal that results when negative portions of Z^(-1.6) and Z^(-7.6) are combined and (1/C) is added. The exact location is in the East Valley area of a small satellite Mandeloid near the shoreline of the main bay, the shape of which is indescribable. I named the image "Feelers" because of the effect of tendrils being sent down toward the remnants of a midget at the center, to feel out what is there. At least that's what I thought of as I studied the rather lively scene. The rating of an above-average 7 is well justified. The image is the best of the lot for April, though with only 2 images to compete with, it is not much of an honor to be number one. The 14-minute render time (on my aging and soon to be replaced fractal machine) can be avoided by downloading the pre-rendered GIF file from one of the FOTD web sites. Paul's site is at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's is at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather varied widely during the week, as did the moods of the fractal cats. The first half featured sunny days with temperatures around 86F 30C, but the week ended with low clouds, rain and drizzle, and temperatures around 36F 2C. The dynamic ones had an uneventful week of exploring in the yard or sulking on their window shelves, depending on the weather. In the garden, the catnip mint is just appearing. The very aromatic new growth always attracts nearly every cat in the neighborhood, so I expect the fractal ones will have a far more exciting time in the week to come. The next, and final, FOTD of April will appear in 7 days. After that, the daily FOTD will resume on May 1. Check back in one week to see the adventures of the fractal duo. Until next FOTD, take care, and be fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Feelers { ; time=0:14:06.89--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.40044529824960200/+0.049515890248186\ 53/37991.03/1/35/-1.06074004441181202e-009 params=-7/-1.6/-1/-7.6/0/1e+100 float=y maxiter=1200 inside=bof61 outside=0 periodicity=10 colors=000zHtzJszJrzKozLnzMmzOjzOizPhzQezRdzRczS`z\ U_zVZzWWzWVzYUzZRz_Qz_Pz`MzbLzcKzdHzdGzeFzgCzhBzhA\ v_KrRUnKcjBmg2wc0zd0zd0zd2ze5ze7zeAzeCzgEzgGzgJzgL\ yhOyhQxhSxiUwiWwiZvi`vjctjetjhsjiskdkk_ekVZkQSkLMk\ GFkB8k62Z74i85hA6hB7gB8eCAeEBdFCcGEcGFbHF`JG`KH_KJ\ ZLKZMLYOMWPOVPPVQQURRSSRSSSRUUQVVQWWPYYOYZOZ_M_`L`\ bL`bH_cEZdAYd7We4Vg0Ug0Sh0Rh0Sg0Ue0Vd0Wc0Wb0Y`1Z_2\ _Z4_Y5`W5bW6cV7dU8dSAeRBgQBhPChOEiMFjLGkKGkKFiJFhH\ FgHFeGEdFEcFEbEE`EEH_CZBCWBCVAZ74BS8BR7BQ7BP6BO5AM\ 5AL4AK2AH28G18F18E08C08B07A07807707607508708A08C28\ E58G7AJAALCAMFAPHARKAUMBVPBYRB_UBbWBcZBe`ChcCjeCkh\ CnjCqmBqrCroEsmFtjGviHwgJxdKycLz`MzZOzYPzVQzSRzRQz\ QPzPUzLYzJ`zGdzEhzBky8ow5sv2wt0zs0zr0zq0zk0zh0zd0z\ `2zY5zS7yPAxLCwHFvEHqCKmCMiCPeCR`BSYBVUBYQB_MBbHAc\ EAeAAh6Aj2Ak5Cj7FiAGhCJgEKeGMeJOdLQcMRbPU`RV`UY_VZ\ ZY`Y_cWbdWdgVehUzEzzFxzGw } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] Bug in float-only 20.02.5
by Jim M. 18 Apr '03

18 Apr '03

At 06:42 AM 4/18/03 -0500, Johnathan O. wrote: No, I had not turned on the evolver. In version 20.02.4 it is not necessary to have the evolver turned on to get the < f6 > screen to come up, and I was using the habitual key-strokes. With the evolver turned on, the version 20.02.5 evolver seems to be working all right. I'll continue using the new version, and report on any other suspected bugs I might find. >On Friday 18 April 2003 06:33 am, Jim M. wrote: > >> I have found a rather serious bug in the evolver feature of the >> float-only version 20.02.5 of Fractint. When the evolver >> feature is on the screen, striking < f6 > should bring up a >> screen that lets the user choose which parameters to change. >> But in the float-only version 20.02.5, striking < f6 > merely >> returns the user to the original image. This feature was >> working correctly in float-only version 20.02.4. > >Have you turned the evolver mode on first? > >I can add some additional code that will turn on the evolver if one of the >function keys is pressed. This assumes that if you have pressed a function >key you do indeed want to use the evolver. > >Jonathan > > >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint >

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Bug in float-only 20.02.5
by Jim M. 18 Apr '03

18 Apr '03

I have found a rather serious bug in the evolver feature of the float-only version 20.02.5 of Fractint. When the evolver feature is on the screen, striking < f6 > should bring up a screen that lets the user choose which parameters to change. But in the float-only version 20.02.5, striking < f6 > merely returns the user to the original image. This feature was working correctly in float-only version 20.02.4. Jim M.

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Reproducing "Fractal Cosmos" images
by Jim White 17 Apr '03

17 Apr '03

Hello to everyone, this is my first post. Has anyone ever tried reproducing the images in Jeff Berkowitz's "Fractal Cosmos" book? Most of them are supposed to be elementary Mandel/Julia-style fractals and he kindly lists the various formulae and parameters for each image shown. Palette differences aside, reproducing similar images in Fractint should be elementary - he provides the formula, the "corners", "maxiter" and "bailout" values (and "c" for the Julia types). But the first 2 I have tried (p3-22 top-left, p2-23 bottom-left) yield images whose apparent structure in no way resembles what he shows in the book. I was trying to reproduce them for technical reasons - I was trying to verify the accuracy of my own Windows-based fractal engine as I had just added the "complex power" opcode to it. Fractint yielded precisely the same image as my own program, so the verification issue is resolved, but I hate loose ends! Cheers Dr Memory __________________________________________________ Yahoo! Plus For a better Internet experience http://www.yahoo.co.uk/btoffer

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FOTD 12-04-03 (merry Chaos [6])
by Jim M. 12 Apr '03

12 Apr '03

FOTD -- April 12, 2003 (Rating 6) Fractal visionaries and enthusiasts: Today's image is another of my evaporated fractal scenes. When I raised the escape radius of the original image to one-googol, the outside material evaporated, leaving only trapped 'inside' points on the screen. But those trapped points wander far afield in their confinement, doing interesting things that the < bof61 > inside fill has revealed. The parent fractal was created by combining negative portions of Z^(-1.8) and Z^(-8), and adding 1/C instead of C. Using 1/C in an iteration generally turns the fractal inside-out, but since fractals with negative exponents of Z are already inside-out, the 1/C merely reverses the natural inside-out and turns the image rightside-out. I named today's image "Merry Chaos". It's kind of a jolly- sounding name, and with its wealth of detail, the image is rather jolly looking. I rated the image at a 6, which is slightly above normal. A residual muddiness prevents me from rating it higher. With a render time of 9 minutes, the parameter file is a bit on the slow side. The better (and faster) way of viewing the scene is to download the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The FOTD-CD is progressing slowly. It is rapidly becoming apparent that I will never bring it to a satisfactory state of absolute perfection, and will have to release it with flaws still remaining. The difficulty is that my artistic nature has kicked in, and for everything I fix, I find something else that needs fixing. And with over 2000 images and discussions, even the slightest change means days or weeks of work. I wasted nearly a week trying to reformat every discussion to the same format before convincing myself that it makes no difference. The only thing I really want to do is rename the GIF images from their present cryptic names to the dates on which they appeared. When this is done, which is no small task, I will declare the job finished and ready for distribution. Thomas and Tippy, the fractal-cat duo, are not concerned with compact disks. They are concerned that we have just ended a solid week of rain, and they have not been outdoors in 4 or 5 days. But this morning the clouds are thinning, and I would not be surprised to see the sun appear in an hour or two. If this happens, the fractal cats will be overjoyed. For myself, it will mean a day of lawn trimming. That's it for this week. The daily FOTD will reappear on May 1. Until next Saturday, take care, and never abandon the search for fractal reality, whatever that is. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Merry_Chaos { ; time=0:09:21.17--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.61822723988747150/-1.726020792269529\ 00/248508.6/1/17.5000000004007603/-6.3497827135217\ 122e-010 params=-1/-1.8/-0.2/-8/0/1e+100 float=y maxiter=1200 inside=bof61 periodicity=10 colors=00002R02P24P64PA6PG6NJ8NN8NTALXAL`CLdCL`JGZ\ RAXZ4Ve0Rk0Ps0Nz0Lz0Jz0Nz0RuGVk`ZbubTzeRziPzkPzoNz\ qNzuLzvLxuHvuEuuCuu8su6qu2qs0os0os0ms0ks0ks0is0io0\ gm0ek0dg6beC`dHZbNXZTVXZTVdRTgRReNPdJPbGN`CLZ8LZ4J\ X0HV0HT0GR0EP0EP0GV0H`0He0Jk6LqCLvHGuRCs`6si2qq0oz\ 0oz0mz0mz0kz0iz0gz0gz0ez0dz0dz0bz0`z0`z0Zz0Xz0Xz0V\ z0Tx0Tv0Nk0Jb0GR0AH0660200000400800E60HC0NJ6RPCXVH\ ``NdgTimZmsdsxivzozzuzzzzzuzzoxzisqdmeZiVTdLNZAHT0\ CP08G048C00N00Z00q00e00k00b00f00`00a00`00X00V00V20\ dH0mX0vk0zz0zv0zs0zo4zk8xgEudHq`NmXRiTVeP`bLdZHiVE\ mRAsN6vJ2zHLmZd`mYX0_T0aP0cN0eJ0gG0iE0kA2m64o44q06\ s08u08w0Ay0Cz0CiKGTUHCcJ0hL0cN0ZJ0UHcUGcYEc0Cc0Ac2\ 8c44Z82eC0kG0qJ0xN0zR0zT0VGJ02i0Ab0GX0LP0RJ0ZC2d64\ i06o02k00g00e00b00`20X40V60R60P80LA0JC0GE0EG0AH08H\ 0NX0`i0ox0zz0zz4zzHkzVZzgJuu6mz0ez0Zz0dz2izEozPuz`\ zzZvzZuzXszXo00V00T00R00R } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Mandelmania
by Albrecht.Niekamp＠t-online.de 06 Apr '03

06 Apr '03

Hi all, Fractals are fun... and here is something to play with. ; The formula combines 3 fractals, mandel or julia types, basic or exponential, totally 16 combinations, not all useful maybe. Each one can be defined by maxiter or border values. Now they work! The point was to allow at least one iteration in order to avoid wrong bailout. Set the border values higher then bailout if you dont want to use them and vv. "Soft transitions" means that "z" is not reset at the crossover. Sometimes a completely different inside is calculated if checked. Of course any other basic formulas can be used if they are ismand compatible. As this probably is not the final version, please report any bugs or anything that could be done better. Thank you! Have fun! -----------------------------start-pars------------------------------- Mandelmania { ; a severe case of.. ; Albrecht Niekamp March,03 ; Version 2002 Patchlevel 4 reset=2002 type=formula formulafile=multi231.frm formulaname=multifrac_231 ismand=y function=exp/exp passes=t center-mag=-0.606061/4.44089e-016/0.9363296 params=-0.5/0.375/1536/2048/513/1025/1/1/2560/2560 float=y maxiter=2048 inside=atan outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=200JJJ<14>iiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0cq0es<3\ >0kz<25>09C08A068<2>022000211<24>oiQqjRslS<3>zsX<25>CB7A96875<3>000400<2\ 3>o00q00s00<3>z00<25>C00A00800<3>000<9>III } Birds_over_Julia { ; Outside exp. julia ; Albrecht Niekamp, March,03 ; Version 2002 Patchlevel 4 ; Version 2002 Patchlevel 4 reset=2002 type=formula formulafile=multi231.frm formulaname=multifrac_231 ismand=n function=exp/exp passes=t center-mag=0/0/0.6666667 params=-0.00180974761192663/-0.2758911404766991/1536/2048/513/1025/-2/3/\ 2560/2560 float=y maxiter=2048 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=200ddd<3>jjjlllnnn<2>sss<25>BBB999777<2>222000012<24>0bo0cq0es<3>\ 0kz<25>09C08A068<2>022000211<24>oiQqjRslS<3>zsX<25>CB7A96875<3>000400<23\ >o00q00s00<3>z00<25>C00A00800<3>000<21>bbb } Mandelmania_2 { ; Julia inside inside ; Albrecht Niekamp, March,03 reset=2002 type=formula formulafile=multi231.frm formulaname=multifrac_231 ismand=y function=exp/sin passes=t center-mag=-0.606061/4.44089e-016/0.9363296 params=-0.5/0.375/1536/2048/513/1025/10/20/2560/2560 float=y maxiter=2048 inside=atan outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=200ggf<18>BBA998776<2>221000011<24>0bn0cp0er<3>0ky<25>09B089067<2\ >021000210<22>keNmgOoiPqjQslRunS<2>zsW<25>CB6A95874653442220000400<23>o0\ 0q00s00<3>z00<25>C00A00800<3>000<2>554776998BBACCB<16>eedggfiihjjillknnm\ <2>ssr<5>iih } Borderline { ; Mix of 3 fractals ; Albrecht Niekamp, March,03 ; Version 2002 Patchlevel 4 reset=2002 type=formula formulafile=multi231.frm formulaname=multifrac_231 ismand=y function=exp/exp passes=t center-mag=-0.30271605328868720/-0.63359923125606620/52.34401 params=-0.00180974761192663/-0.2758911404766991/1536/3072/513/1025/4/2/3\ 300/3300 float=y maxiter=4094 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=200RRR<8>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<25>09C08A068<2>\ 022000211<22>keOmgPoiQqjRslSunT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00\ <3>z00<25>C00A00800<3>000<23>eeegggiiijjjlllnnn<2>sss<15>SSS } --------------------------------start-frm----------------------------------- frm:Multifrac_231 { ; Albrecht Niekamp March,03 ;real(p2) factor ;imag(p2) bailout ;real(p3) maxiter1 ;imag(p3) maxiter2 ;real(p4) inside1: 1_mandel 2_julia 3_expmandel 4_expjulia ; other: *10_soft julia transitions <0_outside=exp ;imag(p4) inside2: 1_mandel 2_julia 3_expmandel 4_expjulia ; other: *10_soft mandel transitions <0_no inside1 ;real(p5) border1 ;imag(p5) border2 fac=real(p2) ba=imag(p2) out1=real(p3) out2=imag(p3) b1=real(p5) b2=imag(p5) d1=real(p4) d2=imag(p4) vb=(d1<0) If (vb) d1=d1*-1 endif tj=(d1<10) if (tj==0) d1=d1/10 endif v1=(d1==3) v2=(d1==4) d1=(d1==2)+(d1==4) st=(d2<0) if (st) d2=d2*-1 endif mj=(d2<10) if (mj==0) d2=d2/10 endif v3=(d2==3) v4=(d2==4) d2=(d2==2)+(d2==4) t=0 start=2-st if (ismand) z=0 c=pixel else c=p1 z=pixel endif : if (vb) z=(z+real(c))^(z+imag(c)) else z=z^2+c endif bo=|z| if (start) t=t+1 if (start==2) if ((t>out1)+(bo>=b1)) u=2*(fn1(t/fac)) if (d1) if (tj) z=pixel endif c=p1*u vb=v2 else z=z*u c=z if (mj) z=0 endif vb=v1 endif start=1 t=0 endif else if (t>out2)+(bo>=b2) u=2*(fn2(t/fac)) if (d2) if (tj) z=pixel endif c=p1*u vb=v4 else z=z*u c=z if (mj) z=0 endif vb=v3 endif start=0 endif endif endif bo<=ba } ------------------------------------end------------------------

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FOTD 05-04-03 (A Delicate Vision [6])
by Jim M. 05 Apr '03

05 Apr '03

FOTD -- April 05, 2003 (Rating 6) Fractal visionaries and enthusiasts: It has been a most busy week here at Fractal Central, but between the periods of rush I somehow managed to produce a fractal. Today's 'evaporated' image was created by combining 1 negative part of (1/Z) with 0.1 negative part of Z^(-10), then adding (1/C). The 'unevaporated' parent fractal consists of a rather tubby Mandeloid with its main stem pointed ENE, with much chaotic material lying farther to the east. Today's scene is located in the East Valley area of this Mandeloid, which in this case is on the WSW side of the main bay. When I say that today's image is evaporated, I do not mean it is all dried up. I mean that the original fractal has been obliterated by raising the escape radius to 10^100 and the blank inside that resulted has been brought to life by rendering it with the bof61 inside option. I named the image "A Delicate Vision". With its fern-like arms and tendrils, the picture does have a rather delicate feeling to it. I rated the image at a 6, which is just slightly above average. The 1/4-hour render time of the parameter file on my tired old P200 unit is a bit much for such an average image. The better way of seeing the image is to download it in finished form from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The week just ended got a mixed review from the fractal duo. Warm sunny weather during the middle of the week made them happy, but the chilly, wet spell that ended the week turned their moods sullen. Today, they are making the most of the clouds and chill by observing the world from their shelf by the window. In a couple hours when they get their tuna, I expect their moods to lighten considerably. For me, it's a weekend, but there's still quite a bit of work to get done. And that FOTD CD is still waiting in the wings to be wrapped up. If I don't have it finished to my satisfaction by the end of this month, I'll distribute it as it is. The next FOTD will appear on April 12. Until then, take care, and the FOTD will return to its daily basis on May 1. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Delicate_Vision { ; time=0:15:01.33--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=-10.76988543003492/-1.604913088734675/5\ 726949/1/-97.5/-1.44472357743730129e-007 params=-1\ /-1/-0.1/-10/0/1e+100/0/0 float=y maxiter=1200 inside=bof61 periodicity=10 colors=000T4BTBZTHMTMSTSXTXdTbiTgnTmtQvwTpyVkyXey`\ `zbXzdSzgMziHzkBzm7zt4zz0zz0z0z00z04z0By0Ir0Oi0T`0\ `S0eK0kB0r00w00z00z00z00z00z00y20y70yB0yD0wS4veFtt\ QrzZvzTyvOzpKzmFzg9zb4zX0zT0zO0zI0zF0zI0zM0zO0zS0z\ V0zX0z`0zd0ze0zi0zm0zn0rr0iv7`yHSzQIzZ9zg0zn9ztHzy\ MrzTmzZhzdAziAzjAzvBzzBzzBzsDzzFzzFvzHnzIgzI`zKTzM\ MzMFzO7zQ0zQ0zS0zS0Se90td0MS00F20B409707904B40D90F\ D0HH0II0HF0HD0HB0F90F70F40F20D00D00D00B00B00B00B00\ F02Z00Z00Z00b02e07i7DmHHpQMrZQvgVypZzydzzgzzmzzpzz\ rzzrzzrzwrzprzktzdtzXtzQtzItzDvz4vz0vz0vz0vz0vz0wz\ 0wz0wz0wy0wv0wr0yn0yk0yg0yd0y`0yZ0zV0zS0zO0zK0zH0z\ D0z90z40z00z00z00z00z00z00w24r7BmDHgIKbOQVSVQXZKbd\ Fgi9gr0km2mi4ne7pb9tZBvVDwSFyOHzKIzHKzDMz7Iz9Oz9Sz\ 9Vz9Zz9bz9ez9iz9mzBpzBtzBwzBzzBzzBzzBzzDzzBzz9zy9z\ w7zv4yt4vr2rr0np0kn0em0bk0Zi0Vg0Se0Me0Id0Fb0B`07Z0\ 0X00V00T00S00T00T00T00T02 } frm:MandelbrotMix2 {; 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 20.0 PAR-FORMULA FILE==================================

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Fractint version 20.2 patch 5
by Jonathan Osuch 03 Apr '03

03 Apr '03

Fractint version 20.2 patch 5 diff and executables are now available on the developer's ftp site: www.fractint.org From the Whats new file ***** Patch 5 Made changes to allow Xfractint to find files that use upper case letters. Fixed a problem with the Cellular type that prevented entering an initial row of greater than 32767 from working. Added a message about not being able to resume after interrupting prior to rows being displayed on screen. Fixed an evolver bug which caused setting evolver parameters to turn evolving on, even though evolving was actually turned off. Added Charlie Chernohorsky's truecolor speed up and his implementation of virtual screen sizes for the VESA modes (dotmode=28). This feature does not work consistently between different video cards, so it may be turned off by using the startup command "virtual=n". Use the <V> screen to set the desired virtual screen size. See {View Window}. Please remember that if either X or Y is greater than 2048, solid guessing is turned off. This is for multiple reasons, so it is likely it will NOT get fixed soon. There is also a problem with the colorbars that appear when saving an image leaving bits of corruption on the screen. This occurs in all the VESA truecolor modes. Added Charlie to the scrolling list of contributors. Added Charlie's fix for the l-system type which occurred when a push-pop combination was on two different lines. Fixed the PAGE-UP/PAGE-DN zoombox in Xfractint so that it now appears on the screen. Fixed ranges= in Xfractint so GIFs save correctly and program doesn't end abruptly. ***** What is not mentioned are changes to the Xfractint X11 interface to improve reliability (I hope), man page update, and the Xfractint source now comes as a tar.gz file. All four sources have their own diff in the 2002p05.zip file. You will need to apply only one of them. See the readme.1st file in 2002p05.zip. I have not yet updated the experimental Allegro port source or made a diff for it. Jonathan

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xfractint 20.2.05
by Natalie 02 Apr '03

02 Apr '03

Hello, Hi, Downloaded the tar.gz, compiled xfractint without any problems. The zoombox works perfectly ok now. The stereogram function works better than in the previous patch. Thank you, programmers! I keep hoping the next version will have colormap editing... ... and a fixed boundary trace Thanks! Natalie -- aabdeehilptz aeginrstu ;) Linux Counter: user 230952

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Splash!!
by Albrecht.Niekamp＠t-online.de 31 Mar '03

31 Mar '03

Hi Paul, thank you for the nice words. I really appreciate that you make it available for downloads. Wonder, how many it will be.. Fractal Greetings, Al.

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FOTD 29-03-03 (Goldiebrot [4])
by JimMuth＠aol.com 29 Mar '03

29 Mar '03

FOTD -- March 29, 2003 (Rating 4) Fractal visionaries and enthusiasts: Today's fractal scene lies in a parent fractal that results when one negative part of Z^(-0.3) is combined with one negative part of Z^(-3) and (1/C) is added to the iterations. This parent resembles an oval island with a pointed east end and a chaotic west end lined with Mandelbrot buds. The island is surrounded by the fractal ocean of infinity. Today's scene lies in a dis- connected area of chaos just inland from the southwest shore- line of the parent, at a point where the shore is lined with fractal buds. When I studied the finished image, searching for a rating, I got the impression that I had been here before -- not to this exact place, but to a place similar. As a result, the rating that started at a 5 dropped to a 4, which is all I can do for such an image. (Strange as it may seem, the fewer FOTD images I post, the lower the quality of the images seems to become. In a week or two when I decide the fate of my overworked FOTD-CD, I'll return to my daily FOTD schedule, and the quality will hopefully pick up.) I named today's image "Goldiebrot" after the well-known fairy- tale character who visited the house where 3 bears lived. The gold coloring in the image inspired the name. The 5-1/2 minute render time of the parameter file is not too long to wait for the image to appear. But downloading the completed image from the web site of Paul at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> will eliminate even the small wait. The weather during the past week here at Fractal Central varied between sunny and warm, and rainy and cold. The mood of the dynamic duo varied between happy and grouchy. This morning is starting dreary with a temperature of 59F 15C and showers expected through the day. I expect it will be a bad day for cats. The FOTD-CD is making steady progress. The problem is that as soon as I fix one problem, I find another. If the present trend continues, I might have to admit that I will never get the disk perfect and resign myself to a production which is adequate but with flaws. Until Saturday, April 05, take care, and searching for truth is one thing; recognizing truth when you find it is another. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Goldiebrot { ; time=0:05:36.36--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.605091404854238/-3.150129979402847/4\ 26694/1/102.5/-2.15061206676470107e-007 params=-1/-0.3/-1/-3/0/525 float=y maxiter=1000 inside=0 logmap=100 periodicity=10 colors=0000RN0VQ0ZSGbVMfYBj`Qnbbsepmjzinxefsb`mZUh\ XNbSGZQ9aS8dV7fX5iZ4l`3nb1qd0tf0wh0yj0zl0zn0zp0zs0\ zt0zq0zn0zl0yi0uf1sd3pa5m`7jY8fVBdSCaQEZNFVKISIJQG\ KNENKBOG8QE5SB3U80V50X73V77U79U8ES8IR8KR8OQ9SO9VO9\ ZN9bMBeMBiKBmJBpJJdURUdZJmXMjVNiSOhRQeORdNSbMU`JXZ\ IYYFZVE`UCaS9bQ8dO5fN4hK3iJ0jI0lF0mE0nC0pB0nB0mB3l\ B5jB8jBBiBFhBIfBKfBNeBQdBSbBVbBY`E`ZGaXJdVMeSOhRQi\ OSlNVnKYpJ`sGatFdwCfxBiz8lz7myCjwIitNhsSepYdmbblf`\ ilZfqYewVbzU`zSZzRt`zb8I`GOZOVXXaVdhSlnRtuOzzNzzMz\ zKywKupJqjJmeIiZIeUG`OFXIFSCEO7EK0CG0CC0FE0IE0KE1M\ E5OE9RFEUFIVFKYFO`FSbGXdG`fGdiGhlGlmGnUIwBIzBIzEMz\ GQzJUzMYyOawReuUitXmsZqpaundymfzldzjbziazh`zfYzeXz\ dVzbUzaRz`QzZOzYNzYKzXJzVIzUGzSEzRCzQBzO9zN7zM5zK4\ zJ3zJ4zM5zO7zQ8zS9zVBzXCzZEzaFzbFzeGzhIziJzlKznMzp\ NzsOzuQzwRzyRzzSzzUzzUzzVzzVzzXzzYzzYzzZzzZzz`zzaz\ zazzbzzbzzdzzezzezzzzzzzz } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] Test to see if new sig works
by Jim M. 28 Mar '03

28 Mar '03

At 03:06 PM 3/28/03 -0500, J. McKenzie wrote: >Did we pass? What was my score? I want the gold star! 8-{> You squeaked by with a C-minus! That gets a green star. ;-) Jim M.

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Test to see if new sig works
by Jim M. 28 Mar '03

28 Mar '03

This is just a test.

2 1

Fractal Universe Calendar 2005
by gumbycat 26 Mar '03

26 Mar '03

This is the last open call for you to submit your fractal artwork for consideration for inclusion in the Fractal Universe Â® Calendar 2005. The deadline is April 15, and this is the last notice we will be making. All the information you will need is detailed on the following website: http://www.fractalforum.com Please make your submissions and any additional enquires you may have via the contact form on the above website. We would love to see images from all of you! Linda Allison and Tina Oloyede ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ http://www.fractalus.com/gumbycat/index.html Copyright, all rights reserved: http://www.fractalus.com/gumbycat/copyright.html +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

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Splash!!
by Albrecht.Niekamp＠t-online.de 24 Mar '03

24 Mar '03

Hi John, when I received the digest, I saw that there was an empty line in the colorparameters. Just remove it and it should work. Anyway here it is again, just in case there are other errors. Fractal Greetings, Al. ----------------------------start-par------------------------------------ Splash!! { ; If U like it, put in your sstools.ini ; Albrecht Niekamp mar,03 reset=2002 type=formula formulafile=splash.frm formulaname=splash_1 ismand=y passes=1 center-mag=-0.650407/4.44089e-016/0.9861933 params=-0.5/0.375/40/0.18/320/0/-100/100/40/10 float=y maxiter=2048 inside=maxiter periodicity=0 rseed=-2436 colors=200oiR<15>KIBIGAGF9<3>875654443221000400<23>o00q00s00<3>z00<25>C0\ 0A00800<3>000<23>eeegggiiijjjlllnnn<2>sss<25>BBB999777<2>222000012<24>0b\ o0cq0es<3>0kz<25>09C08A068<2>022000211<22>keOmgPoiQqjRslSunT<2>zsX<4>qjS } frm:splash_1 { ; Basic data : FractMask08 ; Albrecht Niekamp March,03 ; Lake effect by Sylvie Gallet ; p1: Julia seed ; real (p2) : water level in % of the screen height ; imag (p2) : amplitude of the wave (try 0.2) ; real (p3) : frequency (try 300) ; imag (p3) : size y (>0 smaller -1 no text) ; real (p4) : horizontal factor ; imag (p4) : vertical factor ; real (p5) : size left (>0 smaller) ; imag (p6) : size right (>0 smaller) in=0 t=0 z=0 w=0 start=1 c=pixel if (whitesq) row=imag(scrnpix) rows=imag(scrnmax) y=row/(rows-1) col=real(scrnpix) cols=real(scrnmax) x=col/(cols-1) size=imag(p3)/1000 hf=real(p4)/100 vf=imag(p4)/1000 cl=real(p5)/100 cr=imag(p5)/100 tx=(imag(p3)!=-1) if (tx) xx=x yy=y f=1-y d=x-0.5 cr=cr+hf cl=cl+hf If (x>0.5) e=d*d-0.25 hd=-e*hf g=(0.25-e)/5 x=x+g*cr+((hf*0.005)*(hf<0)) else e=x*x-0.25 hd=e*hf*2 g=(0.25-e)/10 x=x-g*cl+((hf*0.01)*(hf<0)) endif d=1-xx if (y>0.5) if (xx>0.5) e=d*d b=f*(0.5-d)*vf*40*(0.25-e) else e=xx*xx b=f*(0.5-xx)*vf*40*(0.25-e) endif y=y+f*vf*1.6+size else if (xx>0.5) e=d*d b=-(f*(0.5-d)*vf*40*(0.25-e)) else e=xx*xx b=-(f*(0.5-xx)*vf*40*(0.25-e)) endif y=y-y*vf*1.6-size endif e=exp(hd) b=exp(b) in=in+(x>.06*e&&x<.92*e&&y<.693*b&&y>.68*b) in=in+(x>.07*e&&x<.13*e&&y<.626*b&&y>.613*b) in=in+(x>.19*e&&x<.25*e&&y<.626*b&&y>.613*b) in=in+(x>.32*e&&x<.41*e&&y<.626*b&&y>.6*b) in=in+(x>.45*e&&x<.5*e&&y<.626*b&&y>.613*b) in=in+(x>.56*e&&x<.6*e&&y<.626*b&&y>.6*b) in=in+(x>.63*e&&x<.69*e&&y<.626*b&&y>.613*b) in=in+(x>.7*e&&x<.75*e&&y<.626*b&&y>.613*b) in=in+(x>.76*e&&x<.81*e&&y<.626*b&&y>.613*b) in=in+(x>.85*e&&x<.89*e&&y<.626*b&&y>.6*b) in=in+(x>.08*e&&x<.12*e&&y<.613*b&&y>.266*b) in=in+(x>.2*e&&x<.24*e&&y<.613*b&&y>.36*b) in=in+(x>.31*e&&x<.32*e&&y<.613*b&&y>.48*b) in=in+(x>.44*e&&x<.47*e&&y<.613*b&&y>.373*b) in=in+(x>.49*e&&x<.51*e&&y<.613*b&&y>.586*b) in=in+(x>.55*e&&x<.56*e&&y<.613*b&&y>.346*b) in=in+(x>.6*e&&x<.61*e&&y<.613*b&&y>.52*b) in=in+(x>.64*e&&x<.68*e&&y<.613*b&&y>.36*b) in=in+(x>.71*e&&x<.75*e&&y<.613*b&&y>.36*b) in=in+(x>.76*e&&x<.8*e&&y<.613*b&&y>.373*b) in=in+(x>.84*e&&x<.85*e&&y<.613*b&&y>.346*b) in=in+(x>.89*e&&x<.9*e&&y<.613*b&&y>.52*b) in=in+(x>.32*e&&x<.35*e&&y<.6*b&&y>.573*b) in=in+(x>.36*e&&x<.42*e&&y<.6*b&&y>.586*b) in=in+(x>.56*e&&x<.59*e&&y<.6*b&&y>.306*b) in=in+(x>.61*e&&x<.62*e&&y<.6*b&&y>.52*b) in=in+(x>.85*e&&x<.88*e&&y<.6*b&&y>.306*b) in=in+(x>.9*e&&x<.91*e&&y<.6*b&&y>.52*b) in=in+(x>.36*e&&x<.4*e&&y<.586*b&&y>.373*b) in=in+(x>.5*e&&x<.51*e&&y<.586*b&&y>.572*b) in=in+(x>.32*e&&x<.34*e&&y<.573*b&&y>.466*b) in=in+(x>.43*e&&x<.44*e&&y<.573*b&&y>.413*b) in=in+(x>.14*e&&x<.15*e&&y<.52*b&&y>.373*b) in=in+(x>.34*e&&x<.35*e&&y<.52*b&&y>.466*b) in=in+(x>.13*e&&x<.14*e&&y<.493*b&&y>.4*b) in=in+(x>.35*e&&x<.36*e&&y<.48*b&&y>.453*b) in=in+(x>.12*e&&x<.13*e&&y<.466*b&&y>.426*b) in=in+(x>.5*e&&x<.51*e&&y<.412*b&&y>.36*b) in=in+(x>.25*e&&x<.28*e&&y<.44*b&&y>.36*b) in=in+(x>.31*e&&x<.35*e&&y<.44*b&&y>.386*b) in=in+(x>.28*e&&x<.29*e&&y<.426*b&&y>.373*b) in=in+(x>.24*e&&x<.25*e&&y<.413*b&&y>.36*b) in=in+(x>.49*e&&x<.5*e&&y<.413*b&&y>.373*b) in=in+(x>.16*e&&x<.18*e&&y<.4*b&&y>.266*b) in=in+(x>.32*e&&x<.34*e&&y<.386*b&&y>.373*b) in=in+(x>.48*e&&x<.49*e&&y<.386*b&&y>.36*b) in=in+(x>.75*e&&x<.76*e&&y<.386*b&&y>.36*b) in=in+(x>.19*e&&x<.2*e&&y<.373*b&&y>.36*b) in=in+(x>.33*e&&x<.39*e&&y<.373*b&&y>.36*b) in=in+(x>.45*e&&x<.48*e&&y<.373*b&&y>.36*b) in=in+(x>.54*e&&x<.55*e&&y<.373*b&&y>.36*b) in=in+(x>.59*e&&x<.62*e&&y<.373*b&&y>.36*b) in=in+(x>.63*e&&x<.64*e&&y<.373*b&&y>.36*b) in=in+(x>.7*e&&x<.71*e&&y<.373*b&&y>.36*b) in=in+(x>.76*e&&x<.79*e&&y<.373*b&&y>.36*b) in=in+(x>.83*e&&x<.84*e&&y<.373*b&&y>.36*b) in=in+(x>.88*e&&x<.91*e&&y<.373*b&&y>.36*b) in=in+(x>.15*e&&x<.16*e&&y<.346*b&&y>.266*b) in=in+(x>.14*e&&x<.15*e&&y<.306*b&&y>.266*b) in=in+(x>.57*e&&x<.59*e&&y<.306*b&&y>.266*b) in=in+(x>.64*e&&x<.68*e&&y<.306*b&&y>.266*b) in=in+(x>.86*e&&x<.88*e&&y<.306*b&&y>.266*b) in=in+(x>.07*e&&x<.08*e&&y<.28*b&&y>.266*b) in=in+(x>.12*e&&x<.14*e&&y<.28*b&&y>.266*b) endif if (in) w=1 z=(xx+yy/8)*689 else if (imag(p2)>0 && imag(p2)<=100) level=real(p2)/100 ; water level ampl=imag(p2) ; amplitude of the wave freq=real(p3) ; frequency angle=real(rotskew*pi/180) exp_irot=exp(-flip(angle)) h=1/real(magxmag) q=h/0.75*imag(magxmag) tanskew=tan(imag(rotskew*pi/180)) u=2*q*exp_irot v=2*h*(tanskew+flip(1))*exp_irot z3rd=center+(-q-h*tanskew-flip(h))*exp_irot z=pixel-z3rd s=imag(conj(u)*z)/imag(conj(u)*v) if (s<=level) dy=level-s z=z+2*dy*(1+ampl*sin(freq*dy^0.2))*v endif z=z+z3rd if (ismand) c=z z=0 else c=p1 endif endif endif endif : if (w) z=z-1 phc_bailout=|z|>=1 else z=z^2+c if (start) t=t+1 if (|z|>=128) u=2*(exp(t/768)) z=z^u start=0 endif if (t>513) u=2*(sin(t/768)) z=z*u c=p1*u start=0 endif endif phc_Bailout=|z|<=2048 endif phc_bailout } __________________________________________________end_______________________ ___

2 1

Splash!!
by Albrecht.Niekamp＠t-online.de 24 Mar '03

24 Mar '03

Hi, all This is what I did the last days, helps to think of other things. The formula incl. Sylvie Gallets Lake effect can be used with other formulas. As it contains all needed variables copy the whole thing incl. the "if w" procedure and append your formula. The fractal is a "3d-look" mandel with inside Julia, transparent letters and underwater look by double layers. The text is manipulated in two ways, first by a multiplication factor added to each datavalue, which compresses or expands the letters and secondly by imaginary x and y values which change the place and size of the letters. Here`s how it is set up: Use a lores screen, all variables set to zero, for horizontal symmetry checks the zoombox is handy. Real (p4) is the horizontal perspective distortion factor. Positive values compress the outer letters, negative values compress the inner letters. The vertical factor creates a concave distortion if posive and a convex one if negative. All options can be combined and create different views. Both values positive generate a close up view, HF negative a more distant view. The size values can can erase or add cols or rows and do not change the perspective, but help to get rid of evtl. "wrong pixels". With left/right size it`s easy to correct the symmetry. Although the size is autoadjusted to the settings, some correction maybe needed, especially with extreme settings. How about creating your own splash screen and present it here? Fractal greetings, Al ----------------------------start-par------------------------------------ Splash!! { ; If U like it, put in your sstools.ini ; Albrecht Niekamp mar,03 reset=2002 type=formula formulafile=splash.frm formulaname=splash_1 ismand=y passes=1 center-mag=-0.650407/4.44089e-016/0.9861933 params=-0.5/0.375/40/0.18/320/0/-100/100/40/10 float=y maxiter=2048 inside=maxiter periodicity=0 rseed=-2436 colors=200oiR<15>KIBIGAGF9<3>875654443221000400<23>o00q00s00<3>z00<25>C0\ 0A00800<3>000<23>eeegggiiijjjlllnnn<2>sss<25>BBB999777<2>222000012<24>0b\ o0cq0es<3>0kz<25>09C08A068<2>022000211<22>keOmgPoiQqjRslSunT<2>zsX<4>qjS } frm:splash_1 { ; Basic data : FractMask08 ; Albrecht Niekamp March,03 ; Lake effect by Sylvie Gallet ; p1: Julia seed ; real (p2) : water level in % of the screen height ; imag (p2) : amplitude of the wave (try 0.2) ; real (p3) : frequency (try 300) ; imag (p3) : size y (>0 smaller -1 no text) ; real (p4) : horizontal factor ; imag (p4) : vertical factor ; real (p5) : size left (>0 smaller) ; imag (p6) : size right (>0 smaller) in=0 t=0 z=0 w=0 start=1 c=pixel if (whitesq) row=imag(scrnpix) rows=imag(scrnmax) y=row/(rows-1) col=real(scrnpix) cols=real(scrnmax) x=col/(cols-1) size=imag(p3)/1000 hf=real(p4)/100 vf=imag(p4)/1000 cl=real(p5)/100 cr=imag(p5)/100 tx=(imag(p3)!=-1) if (tx) xx=x yy=y f=1-y d=x-0.5 cr=cr+hf cl=cl+hf If (x>0.5) e=d*d-0.25 hd=-e*hf g=(0.25-e)/5 x=x+g*cr+((hf*0.005)*(hf<0)) else e=x*x-0.25 hd=e*hf*2 g=(0.25-e)/10 x=x-g*cl+((hf*0.01)*(hf<0)) endif d=1-xx if (y>0.5) if (xx>0.5) e=d*d b=f*(0.5-d)*vf*40*(0.25-e) else e=xx*xx b=f*(0.5-xx)*vf*40*(0.25-e) endif y=y+f*vf*1.6+size else if (xx>0.5) e=d*d b=-(f*(0.5-d)*vf*40*(0.25-e)) else e=xx*xx b=-(f*(0.5-xx)*vf*40*(0.25-e)) endif y=y-y*vf*1.6-size endif e=exp(hd) b=exp(b) in=in+(x>.06*e&&x<.92*e&&y<.693*b&&y>.68*b) in=in+(x>.07*e&&x<.13*e&&y<.626*b&&y>.613*b) in=in+(x>.19*e&&x<.25*e&&y<.626*b&&y>.613*b) in=in+(x>.32*e&&x<.41*e&&y<.626*b&&y>.6*b) in=in+(x>.45*e&&x<.5*e&&y<.626*b&&y>.613*b) in=in+(x>.56*e&&x<.6*e&&y<.626*b&&y>.6*b) in=in+(x>.63*e&&x<.69*e&&y<.626*b&&y>.613*b) in=in+(x>.7*e&&x<.75*e&&y<.626*b&&y>.613*b) in=in+(x>.76*e&&x<.81*e&&y<.626*b&&y>.613*b) in=in+(x>.85*e&&x<.89*e&&y<.626*b&&y>.6*b) in=in+(x>.08*e&&x<.12*e&&y<.613*b&&y>.266*b) in=in+(x>.2*e&&x<.24*e&&y<.613*b&&y>.36*b) in=in+(x>.31*e&&x<.32*e&&y<.613*b&&y>.48*b) in=in+(x>.44*e&&x<.47*e&&y<.613*b&&y>.373*b) in=in+(x>.49*e&&x<.51*e&&y<.613*b&&y>.586*b) in=in+(x>.55*e&&x<.56*e&&y<.613*b&&y>.346*b) in=in+(x>.6*e&&x<.61*e&&y<.613*b&&y>.52*b) in=in+(x>.64*e&&x<.68*e&&y<.613*b&&y>.36*b) in=in+(x>.71*e&&x<.75*e&&y<.613*b&&y>.36*b) in=in+(x>.76*e&&x<.8*e&&y<.613*b&&y>.373*b) in=in+(x>.84*e&&x<.85*e&&y<.613*b&&y>.346*b) in=in+(x>.89*e&&x<.9*e&&y<.613*b&&y>.52*b) in=in+(x>.32*e&&x<.35*e&&y<.6*b&&y>.573*b) in=in+(x>.36*e&&x<.42*e&&y<.6*b&&y>.586*b) in=in+(x>.56*e&&x<.59*e&&y<.6*b&&y>.306*b) in=in+(x>.61*e&&x<.62*e&&y<.6*b&&y>.52*b) in=in+(x>.85*e&&x<.88*e&&y<.6*b&&y>.306*b) in=in+(x>.9*e&&x<.91*e&&y<.6*b&&y>.52*b) in=in+(x>.36*e&&x<.4*e&&y<.586*b&&y>.373*b) in=in+(x>.5*e&&x<.51*e&&y<.586*b&&y>.572*b) in=in+(x>.32*e&&x<.34*e&&y<.573*b&&y>.466*b) in=in+(x>.43*e&&x<.44*e&&y<.573*b&&y>.413*b) in=in+(x>.14*e&&x<.15*e&&y<.52*b&&y>.373*b) in=in+(x>.34*e&&x<.35*e&&y<.52*b&&y>.466*b) in=in+(x>.13*e&&x<.14*e&&y<.493*b&&y>.4*b) in=in+(x>.35*e&&x<.36*e&&y<.48*b&&y>.453*b) in=in+(x>.12*e&&x<.13*e&&y<.466*b&&y>.426*b) in=in+(x>.5*e&&x<.51*e&&y<.412*b&&y>.36*b) in=in+(x>.25*e&&x<.28*e&&y<.44*b&&y>.36*b) in=in+(x>.31*e&&x<.35*e&&y<.44*b&&y>.386*b) in=in+(x>.28*e&&x<.29*e&&y<.426*b&&y>.373*b) in=in+(x>.24*e&&x<.25*e&&y<.413*b&&y>.36*b) in=in+(x>.49*e&&x<.5*e&&y<.413*b&&y>.373*b) in=in+(x>.16*e&&x<.18*e&&y<.4*b&&y>.266*b) in=in+(x>.32*e&&x<.34*e&&y<.386*b&&y>.373*b) in=in+(x>.48*e&&x<.49*e&&y<.386*b&&y>.36*b) in=in+(x>.75*e&&x<.76*e&&y<.386*b&&y>.36*b) in=in+(x>.19*e&&x<.2*e&&y<.373*b&&y>.36*b) in=in+(x>.33*e&&x<.39*e&&y<.373*b&&y>.36*b) in=in+(x>.45*e&&x<.48*e&&y<.373*b&&y>.36*b) in=in+(x>.54*e&&x<.55*e&&y<.373*b&&y>.36*b) in=in+(x>.59*e&&x<.62*e&&y<.373*b&&y>.36*b) in=in+(x>.63*e&&x<.64*e&&y<.373*b&&y>.36*b) in=in+(x>.7*e&&x<.71*e&&y<.373*b&&y>.36*b) in=in+(x>.76*e&&x<.79*e&&y<.373*b&&y>.36*b) in=in+(x>.83*e&&x<.84*e&&y<.373*b&&y>.36*b) in=in+(x>.88*e&&x<.91*e&&y<.373*b&&y>.36*b) in=in+(x>.15*e&&x<.16*e&&y<.346*b&&y>.266*b) in=in+(x>.14*e&&x<.15*e&&y<.306*b&&y>.266*b) in=in+(x>.57*e&&x<.59*e&&y<.306*b&&y>.266*b) in=in+(x>.64*e&&x<.68*e&&y<.306*b&&y>.266*b) in=in+(x>.86*e&&x<.88*e&&y<.306*b&&y>.266*b) in=in+(x>.07*e&&x<.08*e&&y<.28*b&&y>.266*b) in=in+(x>.12*e&&x<.14*e&&y<.28*b&&y>.266*b) endif if (in) w=1 z=(xx+yy/8)*689 else if (imag(p2)>0 && imag(p2)<=100) level=real(p2)/100 ; water level ampl=imag(p2) ; amplitude of the wave freq=real(p3) ; frequency angle=real(rotskew*pi/180) exp_irot=exp(-flip(angle)) h=1/real(magxmag) q=h/0.75*imag(magxmag) tanskew=tan(imag(rotskew*pi/180)) u=2*q*exp_irot v=2*h*(tanskew+flip(1))*exp_irot z3rd=center+(-q-h*tanskew-flip(h))*exp_irot z=pixel-z3rd s=imag(conj(u)*z)/imag(conj(u)*v) if (s<=level) dy=level-s z=z+2*dy*(1+ampl*sin(freq*dy^0.2))*v endif z=z+z3rd if (ismand) c=z z=0 else c=p1 endif endif endif endif : if (w) z=z-1 phc_bailout=|z|>=1 else z=z^2+c if (start) t=t+1 if (|z|>=128) u=2*(exp(t/768)) z=z^u start=0 endif if (t>513) u=2*(sin(t/768)) z=z*u c=p1*u start=0 endif endif phc_Bailout=|z|<=2048 endif phc_bailout }

3 2

FOTD 22-03-03 (Unseen Mandelbrot [5])
by Jim Muth 22 Mar '03

22 Mar '03

FOTD -- March 22, 2003 (Rating 5) Fractal visionaries and enthusiasts: With no daily FOTD, the Fractint and philofractal lists are basically dead. But, as I have often said, there is no need for concern. I, for one, am not losing enthusiasm for fractals. I am simply in the tedious process of getting the FOTD-CD up to a level where it is worth spending 20 dollars for. This process is being complicated by a seasonal crush of other work, which must be given priority. Also, I must leave town for an appointment early next week, and I have decided to use the appointment as an excuse for a 3-day vacation. I realize that this will slow things down, but I have had no time off since September of 2000. This being covered, it is time to get to the day's image. It is a picture of a midget lying near a larger midget deep in a filament on the second bud out the main negative stem of the Mandelbrot set. Since the chances of this particular midget ever having been previously seen are in effect zero, I have named the picture "Unseen Mandelbrot". The magnitude lies in the upper range of arbitrary precision math, which results in an image that takes just over 1/2 hour to render on my machine. There is not much to be said about the image other than it is a typical deep midget on a filament. Due to its average nature, I gave the image an average rating of 5. The image may be seen by starting the attached parameter file and waiting 1/2 hour, but the better way of viewing it is to download the finished image file from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The week just ended was quite cold, damp and rainy here at Fractal Central. The fractal duo spent the week sitting by the window, wishing conditions were more pleasant. Much tuna and some turkey was needed to keep their moods liveable. Today (Saturday) is starting more pleasantly, with sun and warmer temperatures. I foresee better moods in the near future. As for myself, I'm going to take a well-earned 3-day vacation at the ocean Monday to Wednesday before getting back to work and doing the things that need to be done, such as the CD. The next FOTD will appear on March 29. Until then, take care, and keep fractals alive. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Unseen_Mandelbrot { ; time=0:37:32.66--SF5 on a P200 reset=2002 type=mandel passes=1 center-mag=-1.77856519664430671896/0.0021083398799\ 35524981/2.360665e+016/1/-57.5033632547348361/0.00\ 244756560975039478 params=0/0 float=y maxiter=2200 bailout=625 inside=0 logmap=432 periodicity=10 colors=0000U_0V_0W_0X_0Y_0Z_0__3`_6a`9baBcbEdcHedJ\ fdMhePifSjgUkhXli_mjanjdpkgqljrmlsnotoruptvpsuosto\ rtnrsnqsmqrmpqmpqloplopkooknnknnjmmjmmillilkikkhkj\ hjjgjigjigieehbcg_agX_fUYeRXdOVdLTcIRbFPbCOdEQeGSf\ IUgKWhLXiNZjP`kRblTdmUeoWgpYiq_kramsbntdpufrvhtwjv\ xkwwivvhvvgvufvudvtcvsbusaur_urZuqYuqXupVtoUtoTtnS\ tnQtmPtlOslNskLskKsjJsjIshJrfJqdJpbJo`JnZJnXJmVJlT\ JkRJjPJjNKiLKhJKgHKfFKeDKeBKd9Kc7Kb5Ka4Ka6N_8PYPK6\ 9RWBUVDWTEYRG_PIbOJdMLfKMhIOkHQmFRoDTqBVtAWv8Yx6eJ\ IdNHcQGcUFbXEb_DacCafB`jA`m9_p8_t7Zw6jzAhz9gz9fz8e\ z8dz7bz7az6`z6_z5onNmoLlpKkqJjqIirHhsGgtFftEeuCdvB\ cwAbw9ax8`t7_p6gftecicj_aqP_xFNpVOqTPqSPrRQrQQsPRs\ NRtMStLSuKTuJTuIUvGVvFVwEWwDWxCXxAXy9Yy8Yz7Zz67z09\ z1Bz1Dz1Ez2Gz2Iz2Kz3Lz3Nz3Pz4Rz4Sz4Uz5Wz5Yz5RzDSzC\ TzBUzAVz9Wz8Xz7Yz6Zz5szShzG2zIBzEJzBRz89zLCzJEzIHz\ GJzFLzDOzCCzkBzjAzi9zg8zf } END PARAMETER FILE=========================================

1 0

Are you there ?
by Brian Rankin 21 Mar '03

21 Mar '03

I havent received any postings for some time.Am I still entitled? Brian.

3 3

Re: FOTD 15-03-03 (Floating Tree [9])
by Jim Muth 16 Mar '03

16 Mar '03

At 02:13 AM 3/16/03 -0600, Paul Lee wrote: >Jim Muth wrote: >> >> The image is actually a variation of an >> early FOTD image named Ice Tree.... > >Would that be the one posted to the Fractal-Art >List on January 13, 1998, entitled >"Ice Coated Tree"?? Yes, the 'Ice-Coated Tree' image of Jan 13, 1998 is the earlier image I referred to. Jim M.

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FOTD 15-03-03 (Floating Tree [9])
by Jim Muth 16 Mar '03

16 Mar '03

FOTD -- March 15, 2003 (Rating 9) Fractal visionaries and enthusiasts: Today's fractal is one of my all-time best. (IMO, of course) So I have rated it at a lofty 9, a rating achieved by very few previous images. The image is actually a variation of an early FOTD image named Ice Tree, which will be included on the FOTD CD. That earlier image has the tree firmly rooted in the ground, whereas today's variation shows it floating suspended in mid air. The icy decoration from the earlier image is still coating the branches of the tree, and in addition, two ice-coated bushes appear at either side of the floating tree. The image itself is a scene in the Z^1.5+C Julibrot, sliced in a direction rotated 4 degrees from the Julia direction toward the Elliptic direction. Changing the exponent of Z a few hundredths in either direction causes curious variations in the character of the tree. The coloring is entirely hand-done, and accounts for 99-percent of the image's worth. An extra benefit is the short 2-minute render time of the parameter file. Another good point is that the finished GIF image may be picked up from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather was sunny but quite chilly here at Fractal Central on Friday. The morning low of 26F -3C and afternoon high of 41F 5C kept the dynamic duo, which is no longer quite as dynamic, confined to the sunny porch, which has been cleared of debris but is still roofless. They watched with interest as the meanest tomcat in the neighborhood passed by, finally deciding that discretion is the better part of valor and letting the intruder pass in peace. Today was sunny and milder, and the neighborhood bully did not appear. The duo spent almost an hour roaming the yard. I'm still quite busy, both with the FOTD-CD and more profitable work, but the fractals will continue coming at a weekly rate while the disk is in work. Until next Saturday, take care, and treat fractals with respect. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Floating_Tree { ; time=0:02:26.76--SF5 on a p200 reset=1960 type=formula formulafile=icetree.frm formulaname=multirot-XY-ZW-new function=ident/flip passes=1 center-mag=0.0597552/-1.60982e-015/4.5911\ 12/0.6279/-90/3.88578058618804789e-016 params=90/86/1.5/0/-0.55/0/-0.2/0 float=y maxiter=750 inside=253 logmap=yes periodicity=10 colors=000OezOezOezOezOezOezOezOezOezOezOezOezOezO\ ezOezOezOezOezOezOezOezOezOezOezOezOezOezOezOezOez\ OezOezOezOezOezOezOezOezOezOezOezOezOezOezOezOezOe\ zOezOezOezOezOezOezOezOezOezUAZU9XU8VU7TU6RU5PU4NU\ 3LU2JU1HU0FU0EU0DU0CU0BU0AU09U08U07U07U07U07U07U0A\ U0FU0KU0PU0UU0ZU0cUKhUPm0Ur0ZwKczShzXmzZrzbwzgzzkz\ zzzzzzzzzzzzzzzzzzzOezOezOezOezOezOezOezOezOezOezO\ ezOezOezOezOezOezOezOezOezOezOezOezOezOezOezOezOez\ OezOezOezOezOezOezOezOezOezOezOezOezOezOezOezOezOe\ zOezOezOezOezOezOezOezOezOezOezOezOezOezOezOezOezO\ ezOezOezOezOezOezOezOezOezOezOezOezOezOezOezOezOez\ OezOezOezOezOezOezOezOezOezOezOezOezOezOezOezOezOe\ zOezOezOezOezOezOezOezOezOezOezOezOezOezOezOezOezO\ ezOezOezOezOezOezOezOezOezOezOezOezOezOezOezOezOez\ OezOezOezOezOezOezOezOezOezOezOezOezOezOezOezOezOe\ zOezOezOezOezOezUUcUUcUUc } frm:multirot-XY-ZW-new {; draws 6 planes and 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)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================

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fractint list mailman software upgraded
by Tim Wegner 15 Mar '03

15 Mar '03

Ok, this mailing list is on the new mailman software 2.1.1 now. For the most part this shouldn't make any difference. There may be some new options on your user list options management web page.

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Fractint frm and par files
by Raymond Filiatreault 15 Mar '03

15 Mar '03

John W. wrote: > I ran into a similar problem, here in Fractint, just a short time >ago. = > I believe that your " 3d=3D" and "=3D20" is the result of the = >re-transmission of your files back from Fractint, where the RTF >original = >was re-sent as plain text. > > I was corrected by members of the group, and fixed the problem by = >going into "TOOLS" - "OPTIONS" - "SEND" tab of Outlook Express, and = >changing the "Mail Sending Format" to "Plain Text", I also changed >the = >MIME code settings to "None". I was assured that my problem has been >= >cleared up! Sending the message in plain text will also avoid the dulication of your message. In addition, keeping line length to a maximum of 60 characters/line will prevent the addition of all the "=" signs in the posted frms and pars. When you save par files with Fractint, you have the option of specifying that line length (the default is 72 and is too high for this site). Raymond _________________________________________________________________ MSN 8 helps eliminate e-mail viruses. Get 2 months FREE*. http://join.msn.com/?page=features/virus

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fractint frm and par files
by Albrecht.Niekamp＠t-online.de 14 Mar '03

14 Mar '03

Hi Paul, thanks for your interest. My earlier frms and pars are available on Spanky`s Fractint homepage http://spanky.triumf.ca/pub/fractals/formulas/ Multi5.frm is not yet available as yet. It is the complete formula collection for my present submission. I will mail it to Spanky tomorrow (and on the list in some parts if wanted). I also have a big file with the old frms and a basic update for many of them, I will mail it to you as a zip file if your interested. Multi4.frm features an earlier version of my "3d" effects where I used the iteration of the previous pixel to calculate the "warp" effect, but it tended to be distorted in some parts for obvious reasons.Double iteration was the solution, but anyway, Multi4 features some interesting pictures I think. Fractal Greetings, Al

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Fractint frm and par files
by Albrecht.Niekamp＠t-online.de 14 Mar '03

14 Mar '03

Hi, this is the final part of yesterday`s submission. I noticed that the text was corrupted when I received the confirmation from the fractint mailman, "3d" follows each "=". and "=20" at the end of each line. PLease tell me if the message was corrupted on receipt of the digest. If so, what can I do about it? I use Outlook Express, Mime Version 1.0. Rich text (HTML). Fractal Greetings, Al. --------------------------start--pars----------------------------------------------------------------------------- multi220a { ; Upandaway ; Albrecht Niekamp feb,03 ; Version 2002 Patchlevel 4 reset=2002 type=formula formulafile=multi5.frm formulaname=Multifrac_220a function=exp/exp passes=t center-mag=0.237659/0/0.6666667/1/-90/3.88578058618804789e-016 params=1024/4094/256/512/0.25/0 float=y maxiter=2048 inside=maxiter outside=tdis logmap=6 periodicity=0 colors=2000FK<15>0bo0cq0es<2>0jy0kz0jy<24>09C08A068<2>022000211<24>oiQqj\ RslS<3>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<2\ 5>iiijjjlll<3>sss<25>BBB999777<2>222000012<7>0DI } multi224 { ; Julia Inside Julmandmix ; Albrecht Niekamp feb,03 ; Version 2002 Patchlevel 4 reset=2002 type=formula formulafile=multi5.frm formulaname=Multifrac_224 function=exp/exp passes=t center-mag=0/0/0.6666667 params=1024/4094/512/128/1/0.35 float=y maxiter=2048 inside=maxiter outside=tdis periodicity=0 colors=200FFF<16>iiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0cq0es<2\ >0jy0kz0jy<24>09C08A068<2>022000211<24>oiQqjRslS<3>zsX<25>CB7A96875<3>00\ 0400<23>o00q00s00<3>z00<25>C00A00800<3>000<7>EEE } multi228 { ; Exp_Julia Inside Exp_Mandel ; Albrecht Niekamp feb,03 ; Version 2002 Patchlevel 4 reset=2002 type=formula formulafile=multi5.frm formulaname=multifrac_228 function=sin passes=t center-mag=+0.39608993157380220/-0.83683232220897840/253.449/1.0522 params=1024/4094/512/256/1/0.25 float=y maxiter=2048 inside=maxiter outside=tdis periodicity=0 colors=2000Sa<6>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<22>keOmgPoiQqjR\ slSunT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000\ <23>eeegggiiijjjlllnnn<2>sss<25>BBB999777<2>222000012<16>0R_ } --------------------------------------start--frm---------------------------------------------------------------------------------- FRM:Multifrac_220a {;Albrecht Niekamp Feb,03 fac=real(p1) bailout=imag(p1) border=real(p2) out=imag(p2) z=0 t=0 start=1 c=pixel x=0 : If (x) z=z^(z/u)+c else z=z^z+c endif if (start) t=t+1 if (|z|>=border) u=2*(fn1(t/fac)) z=pixel start=0 x=1 endif if (t>out) u=2*(fn2(t/fac)) z=z/u c=p3/u start=0 endif endif |z|<=bailout } FRM:Multifrac_224 {;Albrecht Niekamp Feb,03 fac=real(p1) bailout=imag(p1) out=real(p2) border=imag(p2) z=pixel t=0 x=0 start=1 c=p3 : if (x) z=z^(z*u)+c else z=z^z+c endif if (start) t=t+1 if (t>out) u=2*(fn1(t/fac)) z=z/u c=p3*u start=0 endif if (|z|>=border) u=2*(fn2(t/fac)) z=z/u c=pixel x=1 start=0 endif endif |z|<=bailout } FRM:Multifrac_228 {;Albrecht Niekamp Feb,03 fac=real(p1) bailout=imag(p1) out=real(p2) border=imag(p2) z=pixel t=0 start=1 c=p3 : if (start) z=(z+real(c))^(z+imag(c)) t=t+1 if (t>out) || (|z|>=border) u=2*(fn1(t/fac)) z=z/u c=pixel start=0 endif else z=(z+real(c))^((z/u)+imag(c)) endif |z|<=bailout } -----------------------------------End-Formulas--------------------------

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Fractint frm and par files
by Albrecht.Niekamp＠t-online.de 14 Mar '03

14 Mar '03

Hi, Miguel, thanks for your fast reply. Of course I`m interested in your messages concerning Fractal Midi Music. I have downloaded your music pars from the Fractint mailbox, but it`s a pity, I cannot access my CMI on board soundchip from dos or in the dos-shell, ("PCI Sound absent") .The dos drivers dont work,although Fractint thinks they are working. Does anybody know a solution?? Fractal Greetings, Al.

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Fractint frm and par files
by Albrecht.Niekamp＠t-online.de 14 Mar '03

14 Mar '03

Hi, I am Albrecht (Al) from Duesseldorf, Germany and I`m new on the list. I have plaid with fractals for a long time, some previous pars and formulas are available on the fractint homepage ("Multifrac"). The pars where not good though, mainly to prove that my formulas at all delivered pictures and to invite others to make own modifications. Please note my new address Albrecht.niekamp(a)-online.de My first contribution is something I came upon when I was meditating about what could make a fractal look 3d. ---..The 4-dimensional room can be seen as a warped 3-dimensional room and a "3d"fractal accordingly should be a warped version of the basic fractal. The way it is warped of course is determined by the depth of the fractal. Also I found out, that double iterating opens the possibilty to use the first pass for the "warp"factor and the second pass lets you control what is inside and what is outside. I dont know if this has been done before, anyway I`ve never seen anything like it, and hope there will be a discussion about this.I know that T-dis has a great part in the 3d-effects, but T-dis alone doesnt do the job. I´ll be happy to get some feedback of any kind! My second main interest is conversion of fractals into fractal (midi) music with "infinite" fractal rhythms that are similar but never repeat. Iïm convinced that there IS something like fractal music. If you`re interested, please email me privately or on the list. This is the first part of my submission. The final part will follow tomorrow. -------------------------------start-pars-and-formulas----------------------------------------------------------------- multi04x { ; Insideworld ; Albrecht Niekamp feb,03 ; Version 2002 Patchlevel 4 reset=2002 type=formula formulafile=multi5.frm formulaname=Multifrac_204f function=exp passes=t center-mag=-0.99816535334584000/+0.27347839866555330/42.19409 params=768/1024/128/512 float=y maxiter=2048 inside=maxiter outside=tdis periodicity=0 colors=200<24>o00q00s00<3>z00<25>C00A00800<3>000<25>iiijjjlll<3>sss<25>B\ BB999777<2>222000012<24>0bo0cq0es<2>0jy0kz0jy<24>09C08A068<2>022000211<2\ 4>oiQqjRslS<3>zsX<31>000 } multi04xa { ; First zoom ; Albrecht Niekamp feb,03 ; Version 2002 Patchlevel 4 reset=2002 type=formula formulafile=multi5.frm formulaname=Multifrac_204f function=exp passes=t center-mag=-0.99215759849906070/+0.28142452043369340/310.2507 params=768/1024/128/512 float=y maxiter=2048 inside=maxiter outside=tdis periodicity=0 colors=2000Uc<13>09C08A068<2>022000111<24>niQpjRrlS<3>ysX<25>BB7996775<3\ >000<24>n00p00r00<3>y00<25>B00900700<2>100000011<24>hiiijjkll<3>rss<25>A\ BB899677<2>122000012<24>0bo0cq0es<2>0jy0kz0jy<9>0We } multi04xb { ; Second zoom ; Albrecht Niekamp feb,03 ; Version 2002 Patchlevel 4 reset=2002 type=formula formulafile=multi5.frm formulaname=multifrac_204f function=exp passes=t center-mag=-1.00006253908692800/+0.28063386155129140/843.8819 params=1536/2048/512/1024 float=y maxiter=4096 inside=maxiter periodicity=0 colors=2000gu0hw0jy0kz<25>09C08A068<2>022000211<22>keOmgPoiQqjRslSunT<2>\ zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<23>eeegg\ giiijjjlllnnn<2>sss<21>IIIGGGFFF<3>777555444222000<27>0es } multi204xc { ; Inoutkey ; Albrecht Niekamp feb,03 ; Version 2002 Patchlevel 4 reset=2002 type=formula formulafile=multi5.frm formulaname=multifrac_204f function=exp passes=t center-mag=-0.99967796372118100/+0.28089082568746140/84388.19 params=1536/2048/512/868 float=y maxiter=2048 inside=maxiter periodicity=0 colors=200777<2>222000012<24>0bo0cq0es<2>0jy0kz0jy<24>09C08A068<2>022000\ 211<24>oiQqjRslS<3>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A0\ 0800<3>000<25>iiijjjlll<3>sss<26>999 } multi215 { ; Based on Multifrac7 ; Albrecht Niekamp feb,03 ; Version 2002 Patchlevel 4 ; reset=2002 type=formula formulafile=multi5.frm formulaname=Multifrac_215 function=exp passes=t center-mag=-0.648135/-3.77476e-015/0.6666667/1/-90/3.88578058618804789e-\ 016 params=768/1024/512/245/0.75/0.375 float=y maxiter=1024 inside=maxiter outside=tdis periodicity=0 colors=000<3>000<9>X0a_0dc0h<3>p0w<4>_0dX0aU0Y<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>f\ 0Ci0Dl0F<3>z0K<6>Z0EV0DR0C<3>A08004000<27>000 } multi215a { ; Brasswork ; Albrecht Niekamp feb,03 ; ; Version 2002 Patchlevel 4 reset=2002 type=formula formulafile=multi5.frm formulaname=Multifrac_215 function=exp passes=t center-mag=-0.648135/-3.9968e-015/0.6666667/1/90/3.88578058618804789e-01\ 6 params=768/1024/512/512/0.5/0.75 float=y maxiter=1024 inside=maxiter outside=tdis periodicity=0 colors=200022000<25>oiQqjRslS<3>zsX<25>CB7A96875<3>000400<23>o00q00s00<3\ >z00<25>C00A00800<3>000<25>iiijjjlll<3>sss<25>BBB999777<2>222000012<24>0\ bo0cq0es<2>0jy0kz0jy<28>034 } multi218 { ; Mandjulin ; Albrecht Niekamp feb,03 ; Mandel with Julia inside ; Version 2002 Patchlevel 4 reset=2002 type=formula formulafile=multi5.frm formulaname=Multifrac_218 function=exp/sin passes=t center-mag=-0.114536/0.775646/7.751938 params=768/2048/128/512/-0.5/0.375 float=y maxiter=1024 inside=maxiter outside=tdis periodicity=0 colors=200iii<3>ppprrrsss<25>BBB999777<2>222000012<24>0bo0cq0es<2>0jy0kz\ 0jy<24>09C08A068<2>022000211<24>oiQqjRslS<3>zsX<25>CB7A96875<3>000400<23\ >o00q00s00<3>z00<25>C00A00800<3>000<24>ggg } multi218a { ; Mandjulin_2 ; Albrecht Niekamp feb,03 ; Mandel with Julia inside ; Version 2002 Patchlevel 4 reset=2002 type=formula formulafile=multi5.frm formulaname=Multifrac_218 function=exp/sin passes=t center-mag=-0.114536/0.775646/7.751938 params=768/2048/128/512/-0.5/0.375 float=y maxiter=1024 inside=maxiter periodicity=0 colors=200554<22>iihjjillk<3>ssr<25>BBA998776<2>221000011<24>0bn0cp0er<2\ >0jx0ky0jx<24>09B089067<2>021000210<24>oiPqjQslR<3>zsW<25>CB6A95874<3>00\ 0400<23>o00q00s00<3>z00<25>C00A00800<3>000110332 } multi218b { ; Mandjulin_3 ; Albrecht Niekamp feb,03 ; inside tdis ; Version 2002 Patchlevel 4 reset=2002 type=formula formulafile=multi5.frm formulaname=Multifrac_218a function=exp/sin passes=t center-mag=-0.550344/3.33067e-016/0.8503401 params=768/2048/256/512/-0.5/0.375 float=y maxiter=2048 inside=maxiter outside=tdis logmap=yes periodicity=0 colors=200G00<4>600<2>000<25>iiijjjlll<3>sss<25>BBB999777<2>222000012<24\ >0bo0cq0es<2>0jy0kz0jy<24>09C08A068<2>022000211<24>oiQqjRslS<3>zsX<25>CB\ 7A96875<3>000400<23>o00q00s00<3>z00<22>I00 } multi219a { ; Inside Exp-Julia ; Albrecht Niekamp feb,03 ; Version 2002 Patchlevel 4 reset=2002 type=formula formulafile=multi5.frm formulaname=Multifrac_219a function=exp/exp passes=t center-mag=-1.00313/0.18015/5.464481 params=1024/4094/256/512/0.5/-0.375 float=y maxiter=2048 inside=maxiter outside=tdis periodicity=0 colors=200G00<4>600<2>000<25>iiijjjlll<3>sss<25>BBB999777<2>222000012<24\ >0bo0cq0es<2>0jy0kz0jy<24>09C08A068<2>022000211<24>oiQqjRslS<3>zsX<25>CB\ 7A96875<3>000400<23>o00q00s00<3>z00<22>I00 } multi219c { ; Mandel Machine ; Albrecht Niekamp feb,03 ; Version 2002 Patchlevel 4 reset=2002 type=formula formulafile=multi5.frm formulaname=Multifrac_219c function=exp/exp passes=t center-mag=-0.597874/2.22045e-016/0.8912656 params=1024/4094/256/512/0.25/0 float=y maxiter=2048 inside=maxiter outside=tdis logmap=yes periodicity=0 colors=200ggg<3>nnnppprrrsss<25>BBB999777<2>222000012<24>0bo0cq0es<2>0jy\ 0kz0jy<24>09C08A068<2>022000211<24>oiQqjRslS<3>zsX<25>CB7A96875<3>000400\ <23>o00q00s00<3>z00<25>C00A00800<3>000<23>eee } multi219d { ; Machinehead ; Albrecht Niekamp feb,03 ; Version 2002 Patchlevel 4 reset=2002 type=formula formulafile=multi5.frm formulaname=Multifrac_219d function=exp/exp passes=t center-mag=0.411007/0.347039/21.09705 params=1024/4094/256/512/-0.125/-0.375 float=y maxiter=2048 inside=maxiter outside=tdis periodicity=0 colors=200SSS<9>iiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0cq0es<2>\ 0jy0kz0jy<24>09C08A068<2>022000211<24>oiQqjRslS<3>zsX<25>CB7A96875<3>000\ 400<23>o00q00s00<3>z00<25>C00A00800<3>000<14>QQQ } ---------------------------------Start-Formulas----------------------------- FRM:Multifrac_204f {;Albrecht Niekamp Feb,03 fac=real(p1) bailout=imag(p1) border=real(p2) out=imag(p2) z=0 t=0 start=1 c=pixel : z=z^2+c if (start) t=t+1 if (|z|>=border) u=2*(fn1(t/fac)) z=z^u start=0 endif if (t>out) u=2*(fn1(t/fac)) z=z/u start=0 endif endif |z|<=bailout } FRM:Multifrac_215 {;Albrecht Niekamp Feb,03 ;p3=julia seed fac=real (p1) bailout=imag(p1) out=real(p2) border=imag(p2) z=pixel c=p3 t=0 start=1 x=0 y=0 : y2=y*y x2=x*x x=x2-y2-real(c) y=2*x*y-imag(c) z=(z*x)^(z*y) if (start) t=t+1 if (|z|>=border) || (t>out) u=2*(fn1(t/fac)) z=pixel c=p3*u start=0 x=0 y=0 endif endif |z| <=bailout } FRM:Multifrac_218 {;Albrecht Niekamp Feb,03 fac=real(p1) bailout=imag(p1) border=real(p2) out=imag(p2) z=0 t=0 start=1 c=pixel : z=z^2+c if (start) t=t+1 if (|z|>=border) u=2*(fn1(t/fac)) z=z^u start=0 endif if (t>out) u=2*(fn2(t/fac)) z=pixel c=p3*u start=0 endif endif |z|<=bailout } FRM:Multifrac_218a {;Albrecht Niekamp Feb,03 fac=real(p1) bailout=imag(p1) border=real(p2) out=imag(p2) z=0 t=0 start=1 c=pixel : z=z^2+c if (start) t=t+1 if (|z|>=border) u=2*(fn1(t/fac)) z=z^u start=0 endif if (t>out) u=2*(fn2(t/fac)) c=p3*u start=0 endif endif |z|<=bailout } FRM:Multifrac_219a {;Albrecht Niekamp Feb,03 fac=real(p1) bailout=imag(p1) border=real(p2) out=imag(p2) z=0 t=0 start=1 c=pixel : if (start) z=z^2+c t=t+1 if (|z|>=border) u=2*(fn1(t/fac)) z=z^u start=0 endif if (t>out) u=2*(fn2(t/fac)) z=z/u c=p3*u start=0 endif else z=z^z+c endif |z|<=bailout } FRM:Multifrac_219c {;Albrecht Niekamp Feb,03 fac=real(p1) bailout=imag(p1) border=real(p2) out=imag(p2) z=0 t=0 start=1 c=pixel : if (start) z=z^2+c t=t+1 if (|z|>=border) u=2*(fn1(t/fac)) z=z^u start=0 endif if (t>out) u=2*(fn2(t/fac)) z=z/u c=p3/u start=0 endif else z=z^z+c endif |z|<=bailout } FRM:Multifrac_219d {;Albrecht Niekamp Feb,03 fac=real(p1) bailout=imag(p1) border=real(p2) out=imag(p2) z=0 t=0 start=1 c=pixel : if (start) z=z^2+c t=t+1 if (|z|>=border) u=2*(fn1(t/fac)) z=z^u start=0 endif if (t>out) u=2*(fn2(t/fac)) z=z/u c=p3^u start=0 endif else z=z^z+c endif |z|<=bailout } --------------------------------------------------end-formulas------------------------------------------------

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Re: [Fractint] Fractint frm and par files
by Franktal Gallery 13 Mar '03

13 Mar '03

Albretch, >My second main interest is conversion of fractals into fractal (midi) >music with "infinite" fractal rhythms that are similar but never repeat. >Iïm convinced that there IS something like fractal music. >If you`re interested, please email me privately or on the list. You might give a look at http://www.geocities.com/franktal2002/sounds.html There's a PAR file with some of my older fractal compositions. On this list there was some discussion a couple of years ago about conversion to MIDI, I could forward some of the messages to you if you´re interested. Regards, Miguel Fliguer - Buenos Aires, Argentina Franktal gallery - http://www.geocities.com/franktal2002 _________________________________________________________________ Add photos to your messages with MSN 8. Get 2 months FREE*. http://join.msn.com/?page=features/featuredemail

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FOTD 08-03-03 (Classic Mandelbrot [5])
by Jim Muth 09 Mar '03

09 Mar '03

FOTD -- March 08, 2003 (Rating 5) Fractal visionaries and enthusiasts: Today's image takes us back to perhaps the most familiar of all fractal areas -- Seahorse Valley of the classic Mandelbrot Set. This is the first area of the first fractal I investigated when I loaded my first fractal-generating program those many years ago, and the area still holds undiscovered surprises. Today's image illustrates a second-order midget that lies in the suburbs of a larger midget that lies fairly deep in the eastern shore of the north branch of Seahorse Valley. The parent midget quite closely resembles the midget in the image, though, being of a much lesser magnitude, the surrounding pattern is packed closer to the midget itself. I named the image "Classic Mandelbrot" for obvious reasons. Since it is part of such a familiar area, I could rate the picture no higher than an average 5. The render time of almost 4 hours, (at least on my machine), makes a download of the finished GIF image almost compulsory. The download may be found on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and on Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The FOTD-CD is moving slowly toward completion. (I do realize I have said this before!) The slowness is caused by the fact that for every problem I fix, I find a new problem that needs fixing. The problem I'm currently working on was created when I altered formulas without changing their names, which causes parameter files to go to the wrong version of the formula and come up blank. When I solve this problem, I can begin changing the cryptic names of the GIF image files to names that corres- pond to the dates of the discussion. Hopefully, when this is done, I will make the big announcement. With a high remperature of 35F 1.5C, the fractal weather Friday was too chilly for the cats' paws. Also, the ground is still snow-covered. As a result, the duo spent the afternoon indoors, impatiently waiting for spring to arrive. But today (Saturday) was warmer, and the duo endured their wet cold paws as they spent a half hour checking their territory in the 50F 10C air temperature. I spent the day working and trying to iron out the problems in the FOTD CD. But Sunday I'm going to take a break, and forget work and fractals until Monday. Until next Saturday, when the next FOTD will appear, take care, and anything worth having is worth waiting for -- especially a few thousand fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Classic_Mandelbrot { ; time=3:57:10.20--SF5 on a P200 reset=2002 type=mandel passes=1 center-mag=-0.74963267010048157994/0.0428524754544\ 0457101/1.854429e+015/1/-14.9995309297261645/0.002\ 6741626797626844 params=0/0 float=y maxiter=32000 inside=0 logmap=3037 periodicity=10 colors=0001KQ2KQ2KQ3KQ3KQ4KQ4KQ5KQ5KQ9KMDKJHKGLKDP\ KATK7XE4ZH8_KBaNEbPHdSKeVNgYQh_TjbXke_mhbnjepmhqok\ snntlqrjpphoofnmdmlblj_kiWjgTjePidLhbIgaEf_AeZ7dX3\ cW0cXAdYFeZKf_Pg`UhaZibcjbhk`ml_nmYonWpoVqpTrqRrrQ\ psOnrMlpLjnJhlHfjGdhEbfC`dBZb9X`7VZ6TX4RV2PT1OR3PQ\ 4QP5QO6RN8RM9SLASKBTJCUIEUHFVGGVFHWEJWDKXCLYBMYANZ\ 9PZ8Q_7R_6S`5T`5UZ8VXBVVDWUGXSJXQLYOOZNRZLT_JW_IY`\ KXaLXbMXcNXdPXeQXfRXgSXhTXhVWiWWjXWkYWlZWm`WnaWobW\ pcWpdWkaYgZ_bW`ZUbURcQOeMMfNOgOPhORiPSjPTkQVlQWmRX\ nRZoS_oSapTbqTcrUesUftVguVivWjwWkwVlsVmpVnmUnjUogU\ pdTqaTqYTrVSsSStPStMRuJRvGRvDSsCSqCUoCZmCckChjCmkC\ rlCwmBznBwoBrpBmqBhrBcsBZtBUuNPvYKtZFs_Fr`JqaNpbRn\ bVmcZldbkefjfjifkkellemmenneooeppeqqdrrdssdttduudu\ vdpxWkyNfzEgzHgzJgzMgzOgzQgzTgzVgzXgz_gzagzdgzfgzh\ gzkgzmgzogzrgztgzvezucztbzs`zr_zqYzpXzoWzlWzjWzhWz\ fVzdVzbVz_MzKFzM7zO0zQ1zQ } END PARAMETER FILE=========================================

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OT: Request for Book on Bitmap Graphics
by Bill Jemison 08 Mar '03

08 Mar '03

Painter is a Corel product (still). They recently that Painter8 will be out later this year. Bill

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Off topic posts
by Harold Lane 08 Mar '03

08 Mar '03

################################################### Jim, You posted off topic and now all of us are reaping the rewards. Please be more sensitive to this. You have indicated you would do so in your previous posts. Thank you - Hal Lane Thu, 6 Mar 2003 > > . . . > > The foolish headlong > >rush into war by certain powerful leaders is a > >not-so-trivial example of a lesson that may not be > >learned until it is too late. > >Jim M. --__--__-- >I entirely agree, and suggest a solution. There's another piece of = >unfinished business out there, dating from the Reagan era, which was = >labelled a National Security threat. The 1983 invasion of Grenada< > . . . >John W. ################################################### Here is another unrelated instance of off topic posting that should have been sent as a private email: Thu, 6 Mar 2003 > > . . . > > Nobody can go to a war is he/she is only > >half-convinced of what he/she is doing. The americans should be sure to > >have many friends in Germany. Independent of a government's decisions. > > . . . > >AND SORRY FOR BEING TOTALLY OFF TOPIC :-/ >No problem at all, Micheal... >David It is a problem, David, Michael. - Hal Lane ###################################################

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Re: [Fractint] Off topic posts
by Jim Muth 08 Mar '03

08 Mar '03

At 05:11 AM 3/8/03 -0500, you wrote: > >Jim, You posted off topic . . . Perhaps . . . but if existence itself is fractal in nature, as the original letter in the thread speculated, it would be impossible for anything to be off-topic. Hovever, I agree that this is the wrong place to discuss politics, be the topic fractal in nature or not. (Next FOTD coming in about 16 hours) Jim M.

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digitale Panoramafotos
by JoWeber 08 Mar '03

08 Mar '03

Hi, I added a new section to my website with digital panoramaphotos - inspired from those on the site of Les St. Clair. http://www.joweber.de Enjoy --Jochen Weber--

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Re: [Fractint] I discovered a great site for adults:
by Jim Muth 08 Mar '03

08 Mar '03

At 05:14 PM 3/7/03 +0000, Betty Trimbo wrote: >Hi, >I was surfing and discovered a great site for Adults: >http://www.HappyHug.com Does the site have adult fractals on it? ;-) Jim M.

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I discovered a great site for adults: http://www.HappyHug.com
by Betty Trimbo 07 Mar '03

07 Mar '03

Hi, I was surfing and discovered a great site for Adults: http://www.HappyHug.com This is a new site for adults. They are operating since 9 december 2002. It looks good to me!! Betty _________________________________________________________________ Help STOP SPAM with the new MSN 8 and get 2 months FREE* http://join.msn.com/?page=features/junkmail

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Re: [Fractint] OT: Request for Book on Bitmap Graphics
by gnome＠hawaii.rr.com 07 Mar '03

07 Mar '03

>Am Dienstag, den 04. März 2003, um 15:16h schrieb gnome(a)hawaii.rr.com: > >> >Am Montag, den 03. März 2003, um 23:44h schrieb Mike Traynor: >> >> a professional commercial artist making a very late transition to computer? >> >As 'traditional' artist he is probably an experienced sketcher. So software >> >like Adobe Photoshop >> >> Forget Photoshop. Get Painter 7. That's the tool for 'traditional' artists. >> Photoshop's a tool for prepress imaging production staff and collage workers, >> not for artists. > >I'm not an artist and I don't know "Painter 7" >is it 'Fractal Painter'? >Does it still exist? (Didn't the Corel monster swallow it?) Still exists. Corel bought it, brought out the excellent v7, then sold it (and the other Fractal Creations products) to Metacreations, IIRC. >so you are probably right... > >although collages are a significant are of computer arts (imho). >Also these amazing (Macromedia) Flash animations and website design in >general is (a new kind of art impossible without computers). Basic animations don't require computers - Disney's been doing animation without computers since the 1920's. But *interactive* animation and such realistically requires computers ... >> >and a sketching tablet (like those from Wacom) >> *Only* those from Wacom. The rest are clunky junk by comparison. (Warning: I've >> been using Wacom tablets for 8 years now.) > >are you just using them together with Windows software? >I've seen them working perfectly under Gimp (Unix/Linux >Photoshop-like software - inexpensive alternative) I know they work with The GIMP (I use it on my Linux box at home). It's free, BTW. I just don't have a graphics tablet set up on the Linux box. >> >are >> >suitable for a painless transition. There are many tutorials on >> >Photoshop on the Internet - a book on Photoshop will also be helpful. >> >> Several books and video tapes and online tutorials will be helpful with Photoshop. >> It has the worst user interface in the graphics business. ;-) > """"""""""""""""""""""""""""""""""""""""""""" >You can't see the Image anymore because all of these toolbars and boxes? ;-) That's part of it. Very cluttered. And too many times you have to change settings at several different places to get the results you want, and sometimes finding those places is very difficult. >> >regards from Germany... >> And how is life in Germany right now? > >here it bursts out of me: > >Many of our politicians (throughout all paries) are populistic flops. >And Media seems to influence politics in a negative way. Really necessary >reforms get spoiled by various lobbies. > >Nearly 5*10^6 (of 82*10^6) people are unemployed. There are more and >more old people and less babies which creates problems with annuities >and social wellfare. > >But justice is consistent and consequential protecting human rights: >Policemen are judged (who threatened a hijacker with torture until he >told where he hid the child - he had already killed). Not to >misunderstand me: As long as justice stands this hard test, everything >is ok. > >but after all life is not too bad ;-) > >And to topic No. 1: >Very few Germans are patriots (in the sense of the American patriotism >sensed here - which worries many Germans) and religious fundamentalists >have no politic influence. Consequently the German foreign politics >sould be more unemotional and logic - but it is not. I think 'Peace' is >the correct answer but not the logic consequence of German foreign politics >(without American/international pressure there wouldn't be any disarming >inspectors and no disarmament). > >If your government thinks it can just replace the dictator it is probably >wrong (but maybe I am wrong, too) (IMO the situtation 1945 in Germany was >totally different). Yes, Hitler was actively attaching and annexing other countries. When Mr Hussein tried it (in Kuwait) the UN and US stepped forward and stopped it. I think a better word for "patriot" would be "nationalist." >Fundamentalistic religious idiots in these countries >see an upcoming crusade, imperial colonialism, ... and their braindead >answer is more fundamentalism, 'Djihad' and violence (see Israel and the >islamic terrorism). Yes, the problem is in many places ... >These countries missed the (historic) Enlightment. Hmm, one could argue that the Enlightenment didn't really change people. It increased the variety of ideas and technologies available, and made some social changes, but people were still eager to rush to war, use the new technologies for war, and (in a sense) it opened the door for changes like the Industrial "Revolution" which primarily led to a lot of social upheaval and mistreatment of individuals and laid the groundwork for the phenomena of modern war, as shown in the two World Wars ... >The people are poor >and feel cheated when they look at the "first class world". The >gonvernments are underdeveloped. But it's up the inhabitants to choose >their government and it's up to us to help them - but not with the "wooden >hammer method" - with education for example (and not with German machine >parts for weapon factories). Catching terrorists is like prescribing a >medicie against headache when the patient needs an antibiotic - it >medicates the symptoms and the patient feels better for a short time >while his situation gets worse. I hope this doesn't sound too arrogant. > >And please don't think the Germans are "anti-americanistic". This is >nonsense. Many Germans agree with the american war plans - perhaps more >don't - including me. But I don't feel anti-americanistic because of >that. An American's situation is - IMHO - more difficult: He/she has to >reason and to justify if and why he/she or one of his/her relatives is >going to war. Patriotism probably helps (while religion is not very >helpful ... even if your president tries to polish this by talking of >"god's own country"). Nobody can go to a war is he/she is only >half-convinced of what he/she is doing. The americans should be sure to >have many friends in Germany. Independent of a government's decisions. > >sorry for my stumble-english ... >AND SORRY FOR BEING TOTALLY OFF TOPIC :-/ No problem at all, Micheal. I wish I had time to respond to the rest of your note, but gotta go out the door right now! David gnome(a)hawaii.rr.com

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New list software coming
by Tim Wegner 06 Mar '03

06 Mar '03

Just a heads up that xmission is upgrading this list's software to the latest version of mailman. This may happen this weekend. I'm alerting you just in case there are any problems. After the change you may want to check your user settings on the user admin web page (in case you didn't know, you have a lot of ability to tweak the your list membership). There may be some new settings. Normally list management is OFF topic, but I don't mind discussing it for a few days through this transition. I'll alert everybody after the change. Tim Fractint List Administrator

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Re: [Fractint] History
by Jim Muth 06 Mar '03

06 Mar '03

At 09:46 AM 3/6/03 -0800, John Wilson wrote: > >All you have to do is seize the moment, and you can >benefit. Go forth and purchase a pump for that >basement of yours, and install it. Then one of >those harsh lessons [of life] will have borne >fruit! :-) A trivial problem that leads to a trivial example of learning from experience. The foolish headlong rush into war by certain powerful leaders is a not-so-trivial example of a lesson that may not be learned until it is too late. Jim M.

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Re: [Fractint] OT: Request for Book on Bitmap Graphics
by gnome＠hawaii.rr.com 06 Mar '03

06 Mar '03

>Hi Mike, > >Am Montag, den 03. März 2003, um 23:44h schrieb Mike Traynor: > >> Would anyone be able to recommend something in the way of a book on >> bitmap graphics for a guy who is >> a professional commercial artist making a very late transition to computer? > >As 'traditional' artist he is probably an experienced sketcher. So software >like Adobe Photoshop Forget Photoshop. Get Painter 7. That's the tool for 'traditional' artists. Photoshop's a tool for prepress imaging production staff and collage workers, not for artists. >and a sketching tablet (like those from Wacom) *Only* those from Wacom. The rest are clunky junk by comparison. (Warning: I've been using Wacom tablets for 8 years now.) >are >suitable for a painless transition. There are many tutorials on >Photoshop on the Internet - a book on Photoshop will also be helpful. Several books and video tapes and online tutorials will be helpful with Photoshop. It has the worst user interface in the graphics business. ;-) >And of course one of these neat digital cameras ... (for doing >collages, ...) > >A 3d-software (like Cinema4D for example) will also be interesting. >Perhaps a less expensive demo-version will do the job ... > >... to frighten him ;-) > >AND OF COURSE A FRACTAL GENERATOR! :-) >let him do some rotations through the fractalus.com 'ifl' web ring. Yes, yes, get him producing some fractals! Someone with so much grapics experience must have a great eye! >regards from Germany... And how is life in Germany right now? David gnome(a)hawaii.rr.com >-- >Michael > Weitzel ... all work and no play makes Jack a dull boy ... > >_______________________________________________ >Fractint mailing list > >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint >

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Re: [Fractint] History
by Jim Muth 06 Mar '03

06 Mar '03

On Wed, 05 Mar 2003 at 22:17 Paul Lee wrote: >>Mark A. Freeze wrote: >> >>Isn't history fractal in nature? >Sadly to say, this is true. Humans are forever doomed to >keep iterating the same mistakes over and over again. A poorly developed system, I would say. When we finally realize how we should have lived our lives, it is too late to put our knowledge into practice. And trying to impart our wisdom to our children is equally futile. Whoever or whatever created the human condition, (random evolution according to science), did amazingly well when it developed our fractally intricate bodies. Too bad it fumbled the ball by giving us so little chance to reap the benefits of the often harsh lessons of our lives. Jim (FOTD-CD is progressing) Muth

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Re: Fractint digest, Vol 1 #415 - 4 msgs
by JackOTradez 06 Mar '03

06 Mar '03

Re: History and Philosophy : For those so inclined, if you can dig up the journal "New Scientist" (it's British) either hardcopy at the library or online, find the August 21, 1999 issue. An article describing the entire Universe as a Fractal. Space and Time are chaotic in nature. Every moment in life has ahead of it an infinite number of "forks" or choices. And yes, if History teaches anything, it teaches that it DOES repeat itself (iterate), over and over . . .. ... ..... ........ or put another way - "there is nothing new under the sun . . .. ... ..... ........ " dreams and hallucinations - JoTz

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Re: [Fractint] History
by Mark Christenson 06 Mar '03

06 Mar '03

At 07:37 AM 3/5/03 -0600, Mr. Freeze wrote: >Isn't history fractal in nature? Certainly, in the same sense as any timeline, including your or my life. Every instant offers a multitude of paths. I am alternately amused and dismayed by the twists and turns *my* timeline takes. Bud

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Missing video parameters
by Stillhard Peter 05 Mar '03

05 Mar '03

Dear sirs I would like to run fractint in 1024x768, 256 colours. My videoard is a GeForce 4 MX-440. Can anybody give me the video parameters for the fractint.cfg file? Thank you in advance. Best regard Peter Stillhard _______________________________________________________________________ Siemens Schweiz AG, Electronic House, DE ID4 Peter Stillhard, EMC Engineer Albisriederstrasse 245, CH-8047 Zürich Telefon +41 (0)585 583 513, Fax +41 (0)585 543 912 mailto:peter.stillhard@siemens.com, Internet: http://www.siemens.ch/ Important Note: This e-mail may contain trade secrets or privileged, undisclosed or otherwise confidential information. If you have received this e-mail in error, you are hereby notified that any review, copying or distribution of it is strictly prohibited. Please inform us immediately and destroy the original transmittal. Thank you for your cooperation.

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OT: Request for Book on Bitmap Graphics
by Mike Traynor 04 Mar '03

04 Mar '03

Fractal folks, Would anyone be able to recommend something in the way of a book on bitmap graphics for a guy who is a professional commercial artist making a very late transition to computer? Mike

4 4

FOTD on vacation
by Jim Muth 02 Mar '03

02 Mar '03

On Vacation. Having a wonderful time. Lots of work yet to do on the CD. Cats remain unhappy. All else is well. Next FOTD on March 8. Jim M.

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stop
by Howard 02 Mar '03

02 Mar '03

stop

2 1

RE: Confiscation of Domain Names
by Harold Lane 02 Mar '03

02 Mar '03

From: "Paul N. Lee" <Paul.N.Lee(a)Worldnet.att.net> Subject: Confiscation of Domain Names > Want to see what happens when the U.S. > Federal Government decides > someone has violated a law and uses a > web site during the process?? > Here is the Domain of someone found > guilty to felony copyright crimes > under the controversial Digital > Millennium Copyright Act (DMCA): Please keep posts on the topic of fractals. You risk many people responding to your post and the consequences this brings with it. - Hal Lane hallane @ compuserve.com

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FOTD 01-03-03 (Ring of Fire [5])
by Jim Muth 01 Mar '03

01 Mar '03

FOTD -- March 01, 2003 (Rating 5) Fractal visionaries and enthusiasts: This will be the last daily FOTD until the Fractal Central chores have been finished and the FOTD-CD is ready. I simply do not have the time to do the work than needs to be done and bring the CD to a fully-functional condition while keeping the FOTD going on a daily basis. Until the other work is finished, the new FOTD's will appear on a weekly basis on Saturday evenings Eastern Standard Time, which is five hours behind Greenwich Time. On the other six days, I will be spending my limited spare time catching up on repairs and doing what I should have done at the start to make the FOTD disk fun to use rather than a puzzle. (As a curious side note, the kind of oversights I made in the preparation of the disk are the same kind that I sometimes criticise my custo- mers for making in the jobs they bring.) Today's image combines portions of Z^2, Z^3, Z^4, and Z^5, a combination that has its critical point at zero, making tedious calculation unnecessary. The parent fractal is a rather normal Mandelbrot set surrounded by disconnected satellites. Today's scene is located in a minor valley on a spurious caterpillar- like feature that appears on the negative X-axis, some distance beyond the tip of the main negative stem. I have named the image "Ring of Fire" not because of any volcanic appearance, but because of the brilliant red-and-yellow ring of fractal elements surrounding the midget. The rating of 5 means I consider the image to be merely average. But it is still an interesting scene, perhaps not quite worth the 24 minutes required to render from the parameter file, but still worth the small effort of downloading it from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather Friday stayed cloudy all day. In the afternoon the temperature rose to 38F 3C, but this just made the snow wet and sloppy -- far too unpleasant for the cats' paws. They passed the day sleeping by the heat and occasionally asking for food. 12-year-old cats are not known for unnecessary activity. As for me, I'm taking a break in the FOTD until the above- mentioned chores are finished and the much-advertised FOTD-CD is ready for distribution. Until next Saturday, take care and have no concern. I am not losing enthusiasm. I will continue to be active on the lists, and the FOTD will resume its daily basis as soon as the other tasks are finished. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Ring_of_Fire { ; time=0:24:43.82--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix3a function=ident passes=1 center-mag=-2.99778179408523300/+0.001233816310509\ 62/9557373/1/170/5.11641841047238977e-008 params=1\ /2/0.2/3/0.1/4/0.03/5/0/0 float=y maxiter=1200 inside=0 logmap=123 periodicity=10 colors=000AKWAKZAKaAKdAKgAKjAKmBKpFLsKStOYtTctXitV\ SnTBiSIdRO_QUVP_QOeLNkGMqBUiT`aigUz_0Db1Gd2If3Kh4M\ j5Ol5Ql5Tl5Wl5Zl5al5dl5g4m37f49_4CT4EN4HG4J94h34u0\ BvZPwcbxmoszgszauzWszRqzLnzFkzAnoCpeDrXFuNGwDIy4Jx\ 9LwDNvIPvMRuRTtVVtZXnTTiOPdIM_DIV8FR7IO7LK7OH7RD6U\ A6X66_36bq8gjFadMWZTQT_KNfEml8mkzmkL8kR5kY2kc0ki6f\ lBbnHZpMVsSRuXNwaJyeIxiHwlGwpGvsFvwEuzEutGonIihKcb\ MZXOTRQNLRIqEcpGgoHkoInnJrmKvmLyOutYgrgUqpHpeDqV9r\ K6rP8nU9kZBgcCdhEamFYrHVvISqJYlKbgLgbLleIihEgkBdn8\ bq5`lD`gK`bR`ZY`V`YRcVOfTKiQHlODoLArJ6uG3wE7xHBxKF\ yNJyPNySRzVVzYYz_ZyYZyX_yW_yV`xU`xTaxSaxQbxPbwOcwN\ cwMdwLdwKUmCJc5I_BHXHGUMFQSENXDKbCHg68X79Y7AZ8A_8B\ `M_MHXHCTC8Q8BPFDPLGOSIOYKOcNNjPNpRNvLbZGqCFoBEmAD\ lACj9Bh8Ag89e78d77hF6kN5oV4rb3vj2yqCzgMzYVzPdzFmz6\ izFfzNbzV_zbWzjTzr_ztfzumzwtzxqzjnzYjzWfzVbzT_zSWz\ QSzPPzOfzFwz6rzEmzMhzUgzY } frm:MandelbrotMix3a {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END 20.0 PAR-FORMULA FILE==================================

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Confiscation of Domain Names
by Paul N. Lee 28 Feb '03

28 Feb '03

Want to see what happens when the U.S. Federal Government decides someone has violated a law and uses a web site during the process?? Here is the Domain of someone found guilty to felony copyright crimes under the controversial Digital Millennium Copyright Act (DMCA): http://www.iSoNews.com/ And here are some other Domains where other laws were allegedly violated: http://www.ColorChangingGlass.com/ http://www.420now.com/ http://www.OmniLounge.com/ http://www.PipesForYou.com/ Sincerely, P.N.L. ------------------------------------------------- http://home.att.net/~Paul.N.Lee/PNL_Fractals.html http://www.Nahee.com/Fractals/

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FOTD 28-02-03 (Minibrot Snowstorm [6])
by Jim Muth 28 Feb '03

28 Feb '03

FOTD -- February 28, 2003 (Rating 6) Fractal visionaries and enthusiasts: For at least a month, the view from the Fractal Central windows has shown everything covered in snow. So why cannot a fractal be in a snowstorm? In fact, as the name "Minibrot Snowstorm" implies, a snowy fractal is exactly what we have today. The snowstorm was created by combining portions of 1/Z, Z, Z^(-1.6) and Z^(-1.4), and then adding 1/C to produce a not-very- impressive parent. At first glance, the parent appears to have no open areas, but a careful examination shows it to be riddled with midgets too small to be visible at the default magnitude. Today's scene is located in the eastern suburbs of a larger but still quite tiny midget. The entire production is through the courtesy of the MandelbrotMix3a formula, which is like the workhorse MandelbrotMix4 formula except that it combines 4 different powers of Z rather than 2, and a critical point must be calculated by hand, an operation that is little fun. The rating of a 6 seems about right for an image that has a brief impact, then soon grows boring -- a sure sign of a work with insufficient artistic merit. The render time of 10 minutes on my 200mhz Pentium-I machine is a bit slow for an image only slightly above what I currently consider average. A more efficient way of viewing the snowstorm is to go to Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or to Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> and download the completed image from there. Thursday was cold and cloudy here at Fractal Central, with the snow flurries that fell during the day turning to steady snow in the evening. The snow plus the high temperature of only freezing kept thoughts of the outdoors far removed from the cats' minds. They satisfied themselves instead with a treat of turkey. Today is starting with light snow and 6 fresh inches 15cm on the ground. I guess this means more turkey for the dynamic ones. For me, it means more sidewalk clearing. I'll wait until the snow stops falling to begin. Until the next FOTD appears, most likely in 24 hours, take care, and savor every fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Minibrot_Snowstorm { ; time=0:10:47.74--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix3a function=recip passes=1 center-mag=+3.26650108165485/-0.05084635835292/4.9\ 03911e+008/1/-112.5/7.4048215368e-006 params=-1/-1\ /1/1/1/-1.6/-1/-1.4/0.2858095886402/0 float=y maxiter=800 inside=0 logmap=103 periodicity=10 colors=000mNzqVzu`zxezzmzzszzxzzzzzzzzzzzzzzzzzzzu\ zzmzzezuXzoPzkGxe8v`0sV0qP0mJ0kG0gC0dA0`80X60V40R2\ 2N06J0AG0EE0HA0L60P20T00X00`00d00g00k00g00e00d00b0\ 0`00Z00X00V00T20T80RE0PJ0NP0LV0K`0Pe0Uk0Zq0cu0hz0m\ z0rz0wz0zz0xz0uz0qz0my2ix4ew4av6Yu8Tu8NuAJuCGuCCuE\ 8uG4uG0uH0uJ0uJ0uL0uL0uN6uNGsPPqPZmRggRqbTzXTzRVzN\ VzRXzVXzXXz`XzbXzeXxgXukXsmXoqXmsXivXgxXdzXbzXZzXX\ zXTzXRzXTzZTz`VzbVzdXzeXzgZziZxk`vm`uobsqbqsdoudmv\ ekxeizegzgdugboiZkiXekT`kRXmNRmLNoHHoGCqC8qA2s60s4\ 0u00u00vE0vREvdRvqevzuvzzqzzmzvizqezkbzeZz`VzVRzPN\ zJJzEGz8Cz28z04z00z00z06z0EzHLz`TzqVxoVxoXxmXxmZxm\ Zxk`xk`xk`xibxibxgdxgdxgexeexeexegudgqdgobikbig`ie\ `ib`kZZkXZkTXkRXmNVmJVmHVmEToATo8Ro4Ro2Rm4Vk4Xk4Zi\ 6`g6dg6ee8ge8id8mb8obAqdAsgAvkCxoCzsCzvCzzEzzEzzEz\ zGzzGzzGzzGzz8zz2zz0zz0zz0zz0zz0zz0zz0zz4zzEzzNzzT\ zzTzzTzzTzzTzzTzzTzzTzzTz } frm:MandelbrotMix3a {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 27-02-03 (Cometary Impact [6])
by Jim Muth 27 Feb '03

27 Feb '03

FOTD -- February 27, 2003 (Rating 6) Fractal visionaries and enthusiasts: For today's fractal we return to the rubber duck that is the parent of yesterday's FOTD image. In today's image the duck has been evaporated and its remains made visible by the < bof60 > inside fill. This fill creates images that consist of sheets and strings of bubbles, a feature that is quite prominent in today's image. I named the image "Cometary Impact". The impression of a cloud of comets streaming toward earth from a vanishing point shaped like a Minibrot is strong. I rated the image at a 6. It could be worth more, but I'm in a rather down mood this morning, and I do not see that much in the picture. The render time of over 3/4 hour is due to the fact that the image consists totally of trapped inside points. The wait may be avoided by downloading the finished image from the W.W.W. at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Light snow that fell all day amounted to 1-1/2inches 4cm, and kept the fractal duo housebound Wednesday. The temperature of 23F -5C helped not a bit. As a result, they were once again sullen, more accurately sleepy, since they did little but sleep. The treat of tuna was changed to turkey, which made their evening brighter. It's snowing again today, so I expect a repeat. I'll be very busy again today -- it's getting to be a habit. Maybe I need a vacation, but if so, it will have to wait, so until tomorrow, take care and don't give up the faith. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Cometary_Impact { ; time=0:48:50.05--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.59436303489694950/+0.011310676304601\ 45/131242.7/1/-152.5/3.79135223216309214e-010 params=-2/-1.8/2/0.75/0/1e+100 float=y maxiter=2500 inside=bof60 logmap=yes periodicity=10 colors=000qX`pWXoVTnUPmTLlSHkRDjQ9iP4hO5gN6fM7eL8d\ K9cJ8bI9aH9`G9_F9ZE9YB9X79X37W49V5BV6DU7FU8HT8IT9K\ SAMRBORCPQDQQDSPEUPFWOGYNH_NHaMIcMJeLKgLLiKMkJMmJN\ oIOqIPsHQtIRtHQuHQtHPtHPrHOqHOoHNnHNmHMlHMkHLiHLhH\ KgHKfHJeHJcHIbHIaHH`IEZHH_HJ_GL`GN`FPaFRaETbEWbDYc\ D_cCadCcdBeeBgeAjfAlf9ng9pg8rh8th7vi8zj7xi7vh7tg6r\ f6pe6ne5ld5jc5ib5ga4ea4c`4a_3_Z3YY3WX2UX2TW2RV2PU1\ NT1LT1JS0HR0FQ0DP0CP3EN5FM7GL9HKBIJDKIFLHHMGKNFMOE\ OPDQRCSSBUTAWU9YV8ZX8_W7_W7_W6`W6`W6`V5`V5aV5aV4aV\ 4aV4`U4_T5_S5ZR5YQ5XQ6WP6WO6VN6UM7TL7SK7SK7OIIKGTG\ EcCCn9AyBDwauP_tOXtNUsMRrLPrKMqJJpIGpHEoGBnF8nE5mD\ 1p83mC4jF6hI7eL9cOA`RCYUDWYFT`GRcIOfJLiLJlMGoNErQF\ nSFjUGfWGcZG_`HWbHSdHP`ITXIWUJZQJaMKeJKhFLkCLnENoF\ OoGPpHQpJSqKTqLUqMVrOXrPYsQZsR_sS`tUbtVcuWduXeuZgv\ _hv`iwajwbkwdhsefpfdmgbjh`giZdjX`kVYlTVmRSKo`Nn`Pn\ aSnaUmbXmcZlcaldckdfkehke } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 26-02-03 (Rubber Duckie-01 [7])
by Jim Muth 26 Feb '03

26 Feb '03

FOTD -- February 26, 2003 (Rating 7) Fractal visionaries and enthusiasts: A day or so ago I mentioned a fractal I had found that is shaped like a rubber duck. That fractal is the parent of today's image, which lies in the valley that forms the chin area of its rubber-duck parent. The image is actually a disconnected one, lying in an isolated spiral some distance inland from the normal shoreline features. I named the image "Rubber Duckie-01" because I expect to find several more FOTD images hidden somewhere in the parent duck. I rated the image at a 7, which is the highest rating in several days. The unusual definition and clarity of the features earns the above-average rating. Plus, I rather like the colors. The render time of over 11 minutes can be avoided by letting Paul and Scott render the image and by then downloading the finished product from their web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Tuesday was a chilly day here at F.C., with a temperature that barely made it up to freezing, little sun, and a brisk north wind. The cats disapproved, but they have been disapproving so much lately that it's hardly worth commenting on. The tradi- tional treat of tuna eased their sullen moods. It's snowing again this morning, so more tuna may be needed. For me, it's another day and another rush. If I'm lucky, tomorrow's FOTD will be better than today's. Check then to see if I'm lucky. Until next time, take care, and what is it all worth? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Rubber_Duckie-01 { ; time=0:11:36.46--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=mandelbrotmix4 function=recip passes=1 center-mag=-0.35298570355113070/+0.250536664003145\ 20/1.41169e+009/1/149.35/-2.30686683135722381e-006 params=-2/-1.75/2/0.75/0/0 float=y maxiter=1200 inside=0 logmap=200 periodicity=10 colors=0006B3582351120AOS9MQ8KO8JM7HKEVtEStDQtCOtC\ LtBJtBHtDLuEOuFRvHUvIYwJ`wKcwMfxNixOmyQpyRszSvzTsz\ PlzMazJDtIEbHFJGGOFHTEIYDJbCKgCKlFJmHJmJJmLJmOJnQJ\ nSJnUJnXIoZIo`IobIoeIpgIpiIpkIplNqlRrmVsmZtnbtnguo\ kvoowpsxpvxntumrrlpoknljliijfhhcgfaccZ`_WYXTUUQ`XR\ aZUbaXcc_dfbehefkhgmkhpnirqjutkwwlyzlvultqlrmlphln\ dll`liWlgSleOlcJlaFl_BlY7kZCjZHi_Lh_Qg_Vg`Zf`ce`hd\ alcaqcauXerRipKmmEqk8ti9sgAreBrcCqbDq`EpZFpYJoaMoe\ PoiTomWoqZouaoxYooVofSoZPoQMoIJjMGePEaTBXW8S_6Ob3J\ f1Fi4R_6aRAcQEdQHePLgPPhPSiOWjO_lObmNfnNioNfnPcmQ`\ lSYlTVkUTjWQiXNiYKh_Hg`FgaDgRCgGEdHGbIH_JJYKKVLMTM\ NQNPONRLOSJPUGQVERXBSY9T_6U`4Ub4Vd4Vg3Vi3Wk3Wm2Wo2\ Xr2Xt1Xv1Yx1Yz1Yw0Wt0Uq0Tn0R120k0Ph0Oe0Mb0L_3JX8HU\ 9GRCEOFCLIBIL9FO8CR69U46X33_1BbJ9eG8hE6kB5n94q72t4\ 1w2jzrdzk_zeVz_QzUKzOFzIAzC5z6XzFVzETzDRzCQzBOzBMz\ AKz9Jz8Hz7Fz7Dz6Cz5Az48z3 } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 25-02-03 (Candy Ring [5])
by Jim Muth 25 Feb '03

25 Feb '03

FOTD -- February 25, 2003 (Rating 5) Fractal visionaries and enthusiasts: Today's image is one of the grainiest of all time. The parent fractal is nothing more than a symmetrical pair of fragmented arcs, with little that appears to hold promise. The arcs do contain midgets however, and some of them are shaped most unusually. But for today's FOTD I have chosen a perfectly normal quadratic midget. I named the picture "Candy Ring". The ring of brightly colored spots surrounding the midget reminds me of a dish of candy that a child would love to dive into. The pattern around the midget is quite ephemeral, and quite dependent on the chosen palette of colors. Without a carefully chosen palette, the entire image deteriorates to a featureless expanse of fractal sand. The rating of 5 is nondescript. The image is neither good nor lacking. It simply exists, a mathematical abstraction that has never before been seen and never again will be seen. But this might not be totally true. If the universe is infinite, there are an infinity of fractalists sitting at an infinity of computers viewing this same image at this very moment. Of course, there is no such thing as this very moment throughout the universe, but that's relative, and therefore another story. I am getting letters asking the status of the FOTD-CD, and when it will be ready for distribution. The disk is basically finished. The material is gathered into one huge directory and ready to be copied onto a CD. The problem is that my artistic nature is exerting itself. I am not yet satisfied with the disk. I want it to be better -- as good as possible. I originally had planned to include on the disk the short stories I have written over the past 20 years or so. The stories are still ready to go onto the CD, but I have developed grave doubts about their worth. I would rather be known as a good fractalist than a marginal want-to-be writer. I also had originally planned to include on the disk the heated philosophical debates that I have had over the years with both believers and skeptics. These are also ready to go, but the more I think about this, the less I like the idea. The CD should be a fun thing, not a forum for fruitless and sometimes angry debate over things such as religion. Another hold-up is that I have been unable to locate a group of my earliest images, dating from way back in the late 1980's. They are not great, and their lack will have little impact on the CD as a whole, but they show how I got started on my insatiable quest for fractals. Another problem is the names of the GIF images, which are currently cryptic 8-letter DOS abbreviations of the longer full names of the images. The people who have tested the disk format have had trouble connecting the images with the corresponding discussions. (Would you know, while scanning a list of 30 GIF files, that the 'tmeandva.gif' image goes with the 'Theme and Variations' discussion?) I could solve this confusion by renaming the images so that the names correspond to the dates of their discussions, or by breaking down the current large monthly directories into 30 smaller daily ones, with one discussion and one image in each sub-directory. Either option would be a sizable task. Since Fractint is a DOS program, I want to keep the disk in DOS format, like the great disk that came with the second edition of "Fractal Creations". With all the other work that I have to do, it might be necessary to put the ongoing FOTD on hiatus while I wrap up the CD. Hopefully it will not be necessary. . . . but we'll see . . . On my machine, today's image requires almost 1/2 hour to render from the parameter file. Much time can be saved by downloading the completed image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather was quite pleasant here at Fractal Central on Monday, with quite a bit of sun and a temperature of 44F 7C. Only the remaining snowpack prevented the duo from enjoying a romp in the yard. As for myself, I have a pile of graphic work to do, a leak to get patched, a basement to get dried, a fallen porch roof to get replaced, a FOTD-CD to wrap up, tomorrow's FOTD to find, and a pair of cats to keep happy. In addition, the central heat is acting up, probably because of the wet basement. All in all, it is just another normal day at Fractal Central, so until next time, take care, and when things are as bad as they could possibly be, barring the appearance of Murphy's law, they can only get better. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Candy_Ring { ; time=0:28:49.35--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.18015306714052880/+0.742625388281597\ 70/1.983779e+007/1/-140/-1.00973908755130903e-007 params=2/-1/-0.3/1/0/0 float=y maxiter=12000 inside=0 logmap=414 periodicity=10 colors=000QVOPVPNVQMVQLVRKVSIVSHVTGVUEWVFVUFUThhhF\ TSFTSFSRmK0FRQFRQGcPGQOGPOGPNGONGOMGNgGNLGMLHMKHLJ\ HLJHKIHKIHJHHUzHIGHIGKJJMKLOKNQLQwMzUMUXNWZOZ`O`bP\ bdPdfQgiRikRkmSmoTpqTrsUtwVxuUvsTuqTtoSsmSrlRqjQoh\ QnfPmdPlcOkaOj_NhYMgWMfVLeTLdRKcPJaNJ`MI_KIZIHYGHW\ HIUIKSJMQKOOLQMMSKNUIOWGPYEQ_CRaASc8Te6Ue4Vd1Ub1T`\ 0RZ0PY0NW0MU0KT0IR0GP0FO0HQ2JR3LT4MU5OV7QX8SY9T_AV\ `CXaDZcE_dFaeGcgIdhJfjKhkLjlNknOmoPoqQqrSrsTtuUvvV\ wwWvtUvqSvoQvlOvjMugKudIubGu_EuYDsWCqVCoUCmTCkSCiR\ CgQCePCcNBaMB_LBYKBXJBVIBTHBRGBPFBNDALCAJBAHAAF9AD\ 8AB7A96A85AA7DB9FCBHDDKEFMGGOHIRIKTJMVKOYMP_NRaOTd\ PVfQXhSYkT_mUaoVcrWetZexXfvVgtThsRhqPipOjnMjmKkkIl\ jGmhEmgDneBod9ob7pa5q_4qZ5rY6sX7tW8uV9vUAwTBxSBySC\ zTDzUEzVFzWFzXGzYHzZIz_Jz`JzaKzbLzcMzdNzeNzfOzgPzh\ QziRzjRzjTzjUziVzhWzgYzfZzf_zeazdbzcczbdzbfzagz`hz\ _hz`iz_izZjzYjzXjzWkzVkzU } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] FOTD 23-02-03 (Something is Wrong [4])
by jlewis 24 Feb '03

24 Feb '03

On Sun, 23 Feb 2003 09:35:53 -0500, Jim Muth wrote: > > FOTD -- February 23, 2003 (Rating 4) > > Fractal visionaries and enthusiasts: > > Due to water problems here at Fractal Central, which need to be > remedied, (leaky roof and flooded basement), today's discussion > will once again be short. Â The fractal is one I found with > little effort using the just-renamed MandelbrotMix3a formula. Â I > renamed it because there were two formulas named MandelbrotMix3, > and this was causing confusion. > > The image was rendered with the outside set to the <Â real > > option. Â In today's image, this option, with often does little, > creates an effect rather like a froth of bubbles surrounding the > central midget. > > I named the image "Something is Wrong" because something > actually *is* wrong with the image. Â A careful inspection will > reveal subtle inconsistencies in the symmetrical pattern > surrounding the midget. Â I leave it to the viewer to find these > inconsistencies. When I downloaded the image it came out as agreen square! Err... it seems correctly named. Best wishes John -- John Lewis, jlewis(a)clara.net on 23/02/2003 -- Using M2, Opera's revolutionary e-mail client: http://www.opera.com/m2/

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Re: [Fractint] Corrected reply
by Jim Muth 24 Feb '03

24 Feb '03

I made another mistake. This reply is correct. In the fourth line of the second paragraph of my first reply, the word 'left' should have been 'right'. This reply corrects the error. At 10:02 AM 2/24/03 -0700, Lee Skinner wrote: >Jim Muth said: > >>> The problem with the FOTD for Feb. 23 was that I forgot to >write the < frm: > before the formula name when I included >it as part of the parameter file. << > >But he also said a day earlier: > >>> I named the image "Something is Wrong" because something >actually *is* wrong with the image. A careful inspection will >reveal subtle inconsistencies in the symmetrical pattern >surrounding the midget. I leave it to the viewer to find these >inconsistencies. << > >I could not determine what the subtle inconsistencies are that >he was referring to. > >Can you elaborate on these, Jim? It's a case of coincidence. When I named the image, I was referring to inconsistencies in the image itself. I did not realize that I had omitted the < frm: > from the formula name, thereby creating an even bigger wrongness. The inconsistencies in the image are subtle. Compare the elements in the lower right corner to the corresponding elements in the upper left corner. You will see that the lower right elements are larger. Also notice the black area near the center (just to the left) of the bottom edge of the image. The corresponding area at the top edge is colored a pale green. This lack of symmetry is not kosher in proper quadratic midgets. Jim M.

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Re: [Fractint] What was really wrong!
by Jim Muth 24 Feb '03

24 Feb '03

At 10:02 AM 2/24/03 -0700, Lee Skinner wrote: >Jim Muth said: > >>> The problem with the FOTD for Feb. 23 was that I forgot to >write the < frm: > before the formula name when I included >it as part of the parameter file. << > >But he also said a day earlier: > >>> I named the image "Something is Wrong" because something >actually *is* wrong with the image. A careful inspection will >reveal subtle inconsistencies in the symmetrical pattern >surrounding the midget. I leave it to the viewer to find these >inconsistencies. << > >I could not determine what the subtle inconsistencies are that >he was referring to. > >Can you elaborate on these, Jim? It's a case of coincidence. When I named the image, I was referring to inconsistencies in the image itself. I did not realize that I had omitted the < frm: > from the formula name, thereby creating an even bigger wrongness. The inconsistencies in the image are subtle. Compare the elements in the lower right corner to the corresponding elements in the upper left corner. You will see that the lower left elements are larger. Also notice the black area near the center (just to the left) of the bottom edge of the image. The corresponding area at the top edge is colored a pale green. This lack of symmetry is not kosher in proper quadratic midgets. Jim M.

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What was really wrong!
by JimMuth＠aol.com 24 Feb '03

24 Feb '03

The problem with the FOTD for Feb. 23 was that I forgot to write the < frm: > before the formula name when I included it as part of the parameter file. Many apologies. Jim M.

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FOTD 24-02-03 (An Improved Image [6])
by Jim Muth 24 Feb '03

24 Feb '03

FOTD -- February 24, 2003 (Rating 6) Fractal visionaries and enthusiasts: It's going to be a hectic day here at Fractal Central. We have the drippy roof to get patched, the musty cellar to get dried, the cats to keep happy, the regular graphic work to do, and the fractal exploration to hopefully get to. There is also that FOTD-CD. I have had it almost ready for weeks, but I still keep finding annoying problems with it that keep me from being satisfied and deciding it is finished. It will be ready in the near future, how near, I cannot say with certainty. With its rating of 6, today's fractal is somewhat improved over the string of 4-rated images that have appeared recently. In recognition of this fact, I named the picture "An Improved Image". The curvilinear effect was achieved by rendering the scene with the outside set to < imag >. The parent fractal, which was created by subtracting 2 parts of Z^(-1.8) from 2 parts of Z^(0.75) then adding (1/C), is quite unusual, resembling nothing as much as a rubber duckie. I will likely return to it in the near future for a source of more FOTD's. The render time of 19 minutes is slow, but for convenience, the completed image has been posted to the two FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Sunday was changeable here at Fractal Central. The day started foggy, then rain showers arrived, which changed to wet snow flurries before they ended by noon. In the afternoon, high winds arose, which scattered the lawn furniture, but the day ended peacefully, with clear skies and diminishing winds. The cats, who appear to be becoming accustomed to less-than-perfect weather, took the day's events in stride, satisfying themselves indoors with warmth and good food. I've got much work to do today, so until next time, take care, and be good. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ An_Improved_Image { ; time=0:19:46.44--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.34306163986039530/+0.194300897396538\ 00/2.699783e+007/1/-37.5/-6.01984598488924938e-008 params=-2/-1.8/2/0.75/0/0 float=y maxiter=1750 inside=0 outside=imag periodicity=10 colors=000u9av9cw9e0jm7inEhoLgpSfqYeqddrkcsrbtxbtu\ _qsYnqWkoUhmRfkPciN`fLYdJVbGT`EQZCNXAKV8IfZDqx8owA\ nvCmvDluFktGjtIisJhrLgrMfoPelRdiUcfWccYaeU_gQYiMWk\ IVmEfePrY_pWaoUcmTdlRfkPhiOihMkgLleMkcNkaNj_OjYOjW\ PiUPiSQiQRhORhMSgKSgITgGTfEUfCUfETeFTdHTcITbKTaLT`\ MT_OTZPTYRTXSTWUTVVTUWTTeOcoJnyExvIwsLwpOwmSvkVvhY\ ve`ubdu_guYjtVmtSqtPtsMwsKzsIvnHriFneEj`CfWBbSAZN8\ VI7RE5N94J43G07Y1Ab1EJ2Hc2LL2OM3Sh3VN3XIIZEW`Aib6w\ SPsIgp8ym9tkApiAkgBgeBcdCZbDV`DQZEMXEIWCRUBZS9gQ8o\ O7wMIwKTwJcwHnwGywFttGpqGknGgkGbhGZeGUbGQ_GMXGQaNT\ eTWiZZndarjdvpgzvZnlRbbISUAGK2VB5b22r23a6IDNHFLGGK\ FIIEKHELFDNECPCBQBAS99U89V78Y87_86a85d95f94h93kA2m\ A2oA_1Uc5`g9fkDmoHssKyqNxpPxoRxnTwlVwkXwjZvi`vgbvf\ duefudhucjuaqh_wWauXbtYcsYbrXbrWbrVarVarUaqT`qT`qS\ `qR`qRcdTeSVgFXfJSfMNfPJeSEeVAeY5e`1_W6USBOOGPKNQH\ UmCJnBLoBNpBQqASrAVsAXt9Z } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 23-02-03 (Something is Wrong [4])
by Jim Muth 23 Feb '03

23 Feb '03

FOTD -- February 23, 2003 (Rating 4) Fractal visionaries and enthusiasts: Due to water problems here at Fractal Central, which need to be remedied, (leaky roof and flooded basement), today's discussion will once again be short. The fractal is one I found with little effort using the just-renamed MandelbrotMix3a formula. I renamed it because there were two formulas named MandelbrotMix3, and this was causing confusion. The image was rendered with the outside set to the < real > option. In today's image, this option, with often does little, creates an effect rather like a froth of bubbles surrounding the central midget. I named the image "Something is Wrong" because something actually *is* wrong with the image. A careful inspection will reveal subtle inconsistencies in the symmetrical pattern surrounding the midget. I leave it to the viewer to find these inconsistencies. Because of the F.C. water problems, I had so little time to search for today's FOTD that I could rate it no higher than a 4. The 17-minute render time adds nothing at all to the rating. For convenience, the completed image is available on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and on Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather Saturday was not fit to be called fractal. The 3 inches 8cm of rain that fell during the day melted half of the nearly one meter of snow still on the ground to cause widespread flooding in the F.C. area, including Fractal Central itself. The chilly temperature of 39F 4C merely added to the unpleasant- ness. Conditions were so bad that the dynamic duo seemed to realize that going out was impossible. They didn't even ask, satisfying themselves by sleeping near the heat and enjoying their tuna treats. If I manage to get the mess cleaned up, which will be difficult but will be accomplished, I'll return in 24 hours with the next FOTD. Until then, take care, and keep your powder dry. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Something_is_Wrong { ; time=0:17:58.24--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix3a function=ident passes=1 center-mag=+7.27918549228332700/+0.284753999303866\ 60/7819.961/1/135/5.50914092817267331e-009 params=-1/1.95/1/2.05/0.2/2.95/-0.2/3.05/3.6736066\ 267525/0 float=y maxiter=3600 inside=0 outside=real logmap=yes periodicity=10 colors=070aC0aC0aC0aC0aC0NG0AZ00tA0zL0zF0zC0z80x43\ t05p08l0Ah0Ed0I`0KX0NT0QR0NZ0Md0Kj0Ir0Gx4EzCCzHAzQ\ 8zX8zbCzdEzgGziIzjKxlMroNlqQfqS`sUVuWPuYKu_EuaCucC\ ueCumCusLuxXsxhoxtjxzgxxixpixhix`jxTjxLjxEjxClsClq\ CloCliCgcCbYC_UCVNCSICLECH8CD3CA0C60C00C00C00C00C0\ 0C00zu0zu0zu0zs0zo0zj0zd0z`0zX0xS0vO0vH0tD0rA0p40n\ 00n00n00n00n00n01n05h08d0CZ0EV0IP2ML6QGASCCWCF_CJc\ COeCSiCVmC_oC`xz0xf6oGTaCq_CiYC`WCVUCOSCHQEAQG4NK0\ MN0KR0IV0GZ0G`0Ma0Qd0Ud0Yf0ah0gh0kj0ol0sl0xn0xn0xp\ 4xrCxrJxtSxv_xvgxxoxzuxzuexuNvu6to0rj0pg0zu0pj00K0\ Lg0Xq0hu0tuIhuqXuxLuxNuxPuuRumRucTuUVuMVuCXu3Zu0Zu\ 0C00zJ0z_0Nu0Vu0`u0fu0lu0ru0xuazjxzCxzDxzDxzDxnDxa\ DxRDxGDxzLxzFxzFxzFxzFxzFxzFxzDqzCezASz8Gz85z60z40\ z20z2CzguzuxN0xT0xZ0sd0ih0an0Ut0Kx6CzC5zH0zL0zT0z`\ 0zi0zq0zu0zu0zu3zdEpiNfjYZoiPqsGuxCuuCuoEsgIsaKqUN\ qNPoIRoMIXQCFUC0YC0aC0aC0 } MandelbrotMix3a {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END 20.0 PAR-FORMULA FILE==================================

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No FOTD for Feb. 22
by Jim Muth 23 Feb '03

23 Feb '03

I've been too busy, up half the night with backed-up work. Look for the next FOTD on Sunday. The same problem is true with the FOTD-CD. It is basically finished, but I can't find the time to wrap it into a completed package. But don't give up hope. The CD *will* appear in the very near future. Jim (the very busy) Muth

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What do these symmetry forcing parameters do?
by Harold Lane 22 Feb '03

22 Feb '03

Does anyone know what the following symmetry forcing parameters do? I only have the 1st edition of Fractal Creations and the 20.0 docs & Bradley Beacham's Formula tutorial don't tell... XAXIS_NOPARM YAXIS_NOPARM XYAXIS_NOPARM ORIGIN_NOPARM PI_SYM_NOPARM XAXIS_NOREAL XAXIS_NOIMAG - Hal Lane hallane @ compuserve.com

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FOTD 21-02-03 (Simply a Minibrot [4])
by Jim Muth 21 Feb '03

21 Feb '03

FOTD -- February 21, 2003 (Rating 4) Fractal visionaries and enthusiasts: Once again, I have little time to search for fractals. But luckily, there is the evolver, which searches automatically. To save time, I put the Fractint evolver to work. When it found an interesting fractal, I rounded off to 2 places and searched for something in the fractal it had found. Not surprisingly, I found a minibrot. I named today's image "Simply a Minibrot", which was the first name that came to mind. I rated it at a 4 because it is too fragmented and muddy for a higher rating. The render time of 12 minutes can be reduced to one minute or so by downloading the image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Had it not been for the deep snow pack and the fallen porch roof, Thursday, with its warm sun, light winds, and temperature of 50F 10C, would have been a fine spring-like day for the fractal cat duo. As it was, they stuck their noses out the side door, tested the snow with their paws, and decided that comfort was better than valor. As for myself, I'll be quite busy for a few days as the work that could not be delivered due to the snow finally comes in all at once. But I'll still find a bit of time for the FOTD. So until tomorrow, take care, and see you soon. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Simply_a_Minibrot { ; time=0:12:00.13--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.68601040546856860/-0.201739505878596\ 30/2.093344e+008/1/60/-3.92330872178714429e-007 params=1.56/0.42/1.35/1.91/0/0 float=y maxiter=2500 inside=0 logmap=182 periodicity=10 colors=000C6C60D00D70JD4PJ9VPD`XIfaMlgQrmVxiYpd_j`\ acYcYTdSPgLLiFIj9DiD9gG4gJ0fM0dP0dS0cX0a_3ac6`f9`j\ D_mGYrLYuOXyQXzXasafjflalpTpvLvzCzz3yz4xz4vz4uz4sz\ 6rz6pz6oz6gmT`VoTDzSIzSLzSOzQQxQTsQXpP`mPcjPffOicO\ l`OoYOrVLuaJvgGxoFyuDzzIyxMyuPysTypYyo`xldxjixglxf\ pxcsxammXgdQaVLXMFQC9L33G00I11J73JD6LJ7MPAMVCO`FPf\ GPlJQrLQxMTmGXdA_X6aO0dF0g60i00OlcPraXgYc_TjQQrGMy\ 7Jz0Fz0Cz0Mz7XxGfsPpmYzidzmazp_sTQgPMdLIcJ4XJ0QL0_\ M7fOFoPMvQTzQ`zTczXdz_guaiodlifmcipYlrSouMrvGsxCrs\ FroGrjJrfLraOr_PrVSrQTrMXrIYrF`rAar6dr1fr0ir0jm1dj\ 9_gFTdMO`TIY_CVf6Sm0Ps0AXQ09sCSlSjdVicYgc_gcafccdc\ fdcgccjccmaco`cr`cs_cvYcxYczXczXcuTaoQ`iO_aMYXJXQG\ VJFTDCS79Q17P96MG6JM6GT4D`4Af47m34u31z30r67i9GaAPT\ DYLFfDIo4Jx0Mz0Oz0Jz0Gp1Cd49V94JD17G00F9FDIVCQjDSi\ DSgFSfFSdGSdGScISaIT`JT_JT_LTYLTXMTVMTTMTTGQ_COd7L\ j3Ip0Fv0Dz3GyCIxTP7OJ9IDA } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 20-02-03 (Mandelbrot Breakoff [4])
by Jim Muth 20 Feb '03

20 Feb '03

FOTD -- February 20, 2003 (Rating 4) Fractal visionaries and enthusiasts: Yesterday morning, the fractal lady decided she simply had to make a trip to the store. I warned her that the roads were still very bad, and if she went out, she would get stuck. She assured me that she could handle it. About an hour later I got a phone call from six blocks away. Guess what had happened . . . Two hours later, when we arrived back at F.C., I justifiably lost my cool, which I have relatively little of even on good days. The rest need not be described. The fractal of the day, which was found despite the distrac- tions, is named "Mandelbrot Breakoff". The name describes the disconnected nature of the scene. The rating of 4 is fair enough for such an ordinary fractal. The render time of under 3 minutes is also fair enough. Those who consider even 3 minutes unfair may download the completely rendered GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Wednesday was not too bad, with some sun and a temperature of 36F 2C. The dynamic cats were out of sight most of the day, most likely avoiding the temper tantrums. It would have made no difference even if they had not gone into hiding. Their porch is still blocked by the fallen roof and the ground is still buried under about a meter of soggy snow. But F.C. has a way of surviving trying times, and the next fractal is but 24 hours off. Until then, take care, and I just don't dig it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ MandelbrotBreakoff { ; time=0:02:49.28--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.3531289942622923/+0.335701792042646/\ 2178754/1/102.5/1.089800562e-008 params=0.25/1.618\ 034/-2/-1.618034/1.2/0 float=y maxiter=400 inside=0 logmap=47 periodicity=10 colors=000AkzAjyAiyAhyAgxAfwAevAduActAbsAarA`qA_p9\ ZofK8kYLqjXwrhprejmcdhaZc_TZXNUVHPTBLRO_g`mxTjuMgr\ FdoG3vLAtQHrVOp_Vndalhhkjjhllfnncpparr_ttXvvVxwTwo\ PvgMu_JtTFsLCrD9r66tC7vI8xO9yU9vXFt_KrbPpeUnhZlkco\ ZQrNDtB0hE2XH3LK49N5U12of0mKDpIBsG9uF7xD5zC3tI4oN5\ jT6eY7`c8Wh9RnAMsBNNNBBBI_TAfR3mP9kKEiFJhB_NHp1N4Q\ SL9AHELDJV9Od6SnOMceHUvCKqIUmNchSmdXvE10eqzdjmz8pz\ BtzEvzGxzNzzUzz`zzczzczzczzczzczzczz_zzTzzNzzPzzQz\ zSzzTzzRzzPzzNzzMzzDzz4zzUzzczzczzczzczzczzczzczzc\ zzczzczzczzczzczzczwcztczqcznczcmzcmzcmzcmzcmzcmzc\ mzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmz\ cmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcm\ zcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzc\ mzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmz\ cmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcm\ zcmzcmzcmzcmzcmzcmzcmzcmz } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 19-02-03 (High-Order Fractal [4])
by Jim Muth 19 Feb '03

19 Feb '03

FOTD -- February 19, 2003 (Rating 4) Fractal visionaries and enthusiasts: Many problems still plague Fractal Central, so we'll have another short discussion today. The digging went well on Tuesday, but in the afternoon, a large pile of wet heavy snow slid off the fractal house roof onto the cats' porch roof and collapsed it. In addition, the house roof has started leaking over the rear bedroom. But between all the other distractions I managed to find a quick fractal. I named it "High-Order Fractal" because it combines 4 different powers of Z before adding 1/C. I use this MandelbrotMix3 formula relatively infrequently because the images it draws tend to be too chaotic, and also because the critical point must be calculated separately and entered as the real(p5) parameter. Though I found the image in only a few minutes, it takes 1/2 hour to render. I could rate the hastily-found result no higher than a 4. The 1/2-hour render time can be avoided by download- ing the completely finished GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Monday and Tuesday was partly cloudy with temparatures around 30F -1C. But the fractal cats are not happy. With their hangout roof collapsed, the dynamic ones were sullen indeed, spending several hours in full-sulk mode, hunkered down with thrashing tails stirring up an indoor breeze. Luckily I stocked up on tuna before the big storm. Tuna always restores a cat's good spirits. (Too bad it doesn't work as well on me.) There is still a lot of digging to do, so until next fractal, take care, and see you in 24 hours. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ High-Order_Fractal { ; time=0:29:38.38--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix3 function=recip passes=1 center-mag=-2.24578194714223/-0.007932233500827/2.\ 324295e+007/1/95/1.171e-007 params=0.3/1.5/0.2/2.5\ /0.1/3.5/1/-1.5/1.037043411258671/0 float=y maxiter=1600 inside=255 logmap=202 periodicity=10 colors=000iC9mA6kC9jEBiFDgHFfIHeKJdLLbNOaPQ`QSZSUY\ TWXVYbVUWW_PWeIWk9TqCWpFYpH_pKapMcpPipSkpUmpXopZqp\ artfsscqp`nmYkkVhhTefQbcN_aKYZHVXFSUCPS9MP6JN3GK1E\ I5GL8INBKQFMSIOULQXPSZSU`VWcZYea_hdajhclkeongqqhsl\ cphZmcUj_QgWLdRGaNBZJ7WQAVXCV`JPdQKhXFlcApj5sq0mo4\ hn7clAYkDTiGOhJIfMDeP7cQ8dS9dTAdVBeWCeYDeZEf`FfaGf\ cKOBGfdVkrTjoSimRhkQgiPggOfeNecMd`LcZKcXJbVIaTH`R7\ d5G`POXgWTz`NneIcjCSn7HmAJlDKkFLjINiKOiNPhQRgSSfVT\ eXVd_WdaXe`Wf_VgZUhYTiXSjWSkVRlUQmTPnSOoROpQNqPMrO\ LsNKsNKqOJpOJnPJmPJkQJjQIhRIgRIfRIdSIcSHaTH`THZUHY\ UHXUHSTONSUIR`DQf8Pm4Os9eVDw6Bs8Ap99mB8jC7gE5cF4`H\ 3YI2VK1SL4RO7RRAQTDQWGQZJP`MPcOPeROhUOkXNm_NpbNseM\ uhMxjMzeKv`JsWHpRGmHPzNFjT3WS6VS8USATSCTSESSHRSJQS\ LQSNPSPOSSNSUNSWMSYLS_KDWWSaKgd7ef9dgBbhDaiF_kGZlI\ YmKWnMVoOTqPSrRQtTPuVMvQOwWPzaRzfSzlTzqUzpUzoUzoVz\ nVzmVzmWzlWzkWzkdz9gz9ccz } frm:MandelbrotMix3 {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] No FOTD for February 18
by gnome＠hawaii.rr.com 18 Feb '03

18 Feb '03

>On Tue, 18 Feb 2003 00:44:54 -0500, Jim Muth wrote: > >>The fractalist is totally exhausted after digging through >6 foot snowdrifts for 4-1/2 hours. He needs a good rest so he> can >finish the digging job tomorrow. As a result, there will be no> FOTD >for February 18. If he survives the remaining 1/3 of the task,> the >fractalist will post the next FOTD on schedule on the 19th. > >Jim > >You have my sympahthy. It is only cold here (ie cold for us). > >Are not snowflakes fractal in nature? IIRC, they are. Haven't seen one in a couple of years, and had to go to the US mainland to see that! David gnome(a)hawaii.rr.com

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Re: [Fractint] No FOTD for February 18
by gnome＠hawaii.rr.com 18 Feb '03

18 Feb '03

Sounds like it's time to relocated to Hawaii, Jim! Not a snowdrift in sight! ;-) David gnome(a)hawaii.rr.com >Fractal enthusiasts and visionaries: > >The fractalist is totally exhausted after digging through >6 foot snowdrifts for 4-1/2 hours. He needs a good rest >so he can finish the digging job tomorrow. As a result, >there will be no FOTD for February 18. If he survives >the remaining 1/3 of the task, the fractalist will post >the next FOTD on schedule on the 19th. > >Jim (the fractalist) Muth

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No FOTD for February 18
by Jim Muth 18 Feb '03

18 Feb '03

Fractal enthusiasts and visionaries: The fractalist is totally exhausted after digging through 6 foot snowdrifts for 4-1/2 hours. He needs a good rest so he can finish the digging job tomorrow. As a result, there will be no FOTD for February 18. If he survives the remaining 1/3 of the task, the fractalist will post the next FOTD on schedule on the 19th. Jim (the fractalist) Muth

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Re: [Fractint] Re: FOTD 14-02-03 (Beach and Cliffs [6])
by Jim Muth 17 Feb '03

17 Feb '03

At 06:43 PM 2/16/03 -0000, you wrote: >Jim Muth said on Friday, February 14, 2003 8:30 PM > >>The version generated by the parameter file *IS* the >>altered image. When I alter an image in a separate >>program, I make only color changes, which I then save >>as a GIF file, load into Fractint and encode into a >>normal parameter file. > >I'm missing something here. I tried taking one of the FOTD >images into Corel Photopaint, changed the brightness, >contrast and intensity and re-saved as a GIF file. >Restoring the new file into Fractint doesn't allow me to zoom >in so I guess the par info saved with the original GIF has been >lost. Where have I gone wrong? Apparently, the Corel program strips out the encoded GIF data when it saves a GIF file. When you save the altered image, do not overwrite the original. Then load the altered image into Fractint and save the new colors as a *.map file. Reload the original unaltered image into Fractint and load the *.map file that you have just saved into the original. Save the resulting image, which now contains both data and altered colors. Jim M.

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FOTD 17-02-03 (Theme and Variations [5])
by Jim Muth 17 Feb '03

17 Feb '03

FOTD -- February 17, 2003 (Rating 4) Fractal visionaries and enthusiasts: I enjoy shoveling snow, but this is ridiculous. Once again, due to an immense quantity of snow that must be moved, the discussion will be very brief. Today's hastily achieved fractal can rate only a 4, but that is only a little below average. The parent fractal, whose formula is Z^1.19+C, resembles a double-lobed lake, with an immense filament extending to the SW, far beyond the borders of the default screen, which BTW has a magnitude of 2/3. Today's scene is located near the tip of this curved filament. I have no idea how I found the mis-shapen minibrot on this totally chaotic filament. I guess I have developed a fractal sixth sense, or more accurately a seventh sense, since I already have precognition. (No, I cannot turn it on at will.) The name, "Theme and Variations", was inspired by the melange of incongruous features that make up the image. Then again, perhaps I should have named the image simply "Variations", since there is no single theme that unifies it. The parameter file runs in 8 minutes. The completed GIF image is available for download on the W.W.Web at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Heavy snow fell all day Sunday here at Fractal Central. This, plus the temperature of 14F -10C, swept all thoughts of the outdoors from the minds of the fractal duo, who spent the day sleeping where it was warm. This morning the snow is still falling. Since the snow on the ground is about three times as deep as the cats are tall, they had best resign themselves to a long confinement. As for me, I've got a lot of shoveling to do, and there is no time like the present to get started. Until tomorrow's FOTD, take care, and, if I get myself dug out of the snow drift, see you then. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ ThemeAndVariations { ; time=0:08:14.44--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-2.64441871745242100/-7.096189677868118\ 00/8.730126e+008/1/2.5/-1.66441295210220663e-005 params=1.19/0/18.6/0 float=y maxiter=12000 inside=0 logmap=118 periodicity=10 colors=000IHFOLIUOL_SOeWRkZUbHXU0ZX9XZHWdRNj`Epi50\ kK7fIDbGKZFQUDXQCbMAiH9oD7u96pCDkFJgIPbLVZNaUQgQTm\ LWsHYyIWwJVuKTsKSqLQoMPmMNkNMiOLgOJePIcQGaQF_RDYSC\ WSBUVATYAT`ATbASeASh9Sk9Sm9Rp9Rs9Ru9RvBSvDTwFUwHVx\ JWxLXyNYyPZzR_zS`n_bcfcTmeItfZefoSfrVVtXJvZ8qY9lYA\ hYAcYB_YCVYCRXDMXDIXEDXF9XF4XG0XG2ZJ4_M6`P8aRAbUBc\ XDdZFeaHfdJgfKhiMilOjnQkqSltTmvXnt_nrbopeoohpmkpkn\ qiqqhtrfwrdzrcwpaun`sl_qjZohXmfWjdVhbUf`SdZRbXQ`VP\ WNIZTO`ZTbdYeibgogiulkzqjsnimlhfih`ggUefObeH`eBZcA\ XaAV_9TY9RW8PU8NS8LQ7JO7HM6FK6DI5BG59E58H7GJ9NMBVO\ CaMOdLZfKiiJtkPmlUgmZ`ncVnhPomIprCqw6qs7pp8om8ni9m\ f9mcAl`AkXBjUCiRCiNDhKDgHEfEEfHIgJLgLOgNRgPUgRYhT`\ hVchXfhZihamf`lh_kiZjjYjkXilWhmVgoUgpTfqSerRdsOfyQ\ dtSboU`kWZfYYb_WYaUTcSPeQKqV9gPGYKNPFTFA_65eB8fFAf\ JCfOEgSGgWIg`LhdNhhPhmRiqTiuVisWgrWfqWeoXdnXcmXakY\ `jY_iYZgZYfZWeZVc_Ub_Tc`T } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-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 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] Re: FOTD 14-02-03 (Beach and Cliffs [6])
by Jim Muth 16 Feb '03

16 Feb '03

At 11:30 AM 2/14/03 -0600, Paul Lee wrote: >If you would send me the image you created, then I >will put that on the web site, instead of the FractInt >version which I generated without your colorings. The version generated by the parameter file *IS* the altered image. When I alter an image in a separate program, I make only color changes, which I then save as a GIF file, load into Fractint and encode into a normal parameter file. (FOTD-CD ordering info to come shortly) Jim M.

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FOTD 16-02-03 (Stringing Along [5])
by Jim Muth 16 Feb '03

16 Feb '03

FOTD -- February 16, 2003 (Rating 5) Fractal visionaries and enthusiasts: The discussion will need to be short. We have a blizzard in progress here at Fractal Central, and I must frequently go out and work to keep things from getting hopelessly buried. Today's fractal is named "Stringing Along". I gave it this name when I noticed its resemblance to strings of something bright and shiny. The parent fractal resembles a vertically stacked pile of bays, with a stray Mandeloid bud in the lower left corner of the bottom bay. Today's scene is located in a spiral near the tip of the filament extending from this bud. The rating of an average five might have been a point or two higher if I had had the time to find the best color palette. But even as imperfect as it is, the image is worth the 7 minutes required to render it from the parameter file. An even faster way of seeing the bright shiny strings is to download the finished GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> We ended up with 3-inches 8cm of new snow here at Fractal Central on Saturday. Combined with a temperature of 27F -3C, the snow kept the fractal cats snug by the heat. This morning is starting with a temperature of 12F -11C and heavy snow accom- panied by lightning and thunder -- everything the duo dislike. The forecast is for up to 3-feet 90cm (that is no mistake) more snow by Monday, with high winds to blow it around. I fear the fractal cats will be unhappy to hear this, but for me it means a break in the design work, with lots of time between bouts of shoveling for sitting by my window, watching the snow and fractaling. Until next FOTD, take care, and I guess I'll be shoveling off. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Stringing_Along { ; time=0:07:00.10--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.82203006880817/-0.85536665031521/6.2\ 94961e+007/1/37.5/3.29673691283616e-007 params=-5/\ -1.5596104695/-0.5/-15.596104695/0/0 maxiter=1200 float=y inside=0 logmap=120 periodicity=10 colors=0000000000000000000000000000000000000000000\ 00030030110300400600903B04C06E09G0BH0CJ0EK0HM0JO0K\ P0MR0KU0JV0HX0GX0EY0E_3Ca4Ba69c97dB7fC6hG4hH3iJ1kM\ 0mO0mP0oU0pV0rX0rY0pV0oU0oR0mP0mO0kM0kK0iJ0iH0hG0f\ E0fC0dB0d90c70c60a40a30d60f71hB4iC7mGBoHEpJJrMMtOP\ xRUzUXzX_zYdz_hzckzdozhrzivzizzkzzmvzorzpozpkzrhzt\ dzvazvYzxVzzRzzOzzKzzHzzEzzBzz7zzBzzEzzGzzJzzKzzOx\ zPvzUrzVpzYoz_kzcizffzhdzkczm_zpYzrXzvUzxRzzPzzOzx\ MzrMzoKziJzfJzaHzYHzUGzOEzKEzGCzCBz7Bz49z09z07z07z\ 06z16z34z44z63z73z71z91zB0zC0zE0zG0zH0zJ0zJ0zK0zM0\ zO0zP0zR0zU0zR0zU0zV0zX0zY3zY4z_7xaBxcCvdGvdJtfKth\ OriRriUpkXpm_ooaopdmphmriktmkvokvpixpixrhzrhzrhztf\ ztfztdzvdzvdzvczxczxazxazzazz_zz_zzYzzYzzYzzXzzVzz\ UzzRzzPzzPzzPzzPzzPzzPzzPzzPzzPzzPzzPzzPzzPzzPzzPz\ zPzzPzzPzzPzzPzzPzzPzzPzzPzzPzzPzzPzzPzzPzzPzzPzzP\ zzPzzPzzPzzPzzPzzPzzPzzPz } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Thanks 4 your help. I'm still getting a sold blue screen.
by Harold Lane 16 Feb '03

16 Feb '03

Thanks for your responses to: >Anyone - in JackOTradez's posting to this forum on >Sun, 9 Feb 2003 he includes a set of parameters and >the formula it refers to. >When I use these I get a solid blue screen. I'm still getting a sold blue screen. Things I have tried unsuccessfully follow: To invoke the .par file, which I have named '6ml08402.par', I hit the '@' key and choose the '6ml08402.par' file and then select the '6ml08402' parameter set (the only one in the file). 1) I tried putting both the par and the formula into the same par file, as suggested. I put the formula 2nd and inserted 'frm:' in front of the formula name. I changed the formula name in the formula from 'MMix4-lake-0084' to 'mmix4-lake-0084' to have the case of the letters in the name match those in the parameter file. The <Tab> screen shows the 'Item file:' as the '6ml08402.par' file. I have found that a file with the name 'mmix_lak.frm' must *not* exist for the formula to be read from the .par file. 2) I have tried placing the formula file in a file named 'mmix_lak.frm' and changing the formula name in the formula from 'MMix4-lake-0084' to 'mmix4-lake-0084' to have the case of the letters in the name match those in the parameter file and *NOT* inserting 'frm:' in front of the formula name. The <Tab> screen shows the 'Item file:' as the 'mmix_lak.frm' file. 3) I have tried placing the formula file in a file named 'mmix_lak.frm' and changing the formula name in the formula from 'MMix4-lake-0084' to 'mmix4-lake-0084' and *inserting* 'frm:' in front of the formula name. I removed the formula definition from the .par file. In this situation I get error messages (which makes sense): 'mmix4-lake-0084' file entry item not found Any key to continue... Could not open file where formula located Any key to continue... Apparently you must *not* have 'frm:' in front of a formula name in a formula file. Note that when no matching formula was found the calculated image was the still the solid blue one! I suspect that this is an important clue (to someone - not me). 4) I have also tried using Robin's Fractint Paste & Go V1.3 utility, changing the name of the formulafile= in the par text window to 'formulafile=pastengo.frm' and changing the formula name in the formula text window from 'MMix4-lake-0084' to 'mmix4-lake-0084' with *no* 'frm:' inserted in front of the formula name. The <Tab> screen shows the 'Item file:' as the 'pastengo.frm' file. The contents of the 'pastengo.par' and 'pastengo.frm' files contain faithful copies of the text I put into the utility's two windows. 5) I have also tried using Robin's Fractint Paste & Go utility, putting *both* the par and the formula info (par 1st) into the par window & removing the 'formulafile=mmix_lak.frm' in the par text window and changing the formula name in the text window from 'MMix4-lake-0084' to 'mmix4-lake-0084' with 'frm:' inserted in front of the formula name. Debug mode of the Paste & Go utility shows 'fractint.exe @pastengo.par/6ml08402' as the command issued. Manually issuing this command in the Fractint directory also creates the blue screen. The <Tab> screen shows the 'Item file:' as the 'pastengo.par' file. The contents of the 'pastengo.par' file contains a faithful copy of the text I put into the utility's parameter window. All five of these methods give a sold blue screen. I am using Fractint V 20.0 (which matches the 'reset=2000' in the .par file) under Windows 98 (orig ed.) on a vanilla Gateway PII 400MHz machine. My SSTOOLS.INI follows: [fractint] textsafe=save sound=off video=SF7 map=goodega.map After creating a blue screen the <Tab> screen is as follows: ########################################## Fractal type: formula Image completed Item name: mmix4-lake-0084 ident Item file: pastengo.par Floating-point flag is activated Savename: fract001 Calculation time: 0:00:18.12 Video: 1024x768x256 SuperVGA/VESA Autodetect Works with most SuperVGA Corners: X Y Top-l -27.3550000223599900 0.1139646348533431 Bot-r -27.5269999776400100 -0.1153686388533431 Bot-l -27.5269999776400100 0.1139646348533431 Ctr-27.4410000000000000 -0.0007020020000000 Mag 1.16279100e+001 X-Mag-Factor 1.0000 Rotation 90.000 Skew -0.000 3: 33.330000000 4: 0.0000 5: 0.200000000 6: 300.000000000 Iteration maximum: 2500 Effective bailout: 25.000000 Press any key to continue, F6 for area, CTRL-TAB for next page ######################################### As a reality check, my copy of Fractint was able to render the Feb 11th, '03 Fractal of the Day and it matches the image at: http://home.att.net/~Fractals_3/FotD_03-02-11.html To create the Fractal of the Day I used Robin's Fractint Paste & Go utility, and put both the parameters and the formula in the parameter window with a 'frm:' in front of the formula. Any further help will be appreciated. - Hal Lane hallane @ compuserve.com

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FOTD 15-02-03 (Poinsettia [5])
by Jim Muth 15 Feb '03

15 Feb '03

FOTD -- February 15, 2003 (Rating 5) Fractal visionaries and enthusiasts: 'What is reality?' philosophers wonder. Is reality an indepen- dent objective thing, or is it something largely determined by the particular culture in which a person happens to live? 'What is a fractal?' I wonder. Is a fractal a real thing or an imaginary thing made visible by a computer? Certain physical objects such as coastlines have a fractal nature, but can the fractal nature be separated from the object and still be consid- ered real? Can a smile be separated from a face, or a mind from a brain? Today's image consists of trapped and evaporated inside stuff made visible by the < bof61 > inside fill option. Does this make it any more or less real than traditional images that consist of outside stuff rendered with equal-escape bands? It all depends on how the word 'real' is defined. If 'real' is taken to mean 'composed of objective physical matter', then all fractals created by computers are unreal. If 'real' is taken to mean 'observable by the senses', then visual fractals, and fractal music as well, are quite real. If we agree with the latter definition, and since it is observable, both on the screen and printed on a sheet of paper, today's image must be considered real. Most importantly, would I have concerned myself all these years with something that is not real? Today's image most certainly is real. I named it "Poinsettia" because it reminds me of one of those plants with red leaves resembling flower petals, which are in demand around Christmas time. As noted above, it is an evaporated scene made visible by < bof61 > inside fill. The parent fractal consists of three vertically stacked bays, with the north bay partially obscured by several intruding, apparently non-critical valleys. But once again, appearances are deceiving, for today's scene lies on the west shore of the intruding valley on the east, which proves to have a few critical features in it after all. I could rate the image no higher than an average 5. There's nothing really wrong with it, there's simply nothing in it that I could focus on to justify a higher rating. With a render time of 6/10 second under 15 minutes on my machine, the parameter file is decidedly slow. Speed may be achieved by downloading the completed GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Clouds and sun combined with an unexpectedly mild temperature of 40F 4C to give the cats a jolly afternoon on the porch Friday afternoon. Their moods were so good in fact that I had no need to break out the tuna. But this morning is colder with 6cm of fresh snow on the ground, snow still falling, and a forecast of a blizzard. The task of keeping them in a good mood throughout the day will be more difficult. As for me, I'm going to think of clearing the sidewalks. I might even decide to do it. Until next time, take care, and patience will soon be rewarded. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Poinsettia { ; time=0:14:59.40--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.7145852718248/+1.29586558138/2322434\ /1/-77.5/1.32154340873325005e-008 params=-5/-1.559\ 6104695/-0.5/-15.596104695/0/1e+100 maxiter=1200 float=y inside=bof61 symmetry=none periodicity=10 colors=000DJ_4GI8HLCHOGIRKITNIWRJZVJ`ZKcbKfeKhdIfd\ HedGdcFccEbcDacC`bBZbAYb9Xb8Wa7VFUoa5Ta4SYMOVcKStH\ aGYdMZgS_jZ`mdapjanlYlnUjpRhrNftJeuGk7ojBnjFnjJnjN\ nfSmbXmZ`lVelRjlNnkFUoFwk`vduuZnr_go``maUjbNgcGed9\ be2`eId1OfCUhN_jYdkhifXnbMsZBZoGRnNJmUBm_Acb9Vd8Lg\ 8CiCClFUoICrLCtIOKOMJVKHVMQXPLZSG`VBbY6d`1aZ5_Y8YX\ BWWFUVIRULPTPNSSLRVJQZGPaEOdCNhAMk8LnGOhNQcUTZaVTz\ YOo_JsQNvHRy8VwJQuULsdHqoCpz8mvBjsDgoFelHbhJ_eMYaO\ VZQSVSQSUNOXKLZIH`FEbCAdA7fEAdHCcKEbNGaQI`TK_WMZZO\ YaQXdSWgUVhTUiTUiSUjSUjRUkRUlQUlQTmPTmPTnOToOToNTp\ NTpNTjQCgRDdSEaTEZUFWVFTWGQXGNYHKZHH_IE`IBaJ9aJDbI\ GcIJdIMeIPfITgIWhIZhIaiHdjHhkHklHnmHqnHtoHwoHxqIxs\ JxuKxwLxyLwqTwi`vagvUovNvqMplLjgLdbK_YKUTJOOIJJIDE\ H7AH2CJ3EK3GL3IM3KN4MO4OP4PQ4RR5TS5VT5XU5ZV6`W6bX6\ cY6aNJ_DVZ3fY7gYAgYDgYGgXKgXNgXQgXTgWXgW_gWbgWegVi\ gVlgVogVrgVsdWOsTNrQNqNNq } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD CD ordering info
by Jim Muth 15 Feb '03

15 Feb '03

I'm still trying to work out a few details about ordering the long-awaited FOTD CD. I'll post the full ordering information sometime tomorrow. Be patient fractal fans . . . Jim M.

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Re: FOTD 14-02-03 (Beach and Cliffs [6])
by Fr. Jim Lacasse 14 Feb '03

14 Feb '03

I tried to run the .par file for today's fractal and I got an error message saying that it could not find a file. Is there a typo in the formula code?? Thanks Fr. Jim >>> Paul.N.Lee(a)Worldnet.att.net 02/14/03 09:30AM >>> Jim Muth wrote: > > Though the coloring of today's image is spectacularly intense, > it was achieved with the aid of an additional graphics program, > and therefore is artificial. If you would send me the image you created, then I will put that on the web site, instead of the FractInt version which I generated without your colorings. Which reminds me, were you able to recreate the exact same colorings of past FOTD images for your CD?? What I mean is the images you tweaked in the past with a graphics progam and then made available in both JPEG and GIF formats. And how did you save the "tweakings" (or steps taken) to be able to get those same colorings for your new CD?? Sincerely, P.N.L. ------------------------------------------------- http://home.att.net/~Paul.N.Lee/PNL_Fractals.html http://www.Nahee.com/Fractals/ _______________________________________________ Fractint mailing list Fractint(a)mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint

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FOTD 14-02-03 (Beach and Cliffs [6])
by Jim Muth 14 Feb '03

14 Feb '03

FOTD -- February 14, 2003 (Rating 6) Fractal visionaries and enthusiasts: Today's spectacularly colored image lies near the tip of the main filament of the fractal that is drawn by the MandelbrotBC1 formula when the real(p2) parameter is not changed from zero. This figure does not fit on the default screen, and the filament extends even farther beyond the border, to the north and west. Midgets of Mandeloids in the exponent range between 1 and 2, such as today's, have a curious characteristic that is well displayed in today's image. Parts of their shoreline form broad, gently sloping beaches, while other parts form sheer cliffs. The northern edges of today's midget are in the form of broad, flat, high-iteration beaches, which I have colored brilliant yellow. The southern edges form sheer cliffs, where the duller, low-iteration, outside material directly abuts the water. I named the image ""Beach and Cliffs" when I noticed the clarity of this contrast. This same beach-cliff effect also exists in the normal quadratic midgets, though it is far less noticeable. In quadratic midgets, the East Valley area represents the sheer cliffs, while the area where the main stem joins the main body of the midget represents the flat beaches, where the iteration count becomes very high, and images take a long time to render. Though the coloring of today's image is spectacularly intense, it was achieved with the aid of an additional graphics program, and therefore is artificial. Combined with the commonplace nature of the midget, this drops the rating from a 7 to the present 6, which is still a bit above average. The render time of 5-1/2 minutes on my 200mhz machine is just about proper for an image that rates just a little above average. The image may be seen faster by downloading it from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Before moving on to the all-unimportant weather, I must find what kind of a demand there will be for the much-heralded FOTD CD-ROM, so that I will know whether it will be worth the effort of having it mass-produced. (which I doubt) The disk is basically finished, and will contain every FOTD image from the start of the series in April 1997 to the end of December 2002, plus many earlier images and some extra controversial philosoph- ical discussions. I currently plan on selling the disks for 20 dollars. If you would purchase a disk at this price, drop me a letter at my mindspring e-mail address. Cold temperatures, clouds and biting winds prevailed all day Thursday here at Fractal Central. The temperature of 28F -2C was far too chilly for sensitive paws and whiskers, so the fractal duo spent the day indoors, wishing they could be more comfortable outside. Luckily, by the time evening arrived, the tuna had been restocked. The treat raised the duo's spirits notably. Today is starting cold again, and more snow is forecast for the week-end. I fear much more tuna will be required. I also fear that if I fail to start the day's tasks, I will never finish before the forecasted snowstorm arrives. (which they often never do) So until 24 hours from now, when the next glorious FOTD will appear, take care, and wait patiently. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Beach_and_Cliffs { ; time=0:05:30.37--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-1.590574411382/+4.488285640669/85143.9\ 2/1/17.7/0.0 params=1.414213562373/0/0/0 float=y maxiter=42000 inside=0 logmap=38 periodicity=10 colors=00060J00O00R00V00_00c00h00m00p00m00j00g00d0\ 0a00Z60WB2UH4SM6PV8McBHjDCrF7yH0uB0q60m00i00e00a00\ Y00U00Q02M08I0FJ0MO0SS0_X0e_0lc0rg0yl0zp0zu0zy0zz0\ zz0zw0zp0zg6raJcVVQMXXDXa6_e0_j0an0ar0aw0er0jp8nlH\ pjSuecyclz_wzXzzSzzQzzVzwXwn_pgaj_ccSeXJgSDj_FgeHe\ lJcrMayO_zQXzSXzQazOczMgzJjzHnzFpzDuzDwzBzz8zz6zz4\ zz2zz0zz0zz0zz0zz0zw0zr0zl0ze0za0zV0zO0zJ0zD0z60z2\ 0zB0zJ0zS0za0zj0zp0zy0zz0zz0zz0zz0zz0zz0zz0zz0zz0z\ z2zz4zz6zz6zzDzwJzuQzpXwnaujgpgnlcugayeczXezOgzFgz\ 6_z0Sz0Jz0Dz06z08z0Bz0Dz0Fz0Hz0Hz0Hz0Jz0Jz0Jz0Jz0M\ z0Mz0Mz4Mz6OzBOzDOzHOzJVzXawggprnlzzgzzczz_zzXzzVz\ zSzzSzzQzzOzzOzzMzzMzzMyzMrzMlzMezJ_zOSzSMzXFza8ze\ 2zj0zn0zr2zw4zz6zz8zzBzzDzzFzzHzzJzzMzzOzzQzzSzzVz\ zXzz_zzazzczzezzgzzjzzlzznzznzzgzzczzXzzSzzOzzHzzD\ zz8zz2zz0zz0zz0zz4zz8zzDzzHzzMzzQzzVzz_zzczzgzzlzz\ pzzuzzyzzDzzwzz0zz0zz0zz0 } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-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 20.0 PAR-FORMULA FILE==================================

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FOTD 13-02-03 (In the Dog's Eye [7])
by Jim Muth 13 Feb '03

13 Feb '03

FOTD -- February 13, 2003 (Rating 7) Fractal visionaries and enthusiasts: Today's image is a blow-up of a midget that lies on the filament extending outward from the main valley of yesterday's 'Fido' image. Since this valley forms the eyes of the dog's head, I named the image "In the Dog's Eye". The image is one of the best scenes I have yet found in the fractured fractals with an exponent of Z between 1 and 2. I rated it at an honest 7. Most of the rating is earned by the < tdis > option, which colored the image. The image is unusu- ally detailed, and benefits greatly by being rendered at a high resolution. An unusual feature of today's fractal is the trip out from it back to the surface of its parent. As the outzoom progresses, one attractive fractal scene after another comes into view. Several of these larger scenes could just as well have qualified as today's FOTD, but I chose the deepest one I could safely reach. On my aging Pentium 200mhz machine the parameter file renders in 7 minutes. On a faster machine it will render in less time. But the fastest way of all to see the image is to download it from Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> As I wrote two days ago, when I read the book "Relativity and Common Sense" by Hermann Bondi, I was forced to change the way I thought about the universe at large. No longer could I assume that the laws of the limited part of the world which I observed through my limited senses were valid over the vast range of physical existence. But even though the vast physical universe worked differently than my limited sensory input led me to assume, it was still out there, solid and real, regardless of whether it was being observed, a firm foundation upon which the discipline of science had been built. After fascinating myself with the curiosities of relativity, I turned to quantum mechanics, went to the local library, and read as many books as I could find which I was able to understand. To begin, I found far fewer popularized books of QM. This is because QM is so strange that it is difficult to accurately express in everyday words. I discovered that the tiny microscopic world is far stranger than the vast world of relativity. QM can be fully described only by arcane mathematics, and can be fully grasped only by those who understand the math. I found that there are several interpretations of what the math means, and that the leading interpretation is, (or was at that time), the Copenhagen Interpretation. This interpretation states (as best I could understand it) that at the atomic level there is no reality -- that reality is somehow created when a quantum thing is measured. Now my curiosity was really aroused. The physical world is real, I thought. My senses show me that it is really out there. I can see it and hear it. Even in the dark, when I cannot see or hear things, I know they are still there because I can feel them when I bump into them. And what about things that really happened when no one was there to observe them, such as the formation of earth's moon? It made no sense at all. How can real physical objects be built of electrons, protons and neutrons that are not real? A house cannot be built of imaginary bricks. Either the atoms must be real or the objects must be unreal. Was the science that I admire based on an illusion? And I found other quantum things that seemed absolutely impossible. I found that a single object (if quantum things are objects) can be in more than one place at a single moment of time. I found that quantum information can be transmitted instantaneously over any distance, faster than light, which relativity had just told me was impossible. I found that sub-atomic things can go forward, backward, or even sideways in time. In short, I found that the universe is not only stranger that I imagined, it is stranger than I could possibly imagine. And even more telling, I found that not even the quantum experts know what is going on down there. There are many competing interpretations of QM, with the ultimate goal being to reduce the quantum world to something that resembles our everyday world, where space is filled with real, spatially separated objects, and time flows forward in a straight line. When I realized how weird the world as described by science had become, the world as described by religious mystics, which I had recently decided was imaginary, seemed ordinary by comparison. This realization marked the beginning of the end of my days as a materialistic, Atheistic skeptic. If I continue this thread, it will be only on the philofractal list. Now let's get on to that all-important weather. Sun and cold winds prevailed here at Fractal Central on Wednesday. The sun tried hard, but the snow-covered ground and temperature of 26F -3C were too much for it to overcome. As a result, the fractal cats endured another day of semi-voluntary confinement. The ultimate insult came in the evening, when I discovered the cats' food shelf devoid of tuna. They satisfied themselves with a few slices of left-over turkey that I managed to dredge up. I see work beside me and the clock on the wall overhead ticking all too fast. I had best get busy doing what needs to be done. Until next time, take care, and if nothing is real, what am I. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ In_the_Dogs_Eye { ; time=0:06:55.07--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=+0.06875740844296324/-2.375913184400092\ 00/2.898133e+011/1/-85/0.00235733226356027 inside=0 params=1.5596104695/0/1234/0 float=y maxiter=8000 outside=tdis periodicity=10 mathtolerance=/1 colors=000o`on_lm_jlZgkYdlVnjYbh_SfbGcc0ed5gdAidFj\ eJleOneTpeYqfasffufkvfoucluajtZgtXesUbsS`rQYrNWqLT\ qIRpGOpEMqEHqECuD6qE7nF8kG9gHAdIBaJCYKDVLESMFDAFPM\ FZXG_YF_ZF`_E`_Ea`DaaDbbCbbCccBcdBdeAdeAef9eg9eg9`\ aDXWHSRLOLPEHNKGSQFXWFaaEegEjmDosDsKeUPdUVdU_cUebU\ l`RjbUicWhdYff_egadhcbjeakg`liamgamfamebmcbnbbnacn\ _cnZcoYdoWdoVdoUemSekQfjOfhMggKgeIhdGhbFh`Di_BiY9j\ X7jV5kU3kS1kR0dS4ZT8SUCMUFKVHJWIHWJGXLEXMDYNBYOAZQ\ 8ZR7_S3aU6_T9YTBWSEVSHTRJRRMPQPOQRMPUKPXIO_EPZHOYK\ OYNOXPOWSOWVNVXNV_NUbNTdNTgMSjMRlMRoMQrMUyPQtMNoKK\ jHHeFE`CBWA8R75M52I34M85QC6TG7XK9`OAcSBgXCk`EndFrh\ GvlHypJuiKrcLnXMkRNgKOdERf2Pa8OYDMUILQNJLTIHYGDbF9\ gE5lQDXaLHuZ2lS1cM0WG0UH2TI4SJ5RK7QL8PMAONBNODMPEL\ QGKRHJSJITKHUMMZBGUNCMdBQZATT9WN6WK8ZIAaGCcFEfDGhC\ IkAKm9Mp7Nr6PeKRTYTGkV3xX6wY8w_Aw`CwbFwcHveJvfLvgO\ viQvjSulUumXuoZup`uqbupar } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-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 20.0 PAR-FORMULA FILE==================================

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FOTD 12-02-03 (Fido [5])
by Jim Muth 12 Feb '03

12 Feb '03

FOTD -- February 12, 2003 (Rating 5) Fractal visionaries and enthusiasts: When I saw today's image, I saw such a clear image of the outline of a dog's head facing right that I had no choice but to name the the picture "Fido", the most generic of all dog's names. The midget that forms the head is actually the largest midget on the largest filament of the fractal that results when the formula Z^(1.5596104695)+C is iterated 1234 levels up the logarithmic spiral. No one has ever seen this spiral, which is even more abstract than the fractals that lie along it. I assume that it is five-dimensional, at least in the case of formulas like today's. But being no math expert, I am only guessing. With so little in the image other than the shadow of a dog's head, I could rate it no higher than a 5. But the lightning- fast render time of only one minute makes the work of running the parameter file worth the effort. For those who prefer to download the finished image, the download is available at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The snow-covered ground and temperature of 27F -3C kept the dynamic cats indoors all day Tuesday. A snow squall in the evening dropped an additional few centimeters that assures they will be in jail again today. Hopefully, the tuna will keep them satisfied. I'll be satisfied when the modestly huge amount of work now before me is behind me. So until tomorrow, take care, and put your faith in things that are real -- that is after you have determined what is real. (clue -- it might not be what it seems) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fido { ; time=0:01:07.72--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor center-mag=0.0780992/-2.39592/42.40069/1/-85/2.166\ 66962149503206e-013 params=1.5596104695/0/1234/0 float=y maxiter=28000 inside=0 logmap=yes colors=00000C00E00G00H00J00L00N02P06R0AT0EV0GX4J`8\ LdEPgJRkPVoTXsZ`zdbziezrjzskzxqzztzzxzztzzpzzmzzkz\ xizvgzugzuezvdzxbzz`zzZxzXvzXuzVszTqzRozPmzNkzLizL\ gzJezHdzGbzE`zCZzAXzAVz8Tz6Rz4Pz2Nx0Lx0Jv0Hv0Gu0Eu\ 0Cs0As08q06q04o04o04m44m84kC4kG4iJ4iN4gR4gV4eX4eZ6\ dZ6dZ6bZ6bZ8`Z8`Z8`Z8bZAbZAdZAe`Ae`Cg`Cg`Ci`Ck`Ek`\ Em`Em`Eo`Gq`GqbGsbGsbHubHvbHvbHxbJxbJzbJzbJzbLzdLz\ dLzdLzdNzdNzdNzdNzdPzdPzdPzdPzdPzdPzdRzeRzeRzeRzgT\ zgTziTziVziVzkVzkVzkXzmXzmXzmXzoZzoZzoZzq`zq`zq`zs\ `zsbzubzubzubzvdzvdzvdzxezxezxezzezzgzzgzzgxzgxzix\ zixzixzizzgzzgzzezzezzdzzdzzbzzbzz`zz`zzZzzZzzXzzX\ zzVzzVzzTzzTzzRzzSzzUzzWzzYzz_zzazzczzezzgzzhzzizz\ jzzkzzlzzmzznzzozzpzzqzzrzzszztzzuzzvzzwzzxzzyzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-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 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] Problem creating JackOTradez's image in Fractint
by Jim Muth 11 Feb '03

11 Feb '03

At 07:59 AM 2/11/03 -0500, Harold lane wrote: Anyone - in JackOTradez's posting to this forum on Sun, 9 Feb 2003 he includes a set of parameters and the formula it refers to. When I use these I get a solid blue screen. REPLY: The original post does not work because the 'frm:' has been omitted before the formula name. Save this letter as a text file with a .par extension and it will run correctly. The image is really quite good. The first few lines are black, so don't be concerned when nothing appears on the screen for a minute or so. Jim M. --------------------------------------------------------- 6ml08402 { ; Image Copyright 2000 by Lee H. Skinner ; Version 2000 Patchlevel 8 reset=2000 type=formula formulafile=mmix_lak.frm formulaname=mmix4-lake-0084 function=ident passes=1 center-mag=-27.441/-0.000702002/11.62791/1/90 params=0/0/33.33/0/0.2/300 float=y maxiter=2500 bailout=25 inside=0 logmap=9 symmetry=none periodicity=10 colors=000D`z<3>7hz5kz4mz2oz0rz<2>1nv2lu3jt4hr4gq\ <10>CPbDN`EL_<2>GGWGFVGFT<5>EALE9KE9J<3>C6DB5CB5B\ <3>A48937B37<36>rG6sH6tH6<2>xI6zJ5zH5zE6<3>ZF7\ SF7LF7E07707<13>JWHKYIK_J<2>NgL<13>ntmpuorvq<2>xy\ wzzzzzx<10>zyVzySzyQzyNzyKzxH<3>zw7zw8<10>zg3ze3z\ d2<2>z_1zY0yX1<3>rR9pPBnODlMFjK0<8>sh`tkeuni<2>xw\ uzzzzxz<8>z`zzYzzVz<3>yKz<3>f7rb3pY0n<7>W8tW9uWAv\ <3>UEyTFzSHz<7>FZz } frm:MMix4-lake-0084 { ; 6990726 - Formula by Sylvie Gallet & Jim Muth ; MandelbrotMix4 parameters (hard-coded): ; ------------------------- p_p1 = (1,2) p_p2 = (81.5,-100) p_p3 = (-0.95,10000) ; Function: i ; User-selectable Lake parameters: ; ------------------------------- ; real part of p2: 0 = lake transform disabled ; any value between 0 and 100: water level in % of ; the screen height (0 = bottom, 100 = top) ; imag part of p2: phase ; real part of p3: amplitude of the wave (try 0.2) ; imag part of p3: frequency (try 300) ; Lake transformation (Sylvie Gallet) ; ------------------- if (real(p2) > 0 && real(p2) <= 100) level = real(p2) / 100 ; water level phase = imag(p2) ; phase 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 + phase)) * v endif pixel = z + z3rd endif ; Modified MandelbrotMix4 formula (Jim Muth) ; ------------------------------- a = real(p_p1) , b = imag(p_p1) , d = real(p_p2) , f = imag(p_p2) g = 1/f , h = 1/d , j = 1/(f-b) , z = (-a*b*g*h)^j k = real(p_p3) + 1 , l = imag(p_p3) + 100 , c = fn1(pixel) : z = k*(a*(z^b) + d*(z^f)) + c |z| < l } ------------------------------------------------

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FOTD 11-02-03 (The Key [6])
by Jim Muth 11 Feb '03

11 Feb '03

FOTD -- February 11, 2003 (Rating 6) Fractal visionaries and enthusiasts: The exponent of Z in today's image -- 1.5596104695 -- is a slightly more accurate refinement of the exponent that created yesterday's lowly image. This number, when raised to the power of itself, comes as close to exactly equaling 2 as is possible to calculate on my 10-digit pocket calculator. The difference in the resulting parent fractal is insignificant. The improvement in image quality is a result of my better fractal luck, plus a bit of skill. Today's scene could just as easily have been found in yesterday's parent fractal, if I had searched for it in today's area. The numbers create the fractal universe; the fractalist must find the goodies in the universe. I named the image "The Key". I have no idea what the key is supposed to unlock. It could be the door to enlightenment, the door to wonder, the door to mystery, or my favorite door -- the door to reality. Unfortunately, even though I now have the key, I have yet to find the door, so the mystery will remain unanswered. The parent of today's image resembles a mis-shapen M-set, with its nose pointed southwest. Today's scene is located in the 'East Valley' of this M-set, which is located off-center on the north-northeast shore of the main bay. The little midget at the center, shining golden in its isolation, was discovered entirely by luck. I found it by toggling into and out of color-cycling mode and searching for points on the screen that blinked. I often use this trick when searching for midgets, but in order for it to work, the inside must be set to the number zero, which in turn must be set to a very dark shade. In fractals of this exponent range, there are very few clues to the location of midgets. Sometimes a convergence of discontinu- ities points to the midgets, sometimes not. Sometimes I simply get a feeling that a certain feature holds a midget, and some- times I am right. The rating of an above average 6 shows that midgets which exist in fractals with exponents of Z in the range between 1 and 2 need not be the nearly hopeless jumble of disorganized bits and pieces that spoiled yesterday's image. The render time of 8 minutes is a bit excessive for an image which, even though it rates 3 points above the image of the day before, is still only slightly above average. The good news is that the wait to see the image can be largely eliminated by downloading the pre-rendered GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> As I mentioned in yesterday's discussion, when I became familiar with the consequences of relativity, I was forced to give up the comfortable and intuitive world image that I, along with most everyone else, had developed in the formative years. No longer could I consider time and space to be two separate things. I now needed to see them as two different ways of seeing the same thing -- spacetime. No longer could I assume that the present moment of time exists throughout the universe. There could be no universal moment of time any more than there could be a uni- versal point of space. Distance and time no longer had absolute- ly fixed measurements. Mass turned out to be a different form of energy, and mass also was no longer fixed. And most impor- tantly, at least to me, was the realization that the universe is actually four-dimensional. But when I discovered relativity, the world, as strange and counter-intuitive as it had become, was still out there, real and almost solid. It seemed counter-intuitive only because in our day-to-day lives we experience such an infinitesimally small range of its vast extent. Then I became interested in quantum mechanics, and my philosophi- cal problems grew far greater but far more interesting. If all goes well, I'll discuss this tomorrow. At this point I will say only that anything based on the assumption of the existence of an independent, objectively real world is opened to cross-exami- nation by the implications of Q.M. The occasional light snow continued most of the day Monday here at F.C. It never amounted to much, but with the temperature at freezing, was just enough to keep the dynamic ones confined to quarters, wishing for better things. The better things eventual- ly appeared in the form of a tuna treat. Today is starting sunny but very cold, with deep snow on the ground. It remains to be seen how the duo will react. I see it's past time for me to get busy, so until tomorrow, take care, and wonder about what to wonder about. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Key { ; time=0:08:14.28--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-0.47182282050367800/+0.633258130587982\ 10/3329459/1/-67.4999999978284535/-7.9310562145495\ 922e-009 params=1.5596104695/0/-80/0 float=y maxiter=3600 inside=0 logmap=197 periodicity=10 colors=000maIkaJhaKfaLcaM`bNYbOWbPTbQQbRNbSKbTBWWD\ QYFK_IEaK8cM2eP5bS7_VAYYCV_FTbHQeKOhMLjPJmRGpUEsWB\ uY9rWAoUBlSCiQDfOEcMF`KGYIHVGISEJPCKMALJ8MG6ND4OA2\ OE1QH1RK1SN1UQ1VT1WW1YZ1Za1_d1ag1bj1ch2af3_d3Yb4X`\ 4VZ5TX5SV6QT6OS7NQ7LO8JM8IK9GI9EGADEABCB9BB8EFCGIF\ JLILOLORPQUSTXVV_YYca_fdbigdljgonirqlutnxwftx_pyTm\ yMizFfzCeqAdh8c_6bR4aI2`A1dN1hZ1lj1pv4ms7kqAioDgmG\ ekIbiL`gOZeRXcUVaWT_VUZUU_TU`SVaRVbQVcPWdOWeNWfNXg\ MWfLVeKWdJVcIVbHVaGV`FV_FVZGWYGWXGWWGWVGWUGVTGUSGU\ RHUQHUPHUOHUNHUMHUMHUMHUMHUMIUOIUPIUQJSRJRSJQTKPVK\ PWKOXLKYLIZLI_MJaMKbMLcNMdNNeNOfLPgKQhIRiHSjFTkEUl\ CVmBWnAXn9Ym9Zl8_l8`k7aj7bj6ci6ei5gh5ig4kg4mf4ofCq\ bJs_RtXYuTevQlwNjxLhyKfzJdzIczGazF_zE_zDbzCezAhz9k\ z8nz7qz6tz4wz3zz2zz1zz0zz1zz1zz2zz2zz3zz3zz4zz4zz4\ zz5zz5zz6zz6zz7zz7zz7zz9zzBzzCzzEzzGzzHzzJzzLzzMzz\ OzzQzzRzzTzzDzzEzzFzzGzzH } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-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 20.0 PAR-FORMULA FILE==================================

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Problem creating JackOTradez's image in Fractint
by Harold Lane 11 Feb '03

11 Feb '03

Anyone - in JackOTradez's posting to this forum on Sun, 9 Feb 2003 he includes a set of parameters and the formula it refers to. When I use these I get a solid blue screen. In looking at the formula I note that the identifiers 'magxmag' and 'rotskew' are used on the right hand side of equations without their having appeared on the left side of an equals sign to define their value. Are some lines of the formula missing? Or are 'magxmag' and 'rotskew' special identifiers that refer to internal Fractint values like 'pixel', 'rand', fn1 & pi and therefore don't need to be assigned values in the formula? <==<< I did a search for 'rotskew' in the fractint.doc file and also in Bradley Beacham's Formula Tutorial and did not find it so I'm thinking that since it is not in the documentation that it is not likely to be a special identifier. w = h / 0.75 * imag(magxmag) tanskew = tan(imag(rotskew * pi / 180)) Did anyone else have a problem creating the image? If so, did anyone else discover how to correct the problem? <==<< The image sounds interesting - any help would be appreciated. - Hal Lane hallane @ compuserve.com

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FOTD 10-02-03 (Stuff [3])
by Jim Muth 10 Feb '03

10 Feb '03

FOTD -- February 10, 2003 (Rating 3) Fractal visionaries and enthusiasts: I named today's less-than-stellar image "Stuff" because it is a good illustration of the fragmented bits and pieces of something, or perhaps nothing, that I call fractal 'stuff'. This stuff is not material, since it has no physical basis; yet it is not a total abstraction, since it can easily be rendered and visualized. It is just 'stuff', and that is what I have always considered it. The exponent of Z in the generating formula is 1.559612. I chose this number because 1.559612^1.559612 almost equals 2. (1.559611 is closer.) This fact has little significance in the appearance of the resulting fractal, and was chosen on a whim. Luckily, the image renders in only a few minutes, for I could honestly rate it no higher than an abysmal 3. But it is still worth a quick glance. As always, the GIF file has been posted to: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and to: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> While rummaging around in the attic yesterday, I came upon the dried-out remnants of a toy chemistry set that I had played with long ago and then grown tired of. I have no idea how it got there, for I have moved several times since I received it as a Christmas gift back in the years when I was filled with wonder and just discovering science. (I also had a toy microscope, a toy telescope, a toy weather station, an erector set that was supposed to build a walking robot, [I never managed to get the robot constructed.], and all the other goodies that boys who have decided to become scientists enjoy.) As fate would have it, I never became a 'scientist', whatever one of them is. I almost accidentally became involved in the printing trade and eventually became a graphic designer. But I have never lost that sense of scientific wonder. However, since those early years, I have become familiar with relativity and quantum theory. As a result, I now wonder more than anything else about the philosophical basis of science. Where I once wondered what the moon is made of, I now wonder if the physical world actually is an 'objective reality' or if 'reality' is an attribute we have invented for convenience and then bestowed upon the aggregate of our sensual impressions. And I wonder whether it makes a difference. The star Sirius is 8 light years away. When I was much younger, this meant that if something were to happen at this moment on that star, we would not know about it for 8 years, because it would take 8 years for the information to reach us. Then I became interested in relativity and found that there is no such thing as a universal present moment of time. The phrase 'at this moment on that star' has different meanings for different observers. Instead of thinking that our present moment of time now exists at the position of the star, but due to the finite speed of light, we on earth are seeing the star as it existed 8 years ago, we can just as accurately think that we are seeing the star as it presently exists and the actual time at the star is now 8 years in the future, and it will take us 8 years to reach that future time. So at this moment, what time actually exists on the star Sirius? The question cannot be answered. Time is relative. Asking such a question is like asking someone to find the center of the surface of a featureless sphere. All that can be said is that wherever a particular observer is located, that observer will find himself in his own private present moment of time. And what does this ambiguity of time mean to us in our everyday lives? It means nothing at all -- that is unless we begin traveling around our galactic vicinity at a velocity which is a sizeable percentage of the velocity of light. When (and if) this time comes, we will find ourselves faced with such present- day absurdities as having a twin who was born at the same time as ourselves, yet is 20 years older or younger. But when this happens, the absurdities will not be absurd at all. This relativistic situation might seen weird enough, but relativity at least leaves us with a real world, objectively out there to serve as a firm foundation for the science we have developed over thousands of years. This is more than quantum theory does when it brings into question the very existence of objective reality. With ample sun and a temperature of 41F 5C, the weather was quite pleasant here at F.C. on Sunday. Had the ground not been snow-covered, the dynamically fractal cats would have had a great day in the yard. As it was, they had a not-quite-as-great day on the porch, chasing the few sunbeams that are just beginning to reach there. Today is starting cloudy and colder, with on-and-off periods of light snow. The duo will not enjoy this. I'll enjoy the day better when I finish the work, and I will not finish until I resume it, so until next time, take care, and never lose that sense of wonder, but be careful what you wonder about. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Stuff {;time=a few minutes-SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=+0.68446783504689930/-0.804007887280942\ 20/1008.977/1/-165/2.03941030729737349e-013 params=1.559612/0/64/0 float=y maxiter=1100 inside=0 logmap=71 periodicity=10 colors=000osiqujrwktyluzmsynrxnqwnpvnovnnuomtolsok\ sojroiqohppgppfopenpdmpcmpail`fiZcfY`cXY`VVYUSVTPS\ RLPQIMOFJNCGM9DK6AJ37I04J47J7AKADKDFKHILKLLNNMQQMU\ TzmVwlYuk`ojbhg`bd_VbZT`XV_WW`VY`TZaS`bRaaPcaOdaNe\ `Lg`Kh`Jj_Hk_Gm_FnZDpZCqZBsY9tY8uY7sW9rVAqUBpTCoSE\ nRFlPGkOHjNIiMKhLLgKMeINdHPcGQbFRaES`DTWMSRURMbRHj\ QDrQFsPHtPJuOLvONwNPxNRyNQxOQxPQwQPwRPwSPvTPvUOvVO\ uWOuXOuYNtZNt_Ns`MsaMsbMrcMrdLreLqfLqgLqhMrlMspOqo\ PonQnmRllSjkTijUgiVehWdgXbfY`eZ_d_Yc`XbY_ZVaWScSQe\ PNgLKiIIkEFmBCo7Aq4Gp9MpDSoHYoLcnQinUomYtmaoo_jpYf\ rWasUXtSTvQOwOKxMSmR_bVgTZoIbv8flCcbFaTJZKMYIOZGP_\ FQ`ERaFTbHUcIVdJWeKXfLYgMZhNZiO_jP`kQ`lRamSbnTboU`\ pV_qWZrX_sY`tZau_cv`cwacxbcycczcczcezcgzchzckzckzc\ lzclzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmz\ cmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcm\ zcmzcmzcmzcmzcmzcmzcmzcmz } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-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 20.0 PAR-FORMULA FILE==================================

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Re: Fractint digest, Vol 1 #390 - 3 msgs
by JackOTradez 09 Feb '03

09 Feb '03

Greetings and Hallucinations fellow Fractal eXplorerZ! I have been playing with Chaos for about 8 years now, and have thousands and thousands of images. Many from CD's I bought, many from downloads; many downloaded formula and PAR files, and the ones I have made myself. Many (>50%) are mediocre and lame, some of the rest are good. About 10% are really good. And every now and then I come across one that literally makes my eyes widen and jaw drop. I am not sure where I downloaded this, but it was very recently. I felt inclined to post it and share it. On a P3-733, the 1600x1200 image takes 22 minutes. Copy and paste this into notepad, name the file: mmix_lak.frm ;;;;;;;;;;;;;;;;;;; BEGIN mmix_lak.frm ;;;;;;;;;;;;;;;;;;; MMix4-lake-0084 { ; 6990726 - Formula by Sylvie Gallet & Jim Muth ; MandelbrotMix4 parameters (hard-coded): ; ------------------------- p_p1 = (1,2) p_p2 = (81.5,-100) p_p3 = (-0.95,10000) ; Function: i ; User-selectable Lake parameters: ; ------------------------------- ; real part of p2: 0 = lake transform disabled ; any value between 0 and 100: water level in % of ; the screen height (0 = bottom, 100 = top) ; imag part of p2: phase ; real part of p3: amplitude of the wave (try 0.2) ; imag part of p3: frequency (try 300) ; Lake transformation (Sylvie Gallet) ; ------------------- if (real(p2) > 0 && real(p2) <= 100) level = real(p2) / 100 ; water level phase = imag(p2) ; phase 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 + phase)) * v endif pixel = z + z3rd endif ; Modified MandelbrotMix4 formula (Jim Muth) ; ------------------------------- a = real(p_p1) , b = imag(p_p1) , d = real(p_p2) , f = imag(p_p2) g = 1/f , h = 1/d , j = 1/(f-b) , z = (-a*b*g*h)^j k = real(p_p3) + 1 , l = imag(p_p3) + 100 , c = fn1(pixel) : z = k*(a*(z^b) + d*(z^f)) + c |z| < l } ;;;;;;;;;;;;;;;;;;; END mmix_lak.frm ;;;;;;;;;;;;;;;;;;; Copy and paste this into notepad, name the file: lhslakes.par ;;;;;;;;;;;;;;;;;;; BEGIN LHSLAKES.PAR ;;;;;;;;;;;;;;;;;;; 6ml08402 { ; ; ; Image Copyright 2000 by Lee H. Skinner ver=2000 ; Version 2000 Patchlevel 8 reset=2000 type=formula formulafile=mmix_lak.frm formulaname=mmix4-lake-0084 function=ident passes=1 center-mag=-27.441/-0.000702002/11.62791/1/90 params=0/0/33.33/0/0.2/300 float=y maxiter=2500 bailout=25 inside=0 logmap=9 symmetry=none periodicity=10 colors=000D`z<3>7hz5kz4mz2oz0rz<2>1nv2lu3jt4hr4gq<10>CPbDN`EL_<2>GGWGFVG\ FT<5>EALE9KE9J<3>C6DB5CB5B<3>A48937B37<36>rG6sH6tH6<2>xI6zJ5zH5zE6<3>ZF7\ SF7LF7E07707<13>JWHKYIK_J<2>NgL<13>ntmpuorvq<2>xywzzzzzx<10>zyVzySzyQzyN\ zyKzxH<3>zw7zw8<10>zg3ze3zd2<2>z_1zY0yX1<3>rR9pPBnODlMFjK0<8>sh`tkeuni<2\ >xwuzzzzxz<8>z`zzYzzVz<3>yKz<3>f7rb3pY0n<7>W8tW9uWAv<3>UEyTFzSHz<7>FZz } ;;;;;;;;;;;;;;;;;;; END LHSLAKES.PAR ;;;;;;;;;;;;;;;;;;; "As I stand on a tropical beach gazing out across the Ocean to the horizon, Behold! The gates of Heaven have opened and the Throne of thrones arises, adorned in turquoise and gold. Let all stand in awe and wonder and give Praise, for the Great One has come!" (now if I can figure a way to animate this one ...) Stay Amazed! JoTz

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FOTD 09-02-03 (Irregular Minibrot [5])
by Jim Muth 09 Feb '03

09 Feb '03

FOTD -- February 09, 2003 (Rating 5) Fractal visionaries and enthusiasts: Today's fractal is named "Irregular Minibrot". The reason for the name is the shape of the midget and the irregularity of the features around it. The midget is irregular because instead of iterating Z^2, I iterated Z^sqrt(2) and chose a spot 14.142 levels down the logarithmic spiral to do the rendering. When this low a power of Z is iterated to make a fractal, the results are totally unpredictable. Mandeloids generally have a number of lobes one less than the exponent of Z in the generating expression. Thus the formula Z^5+C draws a Mandeloid with 4 lobes, and the Z^2+C Mandeloid, which is the classic Mandelbrot set, has one lobe. Following this progression, the Z^1.4142 Mandeloid has only 0.4142 lobe, less than half a lobe, but there is no easy rule determining which fraction of a single lobe will appear either in the parent fractal or in the midgets it contains. Theoretically, today's midget is only less than half there. Its buds are smaller than those of the classic M-set and more widely spaced. In addition, the buds are in the wrong places and mis- shapen as well. There are several smaller midgets in the image, which are easily found by toggling into and out of color mode. Some of these may also be interesting. I have not checked to see. With all its imperfections, today's FOTD makes an interesting image, though not interesting enough to rise above the rating of an average 5 that I gave it. The render time of 7 minutes is fair enough for such a mediocre image, and most of that time can be saved by downloading the fully-rendered GIF image from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather remained sunny all day Saturday here at Fractal Central, but the temperature of 25F -4C proved far too extreme for the whiskers of the cats, who poked their noses out the door only long enough to sample the chill and determine that they did not want to be outside. Today is starting warmer, but it is cloudy, so the effect on the dynamic duo will likely be the same. I have nothing much planned for the day, other than exploring Fractal Land that is, so I'll take it an hour at a time. Until next FOTD, take care, and can the shape of fractals be influenced by the power of thought? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Irregular_Minibrot { ; time=0:07:26:88--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=+0.86416652796344500/+0.512463707154294\ 50/1904.762/1/67.5/-5.01217123360930827e-012 params=1.4142/0/-14.142/0 float=y maxiter=6000 inside=0 logmap=73 periodicity=10 colors=000SZSQYROXQMWPKVOIUNFTMCSL9RK6QJ3PH4OI4NI4\ MI5LI5KJ5JJ5IJ6HJ6GK6FK7FK7EK7DL7CL8BL8AL89M98M97M\ 96M72L84M96MA8NBANCCOCEODGPEIPFKQGMQHORHQRISSJUSKW\ TMYTOYTQXVSXWUWXWWXYVY_VZaU_cU_eT_gT_iS_kR_mQ_oP_m\ OYkNXiMWfLVdKUbJU`ITYHTWGSUFSSESPDRNCRLBQIAQG9PE8P\ C8O97O77N57N37N49N5AN5CN6DN7EN7GN8HN9IN9KNALNBMNBO\ NCPN5PQCQNIULPXJV`GacEggCmjAnhBngCofDoeEpdFpcGqbHq\ aIr`JsYGrZIr_Jr`KraLqbMqcOqdPqeQpfRpgSphTpiVpjWokX\ olYomZon`noanpbnqcnrdpxcnselnfkjhieig`jfXldSmbOscO\ pcOndOldOidOgeOeeOceO`fOZfOXgOVgOSgOQhOOhOMhOJiOHi\ OFoIAiODdTF_ZIVcKQiNLnPGsRKnQOjRSeSV_TZXUbWVfUWeWX\ eYYd_Zda_cc`ceabhbbkcandaqe`tfdwgbzh`ziZzjXzkVzlTz\ mRznPzoNzpLzqJzrHzsFztDzuBzv6zwAzxEzyIzzMzzQzzUzzX\ zz`zzdzzhzzlzzpzztzzxzzwzzwzzwzzwzzwzzwzzyzzwzzuzz\ szzqzzozzmzzkzzizzgzzezzczzazz_zzYzzWzzUzzSzzQzzOz\ zMzzKzzIzzJzzHzzGzzFzzDzz } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-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 20.0 PAR-FORMULA FILE==================================

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Automatic processing of whole par-file
by paal.paal＠gmx.net 09 Feb '03

09 Feb '03

Hello group, I've collected a bunch of par-files from you nice guys out there and now that I have a second computer with lots of disk space I would like to have fractint work through this pile and present me with a ton of ready images. Is there a hassle-free way of doing this? I found the batch mode but I have to name every single item to be processed (or are there any wildcards?). Thanx a lot Jaan

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FOTD 08-02-03 (Lava-Ring [5])
by Jim Muth 08 Feb '03

08 Feb '03

FOTD -- February 08, 2003 (Rating 5) Fractal visionaries and enthusiasts: Today's image is yet another of my evaporated ones, created this time by subtracting a portion of Z^(-7.17) from an equal portion of Z^(-1.717) before adding 1/C. The scene was then 'evaporated' by raising the bailout radius to one-googol and rendering the resulting blank screen with the inside option set to < bof61 >. The real(p3) parameter is so awkward because its value was determined using the evolver feature. I use this feature in my fractal travels more often than is apparent, but in most cases I round off the value to something more aesthetic. In today's case, I was searching for the point where the entire fractal expands to infinity and returns from the opposite direction, and once I had found this point with the evolver, I did not bother with the rounding. Infinity is a curious concept, in some ways quite counter- intuitive. The arithmetic of infinity is very simple -- regardless of what is done to it, infinity remains unchanged. When geometry is expanded to infinity, some even more surprising things happen. An infinitely long line has a single point at infinity. It does not have the two points that intuition would demand. This can be better understood by thinking of two infinitely long parallel lines lying in a flat Euclidian plane, which can be considered either as never intersecting or as intersecting at infinity. (This is two different ways of saying the same thing.) Then imagine a finite point where the two lines intersect. It is only a single point, but as the lines are rotated, this point of intersection moves off in one direction, reaches infinity, then returns from the opposite direction. The point at infinity of the line lies in both directions. At no time during the rotation does a second point of intersection magically appear. The same situation prevails with an infinite plane, which has a straight line at infinity. Points that go off in any one direction and pass beyond infinity return from the opposite direction. (Actually, we're getting into projective geometry, and such a plane is actually a projective plane, but that's a different topic.) I named today's image "Lava-Ring". If enough imagination is used, the boiling pit of molten lava can actually be seen. But since molten lava is not my favorite substance, I could rate the resulting image no higher than a 5. The 24-minute render time also holds down the rating, but this wait can be avoided by downloading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The snow ended by noon on Friday, but the damage had already been done. With 8 inches 20cm of ice-crystals covering the yard, and a temperature around freezing, the fractal cats were confined to the near side of the porch, under the cover, where only a dusting of snow had settled. With such cramped quarters and cold paws, they stayed outside only a few minutes. The snow is still there this morning, so I suppose it will be another bad day for the aging duo. For me, it will be a passable day, but only if the small amount of work goes well. But regardless of how the work goes, I shall return in 24 hours with the next in the near-eternal series of fractals. Until then, take care, and be kind to web-footed fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Lava-Ring { ; time=0:24:05.69--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.79396508590478570/+0.640345353073420\ 90/5.261436e+008/1/-15/1.94124406955459294e-006 params=-1/-1.717/1/-7.17/-5.453445844904936/1e+100 float=y maxiter=1200 inside=bof61 logmap=122 periodicity=10 colors=00000X34A3JD3Fc3AQ36f9A`DDXIGSMJOSMJXPF`S9d\ V4jY0o`0sc0xf0za0s_0vX0oS0lP0vM0YI0lF0PC0V70_40P10\ V00T00Q01P01Q09Q3FQALSIQSPXSYcTfiTooTxuTzzSzxSvuSr\ rSmoSlmXgi_cfc_afV_jQVmOSpJOuFLxAGz6Dz19z06z7CzGGz\ PMzXQydVxm`vvduzixufylczd`zXYzOVzGTxJPoLMgMJ_OGQPD\ JQAAS73T44V76YA6_C7`F7cG9dJ9fLGdTOd`Vdgadogdvfcsdf\ pcimall`ri_vfYmcQzaJraJzaJzaJzaJmcJzcJzcJzcJzcJzcJ\ mcJmcJzcJmcJzcJzcJzcJzcJzcJzcJmcImdIzdImdIzdIzdIzd\ ImdIzfIzfIzfIzfImfIzfIzfIzfIygIygIygIxgIxgIxgIvgIv\ gIviIuiIuiIuiIsiIsiIsiIriGrjGrjGpjGpjGpjGojGojGolG\ mlGmlGmlGllGllGclGjlGjmGjmGimGimGimGgmGgmGgmGfoGfo\ GfoGdoGdoGdoGcoGcoFcpFapFapFapF`pF`pF`pF_rF_rF_rFY\ rFYrFYrFXrFXrFXsFVsFVsFVsFTsFTsFTsFSsFSuFSuFQuFQuF\ QuFPuFQuFTsDXoC_gAa`9dT7gM0jF0iC0fG0dL0cP1`V3__4Yc\ 7VgFTlMTpTTr`TsgTuoTusTuxTszVjzXazYTzYMz_Dz`4z`0z`\ 0y`0CmYAlX7jT4iS3gQ3aT3YV } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] Fractint and Win XP
by BillatNY＠aol.com 08 Feb '03

08 Feb '03

George, Yes, I'm afraid I initiated quite a long discussion about this. The bottom line I think was that most folks did not have any real problems. I have some with going above 640 x 480 rsolution while in XP. I can go higher if I boot to DOS, but that's a story hopefully you won't need to go into. If you do run into problems, I have saved every email from the discussion. The answer will likely be there. Bill Rossi <A HREF="http://members.aol.com/billatny/">http://members.aol.com/billatny/</A> <A HREF="http://www.arts4u.org/rossi/">http://www.arts4u.org/rossi/</A>

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Re: [Fractint] Mandelbrot and Julia Sets Explored by RareEvent Theory
by Russ Walsmith 07 Feb '03

07 Feb '03

>[2] A shortage of parameters (contributes to excuse [1] - why write it if >it won't work anyway?) >[3] Needed some unified approach to specifying rotations ([2] gets in the >way of this, of course) > >The last feature was crucial in my opinion. There seemed little point to me >in going on about the thing being 8-dimensional if one couldn't cut said >8-dimensional object with an arbitrary 2-dimensional plane for rendering. >What would be a reasonable way of specifying such a thing to make >navigation convenient? I was thinking something involving hyperspherical >coordinates to establish an orientation, and then offsetting it from the >origin. The tricky bit is to minimise the number of user parameters - >basically, it makes sense to define the system so that the normal viewport >translations/rotations are part of it, 'cos then we don't need to specify >them in the user parameters. > >Morgan L. Owens I agree. Sounds like a job for the SSG... _________________________________________________________________ STOP MORE SPAM with the new MSN 8 and get 2 months FREE* http://join.msn.com/?page=features/junkmail

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Fractint and Win XP
by George Priest 07 Feb '03

07 Feb '03

Hi: Please forgive me if I have not been paying proper attention but, is there any problem running Fractint under Windows XP? I just bought a new computer (Dell) with XP and I was wondering if I am going to encounter any problems with Fractint. Thanks George Priest

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FOTD 07-02-03 (Fractal Tendrils [7])
by Jim Muth 07 Feb '03

07 Feb '03

FOTD -- February 07, 2003 (Rating 7) Fractal visionaries and enthusiasts: I notice a letter on the Fractint list requesting the method of running the parameter files that I attach to the FOTD discussions. The process is simple. First, save the entire FOTD message in the Fractint directory as a pure text file with a .par extension. Be sure no lines wrap around and no extra characters (such as =3d) are inserted into the text by your e-mail reader. Then load Fractint and run the saved parameter file as you would any other parameter file. If all goes well, and it usually but not always does, the image will begin rendering, and when it is finished, can be explored like any other fractal. Today's image runs from the attached parameter file in 17 minutes on my machine at a resolution of 640x480x256. It is another of my evaporated images, and a very good one at that. The formula that created the image combines 12 negative parts of Z^(-1.6) with 9 negative parts of Z^(-10), then adds 1/C instead of C. The 1/C turns the normally inside-out parent fractal inside-out again, which results in a rightside-out fractal. In its un-evaporated form, this parent is a large, indescribable main open area, with many bays and estuaries, and a smaller, cut-off, more-Mandel-shaped figure to the east. The main bud of this cut-off feature is split down the middle by a spurious valley. Today's scene is located near the end of a filament extending from a bud on the shoreline of this valley, very near the point where the filament terminates in a large, oval open area. For this particular image, I used the MandelbrotMix2 formula rather than the MandelbrotMix4. Finding the name for today's image was easy. The detail in the converging arms so closely resembles the tendrils of a vine that the name "Fractal Tendrils" came almost automatically. Considering the unusually close resemblance of the fractal image to an actual physical object, the rating of a 7 is well justified. I have long considered the names I give to my fractal images. Fractals are abstract things, so should they be given the names of the physical things which, in my opinion, they resemble? Perhaps I should invent clever sounding nonsense words and phrases to serve as names for my images. I briefly considered a name such as "Vineroptera" for today's image. A whole new situation arises with languages other than English. For example, the Julibrot, which I explore so often, when translated into German, means something like "Bread of July" -- an interesting title, but one with little to do with the four- dimensional object in question. As I mentioned earlier, the parameter file of today's image renders in 17 minutes. That time may be cut to a minute or so by going to Paul's web site at" <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or to Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> and downloading the pre-rendered GIF image file from there. The clouds increased all day Thursday here at Fractal Central, but the snow held off until after dark. The high temperature of 34F 1C was quite chilly for the sensitive whiskers of the dynamic duo. The extra outing I gave them right before sunset will have to hold them for a few days, for the snow is still falling lightly this morning, with 7in 18cm on the ground. Luckily for me, the work is not piling up as fast as the snow. In fact, I should have most of it behind me by lunch time. That will leave me with nothing to do but watch the snow and search for the next FOTD. Until tomorrow, take care, and be of stout mind and slim body. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Tendrils { ; time=0:17:43.85--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+1.47367288202595900/+0.009826951264489\ 44/6.910667e+008/1/-65/-7.88200783911896519e-006 params=-12/-1.6/-9/-10/0/1e+100/0/0 float=y maxiter=600 inside=bof61 logmap=166 periodicity=10 colors=000OT_OUZOUYOVXPVXPWWPWVPXUPXTQYSQYRQZQQZPR\ _OR_NR`MR`LRaKSaJSbISbHScGQcBScGTcKVcOWcSYcWZc_`cc\ acgcckdcoecsfcsfdtfdtfdtdeqcfnbfk`gh_geZhbXh_WiXVi\ VUjSSjPRkMQkJOlGNlDMmAMn9Lm8Ll8Lk8Lj8Lj8Li8Lh8Kg8K\ f7Kf7Ke7Kd7Kc7Kb7Jb7Ja7J`7J_6JZ6JZ6JY6IX6IW6IV6IV6\ IU6IT5IS5HR5HR5HQ5HP5HO5HN5HN5MP6RR6VS6_U6dV6hX6mY\ 6t_6xa5xc6we6wf7xk7yc7yc8z`8za8z_9zg9zW9zcAtTAuaAu\ SBvZBuRBsYCrQCqPCoODoUDmNElNEkMEiLFhLFgKFeJGdJGcIG\ aIHaHHaGH`GI`FI`EI_EJ_DJ`CH_DJZDKYDLXDMXDNXDOXDPXD\ QXDRYDSYDTYDUYDVYDWXDXWDYVDZUD_TD`UCbTDaTD`TD_TDZS\ DYSDXSDWSDWREVREURETRESRERQEQQEQQEPQEOPFNPFMPFLPFK\ PFKOFJOFIOFHOFGNGFNGENGDNGDMGCMGBMGAMG9MG8LH7LH7LH\ 6LH5KH4KH3KH2KH1JF0KH1LI1MK1ML2NN2OO2PQ3PR3QT3RU4R\ W4SX4TZ5U_5Ua5Vb5Wc6Xc6Xc6Yc7Zc7Zm7_m8`m8am8am9bc9\ cc9cc9bcBbcCacEacFacG`aI`YJ`VK_SM_ONZLPZIQZERYBTY8\ UY5VMQfMQeNRdNRcNSbNSaOT` } frm:MandelbrotMix2 {; 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 20.0 PAR-FORMULA FILE==================================

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FOTD 06-02-03 (Hairybrot [5])
by Jim Muth 06 Feb '03

06 Feb '03

FOTD -- February 06, 2003 (Rating 5) Fractal visionaries and enthusiasts: Somewhere in the world, today is Waitangi day. I have no idea where it is celebrated or what a waitangi is. I assume that by mentioning a waitangi, I am not offending any ethnic group and thereby violating the rules of political correctness. So to all for whom it has significance, Happy Waitangi Day, or if the day is celebrated in the far east where the date has already passed, Happy Belated Waitangi Day. Today's fractal is named "Hairybrot". I gave it this name when, after studying the image for several minutes, half closing my eyes and all that kind of stuff, I could see nothing but a fractal pattern with porcupine-like hairs sticking out of it. The parent fractal is the same as yesterday's, with the slight exception that I changed the portion of Z^3.5 from 3.67 to 3.7. Today's scene lies in the suburbs of a larger midget in the East Valley area of a small Mandelbrot set that lies just beyond the southern point of the shapeless main bay of the parent. Like yesterday's image, today's image features disconnected elements, which normally indicate a non-critical area. But fractals don't seem to care about what is normal, and despite the surface appearance, the tiny midget is there at the center in all its unseen glory. I included the mathtolerance entry in the parameter file because the magnitude of the image is so great that it might otherwise render incorrectly. The rating of an average 5 reflects my current feelings about the image. Others may consider the image worth a higher or lower rating. The render time of 9 minutes can be avoided by downloading the pre-rendered GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Wednesday passed uneventfully here at Fractal Central. The dynamic fractal cats did not complain too loudly, though it was obvious that they would have preferred a temperature quite a bit warmer than the high of 34F 1C. At the end of the day I rewarded them for their patience with a treat of tuna. Today is starting just as cold, with clouds moving in and a threat of snow. If the duo have any plans at all of going outside, they had best do it early. My immediate plans involve finishing the work and finding a fractal for tomorrow's FOTD that would be above average. And this isn't Lake Wobegon, where every child is above average. This is the 'real' world, where only half of any distribution can be above average (more correctly, above the median). Until tomorrow, take care, and, unless it is politically incorrect, search for that waitangi. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Hairybrot { ; time=0:09:15.13--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.02872664355981464/-0.580735855227059\ 2/1.307901e+012/1/-42.5/0.00257131772770670397 params=3.7/3.5/3.7/5.5/0/0 float=y maxiter=600 inside=0 logmap=190 mathtolerance=/1 periodicity=10 colors=000nP8oQ7pR6qS6rT5rU5sV4tW4uX3vY3vZ2w_2x`1y\ a1zb0zb0tZ1oW2jT3eQ4`N5WK6QH7LE8GB9B8A65B12C67FABH\ EFJIJLMNOQRQUVSYZUabXefZij`mnbplWrjQthKvfDxd7zc1ue\ 5pg8qcCr_FsWJsSMtNQtMUuLYuKau8et9isAhsAfrBeqBcqCbp\ C`pD_oEZnEXnFWmFUlGTlGRkHQkHPhLNeOMbSK`VJYZIVaGTeF\ QhDNlCLoBJnCInCGnCFmCEmCCmCBmCAlC8lC7lC6kC4kC3kC2k\ C4jG5iJ7iM8hPAhSBgVCgYGd`JabMZePWgSUjVRlYOo`LqcItf\ GvdHtbIraJp_KnYLmXMkVNiTOgSPeQQdORbNS`LTZJUXIUWJTS\ JSOJRLKQHKQEKPALO7LN3LN0OM2QM3SM4UM5XL7ZL8`L9bLAJK\ mOKiSKeXKa`KYdPUiOQmIMrDIv8Ez3BrBDkJFdRHXSJQTLJUNC\ UPJUMPUJVUG`LDfBAl28j7BiBEhFHgJKeNNdRQcVTbZWabZbc`\ bdabdcbedbffbfgbgibgjchkcimcincjpckqckrclscltYhuTe\ vObwJ_xEXy9Uz4RzCKzPEzT7zU1zW3zY4z_5za6zc7ze8zg9zi\ CzkFzmIzoLzqNzsQzuTzwWzxZzz`zzYzzVzzTzzVzzXzzYzz_z\ z`zzbzzczzezzfzzczzazzZzzXzzUzzSzzPzzNzzKzzIzzFzzD\ zzUzz_zzBzzCzzDzzEzzFzzGz } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] Mandelbrot and Julia Sets Explored by RareEvent Theory
by Russ Walsmith 06 Feb '03

06 Feb '03

>From: "Morgan L. Owens" <packrat(a)nznet.gen.nz> >Reply-To: fractint(a)mailman.xmission.com >To: fractint(a)mailman.xmission.com >Subject: Re: [Fractint] Mandelbrot and Julia Sets Explored by RareEvent >Theory >Date: Fri, 31 Jan 2003 21:11:05 +1300 > >The broadest generalisation (while still keeping within the gambit of >quadratic maps) would be > >Quadraticmap{ >bailout=1000000 >z=pixel: >x=real(z) >y=imag(z) >nx=ca+(cb+cc*x+cd*y)*x+(ce+cf*y)*y >ny=cg+(ch+ci*x+cj*y)*x+(ck+cl*y)*y >z=nx+flip(ny) >|z|<bailout >} Right on thats not the way I mean to go with it, but its nicely done. Hearkening to the adage that one good formula deserves another, I present you with D3e { x=real(pixel), y=imag(pixel), v=p1 x1=x2=y1=y2=v1=v2=0: a1=x1^2+x2^2+y1^2+v2^2+2*y1*v1 a2=2*x1*x2+y1*y2+v1*v2+y2*v1+v2*y1 b1=v1^2+2*x1*y1+x2*y2+y2*v2+v2*x2 b2=2*x1*y2+y1*v2+v1*x2+x2*y1+v2*v1 c1=y1^2+2*x1*v1+x2*v2+y2*x2+v2*y2 c2=2*x1*v2+y1*x2+v1*y2+x2*v1+y2*y1 x1=a1+x, x2=a2-x, y1=b1+y, y2=b2-y, v1=c1+v, v2=c2-v z=sqrt((a1-a2)^2+(b1-b2)^2+(c1-c2)^2) z < 8 } The e means that its of the extended formula family; this is a template by which all of a groups elements are incorporated in the frm. This version of D3 shows it to be related to the Klein four-group fractal (K4e, below). Both are easily changed to Msets by y=imag(pixel)*(0,1). K4e { x=real(pixel), y=imag(pixel), x1=x2=y1=y2=0: a1=x1^2+x2^2+y1^2+y2^2 a2=2*x1*x2+2*y1*y2 b1=2*x1*y1+2*x2*y2 b2=2*x1*y2+2*x2*y1 x1=a1+x, x2=a2-x, y1=b1+y, y2=b2-y z=sqrt((a1-a2)^2+(b1-b2)^2) z < 8 } The order 4 dihedral group fractal (D4e below) also shares some of these characteristics when viewed from other axial perspectives. Since C4 is a subset of D4, the complex plane is in this 4-space, and the view in X,Y is of an Mset. D4e { x=real(pixel),y=imag(pixel),v=p1,w=p2 x1=x2=y1=y2=v1=v2=w1=w2=0: a1=x1^2+x2^2+v1^2+w1^2+v2^2+w2^2+2*y1*y2 a2=y1^2+y2^2+2*x1*x2+2*v1*v2+2*w1*w2 b1=2*x1*y1+2*x2*y2+v1*w1+w1*v2+v2*w2+w2*v1 b2=2*x1*y2+2*x2*y1+v1*w2+w1*v1+v2*w1+w2*v2 c1=2*x1*v1+2*x2*v2+y1*w1+y2*w2+w1*y2+w2*y1 c2=2*x1*v2+2*x2*v1+y1*w2+y2*w1+w1*y1+w2*y2 d1=2*x1*w1+2*x2*w2+y1*v2+y2*v1+v1*y1+v2*y2 d2=2*x1*w2+2*x2*w1+y1*v1+y2*v2+v1*y2+v2*y1 x1=a1+x,x2=a2-x,y1=b1+y,y2=b2-y, v1=c1+v,v2=c2-v,w1=d1+w,w2=d2-w z=sqrt((a1-a2)^2+(b1-b2)^2+(c1-c2)^2+(d1-d2)^2) z < 16 } This seems to be an easy way to fit any of the smaller groups into fractal formulae, and it will be interesting to see where it leads _________________________________________________________________ Tired of spam? Get advanced junk mail protection with MSN 8. http://join.msn.com/?page=features/junkmail

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Re: [Fractint] Running Fractint on a Parhelia
by Russ Walsmith 05 Feb '03

05 Feb '03

Fractint usually doesnt run properly on WinXP? Dang, I didnt know that Ive been running it on XP Pro from the git-go. Maybe that accounts for certain anomalies that I often encounter. E.g., if I use anything other than z for the bailout comparison, the image usually appears as if the iteration count was set to around 35 or so The program seems to be performing otherwise very well, but I guess I should someday vet a bunch of formulas in both 98 and XP to see what discrepancies are there to discover >From: "Paul N. Lee" <Paul.N.Lee(a)Worldnet.att.net> >Reply-To: fractint(a)mailman.xmission.com >To: fractint(a)mailman.xmission.com >Subject: Re: [Fractint] Running Fractint on a Parhelia >Date: Mon, 03 Feb 2003 23:23:17 -0600 > >Burnett, David wrote: > > > > ...trying to run Fractint on a matrox parhelia. > > ...... System is Athlon 1.4 / 512m with XP pro > >I have only heard of a couple of individuals successfully running >FractInt under MS-Windows XP, and achieving an image size greater than >300x400. > >The quickest and easiest resolution is to create a DOS boot disk from a >Win-95/98 system and use that to run FractInt. But you still may need >to do some adjustments to get those higher resolutions, though nothing >more than a 256-color image. > >Sincerely, >P.N.L. >------------------------------------------------- >http://home.att.net/~Paul.N.Lee/PNL_Fractals.html > >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint _________________________________________________________________ Help STOP SPAM with the new MSN 8 and get 2 months FREE* http://join.msn.com/?page=features/junkmail

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Re: [Fractint] Re: Mandelbrot and Julia Sets Explored by RareEvent Theory
by Russ Walsmith 05 Feb '03

05 Feb '03

Osher, Your posted reference to J. C, Sprotts work (Mandelbrot and Julia Sets Explored by Rare Event Theory, 29 Jan 2003) came along just as I was finding my way into related outcomes based on groups. The approach of using the order 4 cyclic group (C4) to generate the Mset in Fractint leads to a (WinXP friendly) formula such as Mset { x=real(pixel), y=imag(pixel), x1=y1=0: a=x1^2-y1^2+x b=2*x1*y1+y x1=a, y1=b z=sqrt(a^2+b^2) z < 10000 } I subsequently found a generalized formula that apparently works for groups of any order. In it, the Mset looks like this: C4e { x=real(pixel), y=imag(pixel), x1=x2=y1=y2=0: a1=x1^2+x2^2+2*y1*y2+x a2=2*x1*x2+y1^2+y2^2-x b1=2*x1*y1+2*x2*y2+y b2=2*x1*y2+2*x2*y1-y x1=a1, x2=a2, y1=b1, y2=b2 z=sqrt((a1-a2)^2+(b1-b2)^2) z < 10000 } But looking back at the first Mset formula, I saw it as a configuration of the pieces of the expansion of (a+b)^2. What would other arrangements lead to? For example: Mtest { x=real(pixel), y=imag(pixel)*p1, a=b=0: a1=a^2+a*b+x b1=b^2+a*b+y a=a1, b=b1 z=sqrt(a^2+b^2) z < 10000 } For p1=1, the result wasnt all that interesting, but for p1=(0,1), I got a bit of a surprise. That this too produces an Mset led to curiosity about other polynomial expansions, e.g., (a+b+c)^2 = a^2+b^2+c^2+2*a*b +2*a*c+2*b*c. I discovered that I could mix these up in about any arbitrary fashion and get a fractal object, and the more symmetry in the formula statements, the more to be found in the fractal itself. In the following example, p2 is meant to toggle between 1 and (0,1). Ptest {;use floating point x=real(pixel),y=imag(pixel)*p2,v=p1 a=b=c=0: a1=a^2-p2^2*a*b-p2^2*a*c b1=b^2-p2^2*a*b-p2^2*b*c c1=c^2-p2^2*c*b-p2^2*a*c a=a1+x,b=b1+y,c=c1+v z=sqrt(a^2+b^2+c^2) z < 10000} Where p2=1 produces a symmetrical object oriented toward the vertical, p2=i is an Mset again. Something I find interesting about Ptest is p1s effect on M. Plus/minus real p1 shift M left or right, imaginary p1 shift it up or down, and complex p1 at a corresponding angle. There seems to be zero distortion, as long as p1 isnt too close to the bailout value. Here are some examples of frm files created from (a+b+c)^3 Ptest2 { x=real(pixel),y=imag(pixel)*p2,v=p1 a=b=c=0: a1=a^3+3*b^2*a+3*c^2*a+2*a*b*c b1=b^3+3*a^2*b+3*c^2*b+2*a*b*c c1=c^3+3*a^2*c+3*b^2*c+2*a*b*c a=a1+x,b=b1+y,c=c1+v z=sqrt(a^2+b^2+c^2) z < 10000 } Ptest2 forms a square for p2=1,for p2=i an object similar to a third degree Mset (i.e., z1=z^3+c) and for p2=(1,1), a nice combination of the two. Ptest3 has an OK fractal in p2=i but nothing too exciting elsewhere that I discerned. Ptest3 { x=real(pixel),y=imag(pixel)*p2,v=p1 a=b=c=0: a1=a^3+b^3+c^3+6*x*y*z b1=3*b^2*c+3*c^2*a+3*a^2*b c1=3*c^2*b+3*a^2*c+3*b^2*a a=a1+x,b=b1+y,c=c1+v z=sqrt(a^2+b^2+c^2) z < 10000 } Thats a cursory look at it, but the idea of a class or classes of fractals based on polynomial expansions may prove eventually to harbor some interesting things... Ciao, Russ _________________________________________________________________ The new MSN 8: advanced junk mail protection and 2 months FREE* http://join.msn.com/?page=features/junkmail

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FOTD 05-02-03 (Classical Minibrot [5])
by Jim Muth 05 Feb '03

05 Feb '03

FOTD -- February 05, 2003 (Rating 5) Fractal visionaries and enthusiasts: It's a bit hard to find an outstanding characteristic in today's FOTD image that might serve as the basis for a name. It's a simple scene of a classic quadratic midget located in a very un-classic fractal. When nothing better came to mind, I named the image "Classical Minibrot". The parent fractal, which was created by combining portions of Z^3.5 and Z^5.5, is anything but classic however. It consists of a long, narrow, large but shapeless body of open 'water' with a well-defined but rather distorted M-set lying some distance to the south. At first glance, the shapeless body appears totally non- critical, and therefore would not be expected to hold intact midgets. But in the world of fractals, things are not always as they seem. At least two rudimentary valleys appear on the western shore of the shapeless body. At first glance, these valleys also appear as though they would hold no midgets. The appearance is deceiving. Curious as to what other than midgets might lie in these valleys, I zoomed into the southern one and focused on an interesting feature. In this feature I noticed a pair of seahorse-like spirals with the symmetry that usually indicates the presence of a midget. I zoomed into the center of symmetry and found today's image. It's not a great fractal, in fact it's merely average, but it is still a significant improvement over yesterday's abysmal image, and if the present trend continues, we'll be back in positive territory within a day. One way to see the classical midget is to run the parameter file and wait 6 minutes or so. A faster way is to let Paul and Scott render the image and download it from one of their FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Tuesday morning at Fractal Central began rainy. It cleared shortly after noon, and the temperature reached a relatively mild 50F 10C, but high winds kept the fractal cats skittish, and they came inside after only a few minutes in the yard. They slept by the heat for the rest of the day. This morning is starting notably colder, though the high winds have died down. It's too early to say what the dynamic duo will do. What I'm going to do is first finish a bit of work and then try to find a better fractal. I've got a few ideas of where to look, but no success is guaranteed. Whatever I find will be tomorrow's FOTD. Until then, take care, and the quest for the perfect fractal might never end. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Classical_Minibrot { ; time=0:06:11.96--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.21829760034047560/-0.145214873755854\ 30/1.211417e+007/1/-152.5/1.45066905959945203e-007 params=3.67/3.5/3.7/5.5/0/0 float=y maxiter=1200 inside=0 logmap=86 periodicity=10 colors=000MEALB6L93ND7PGBQKESNIUQMVUPXXTZ`X_c_afcc\ jgdmjfqnhtriuuatjVp`OkRHfHAb7D_8GX9IWALVBOUCQTCTSD\ VREYQF`PGbOGeNHhMIjLJmKKoJKnMImPHlSFkUEjXCi_BhaAgd\ 8fg7ej5dl4co2br1at0Zs5WrATqEQpJNoOKnSHmXElaBke8jj6\ jn8ekA`hBWeDRbFN_GIXIDUK8RL4PTBV_H`gOfnUkiTfdSb_RZ\ VRVQQRLPNHPJE_KCiKBhIBhHBhFBgEBgCBgBBgAAf8Af7Af5Ae\ 4Ae2Ae1Ae0G`3MW5RR8XMAbHDgCFm7Ir3Kp6Jo9JmBJlEIjGIi\ JIgMIfOHdRHcTHaWH`ZGZ`GYcGXeGzAYwCXtEXqGXnIXlKWiMW\ fNWcPWaRVZTVWVVTXVRYVSWUSVTTUSTTRUSQUQPVPOVONWNMWM\ M_LRVNMROHNPDJQ8FR4MVISZWZbidevchvbkvamvapv`rv_uv_\ wvSkvL`vEQvGUsHXqJ`nKclLfiNjgOmdPpbQn`QmZQkXQjVQhT\ QgRQePQdNQcLTdKVeKXfKZfK`gKbhJdhJfiJhjJjjJfcJbYJZR\ JWLJUPHSSGRVFPZDOaCMdBLgAJiAIkAHmAGoAFqAEsAIuEMwIP\ xMTyPXzT_zXcz`fzcezeezfezgezheziezjfzegzagzYhzUizP\ izLjzHjzDhzGfzIdzLbzN`zP_zSYzUWzWUzZSz`RzbPzZNzWLz\ SJzPIzLGzIEzECzBAz79z4BzH } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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RE: [Fractint] Running Fractint on a Parhelia
by Burnett, David 05 Feb '03

05 Feb '03

Strangely enough my work machine (P4 1.6/TNT2/XP pro) will run fractint. I can get 1280 * 1024 * 256c, so I don't think it's XP at fault. Will try the boot disk thing tonight, but I really think it's down to the Parhelia. Anyone else out there with a parhelia ...... db > -----Original Message----- > From: Paul N. Lee [mailto:Paul.N.Lee@Worldnet.att.net] > Sent: Tuesday, February 04, 2003 4:23 PM > To: fractint(a)mailman.xmission.com > Subject: Re: [Fractint] Running Fractint on a Parhelia > > > Burnett, David wrote: > > > > ...trying to run Fractint on a matrox parhelia. > > ...... System is Athlon 1.4 / 512m with XP pro > > I have only heard of a couple of individuals successfully running > FractInt under MS-Windows XP, and achieving an image size greater than > 300x400. > > The quickest and easiest resolution is to create a DOS boot > disk from a > Win-95/98 system and use that to run FractInt. But you still may need > to do some adjustments to get those higher resolutions, though nothing > more than a 256-color image. > > Sincerely, > P.N.L. > ------------------------------------------------- > http://home.att.net/~Paul.N.Lee/PNL_Fractals.html > > _______________________________________________ > Fractint mailing list > Fractint(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint >

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FOTD 04-02-03 (Quagmire [3])
by Jim Muth 04 Feb '03

04 Feb '03

FOTD -- February 04, 2003 (Rating 3) Fractal visionaries and enthusiasts: There's nothing like a comical junk e-mail to take some of the depression out of an otherwise bad day. Things were already going bad enough, then the fractal for the day turned out to be a loser that I could rate no better than a 3. And then, to make things even worse, I checked my e-mail box and found the usual jumble of junk. I deleted the junk at once without downloading it, all but one letter that is. That letter had a subject line telling me that I am something special. OK, I told myself, I'll take a quick look at this one. As expected, the letter was a typical piece of junk directing me to an x-rated web site. The text began by telling me that the sender had seen my profile and that I was exactly the type of person she had been searching for all her life. The sender then described a gorgeous young woman eager to meet me. The letter might have been effective had it not been for the long list of carbon-copy addresses to which the same letter had also been sent, which somehow had inadvertently been included at the start of the text. Disappointed, I deleted the final piece of junk. This comical disappointment eased my disappointment over finding nothing better that a miserable 3-rated image for today's FOTD. I did all the right things, but it seemed as though fate itself was working against me. Regardless of what I tried, the images were as junky as an unwanted e-mail. I finally settled on an evaporated scene in the fractal that results when three parts of Z^(-14.56) are subtracted from 7 negative parts of Z^(-1.456) and 1/C is added instead of plain C. I named the image "Quagmire", mostly because that's how I felt. I rated it at a lowly 3 because that's all it is worth. A render time of 1 minute would be too much to ask for today's image. The actual 12-minute render time is verging on the ridiculous. Luckily, the image, for what it is worth, is available on the web at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Bland weather once again prevailed here at Fractal Central on Monday, with some sun, some clouds, a bit of a breeze and a temperature of 45F 7C. Taking advantage of the blandness, the dynamic cats were as lively as they have been in some time as they romped in the yard for several hours. Of course, at their age of 12 years, their romping is not what it used to be, but Tippy the tabby still managed to climb two meters up a holly tree. Today is starting rainy. It remains to be seen how the dynamic ones will cope with the latest inconvenience. Being well in excess of 12 years, my tree-climbing days ended long ago. My romping is also suffering. But the fractals keep coming. Until next FOTD, take care, and does space end where time begins? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Quagmire { ; time=0:12:16.28--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.89508650616089440/-0.815728148775334\ 10/6369148/1/-140/-4.15605366371751828e-008 params=-7/-1.456/-3/-14.56/0/1e+100 float=y maxiter=900 inside=bof61 periodicity=10 colors=0007tZ6t`5ua4ub4vd3ve2wf2wg5ug7tg9sgBrgDpgF\ ogHngJmgMkgOjgQigShgUfgWegYdg`bi_ch_cgZdfZdeYedYec\ XebXfaWf`Wg_VgZVhYVhXUhWUiVTiUTjTSjSSkRRkQRkPQlOQl\ NQmMPmLPnKOnJOnINoHNoGMpFMpELqDLqCLqBPoGSmLWkPZiUb\ hZefbidglbloapk`kk_liZjgZheYfcXeaWc_WaYV_WUYUTWTTV\ RSTPRRNQPLQNJPLHOKFNIDNGBME9LC7KA6K98MB9NCBPECQFDR\ GFTIGUJHWKJXMKYNL_ON`QObRPcSRdUSfVTgWViYWjZZlZXk_V\ k`TkaRjaQjbOjcMidKidIieHhfFhgDhgBgh9gi7fh8gi9gi9gi\ AgiAhiBhiBhiChiDiiDiiEiiEiiFjiFjiGjiHjiHkiIkiIkjJk\ jJljKljLljLljMmjMmjNmjNmjOnjPnjPnjQnjQojRojRojSojS\ ojTicTdXT_QTVJUPBTQCSQDSQERQFRRGQRGQRHPRIPSJOSKOSL\ NSLNSMMTNMTOLTPLTQKUQKURJUSIUTIUUHVUHVVGVWGVXFWYFW\ ZEWZEW_DW`DXaCXbCXcBXcBYdAYeAYf9Yg9Yg9Zg8`h7ai7ci6\ dj5fk5gk4il3jm3lm2mn1oo1po6mpAkpEiqJfqNdrRbrV`rY_q\ __qa_pd_pf_ph_oj_om_oo_nq_ns_noaklbhhceeebbf_ZgXWh\ VTjSPkPMlMAqT9rU9rW8sX7sY } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Running Fractint on a Parhelia
by Burnett, David 04 Feb '03

04 Feb '03

As the title says, I have been trying to run Fractint on a matrox parhelia. The best res I can get seems to be about 300 * 400 * 256 colours. I am not expecting to be able to use all three monitors (one would do). Does anyone have any ideas how I can coax better res out of fractint. System is Athlon 1.4 / 512m with XP pro (if that's relevant). regards David

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Re: [Fractint] Triternions
by Russ Walsmith 03 Feb '03

03 Feb '03

>From: "Gerald K. Dobiasovsky" <gerald.dob(a)aon.at> >Reply-To: fractint(a)mailman.xmission.com >To: <fractint(a)mailman.xmission.com> >Subject: Re: [Fractint] Triternions >Date: Fri, 31 Jan 2003 02:01:14 +0100 > >But why shouldn't it be possible for the fractal's cross- >section for c2=real to look identical to the cross-section >for c2=imag? Gerald, Indeed, why not? There are, never the less, some strange things going on here, but Im starting to get a handle on a few of them E.g., MrT: MrT { x=real(pixel),y=imag(pixel),v=p1 x1=y1=v1=0: a=x1^2+2*y1*v1 b= v1^2+2*x1*y1 c= y1^2+2*x1*v1 x1=a+x,y1=b+y,v1=c+v z=sqrt(a^2+b^2+c^2) z < 8 } It was y1=b y*y that turned MrT into the TMan, and its obvious that squaring all of the Y-axis values creates symmetry across the X-axis. y=sqrt(imag(pixel))^2 does this with no distortion. Then flipping the y values into the x positions gives symmetry across Y, whence TMan1. The 3-space were working in here is ruled by the X,Y,V axes, but actually defined as the intersection of three planes, as is borne out in the 3D effects seen in many of the fractal images. Yes, it seems that y=imag(pixel)*(0,1), which I once perceived as removing an imaginary component, is in fact introducing a 4th degree root which is not otherwise present, and hence expanding the space to 6D (Now I see that earlier discussions regarding this make sense) So it feels like Im gradually getting my mind wrapped around this stuff Ive also come upon a general template, a pattern by which in theory all of the proper mathematical groups are uniformly configured as fractal generators The extended version of MrT is below. MrTe { x=real(pixel), y=imag(pixel), v=p1 x1=x2=y1=y2=v1=v2=0: a1=x1^2+x2^2+2*y1*v1+2*y2*v2 a2=2*x1*x2+2*y1*v2+2*y2*v1 b1=v1^2+v2^2+2*x1*y1+2*x2*y2 b2=2*x1*y2+2*x2*y1+2*v1*v2 c1=y1^2+y2^2+2*x1*v1+2*x2*v2 c2=2*x1*v2+2*x2*v1+2*y1*y2 x1=a1+x,x2=a2-x,y1=b1+y,y2=b2-y,v1=c1+v,v2=c2-v z=sqrt((a1-a2)^2+(b1-b2)^2+(c1-c2)^2) z < 8 } This inclusive pattern is not always necessary; e.g., MrT vis-à-vis MrTe: When certain symmetries are present in the group table, just the upper left quadrant suffices. This wasnt enough though for the order 8 cyclic group in the earlier CP8 form; its expressed as CP8e below. CP8e { x=real(pixel),y=imag(pixel),v=p1,w=p2 x1=x2=y1=y2=v1=v2=w1=w2=0: a1=x1^2+x2^2+2*y1*y2+2*v1*v2+2*w1*w2 a2=y1^2+y2^2+2*x1*x2+2*v1*w1+2*v2*w2 b1=v1^2+w2^2+2*x1*y1+2*x2*y2+2*v2*w1 b2=v2^2+w2^2+2*x1*y2+2*x2*y1+2*v1*w2 c1=2*x1*v1+2*x2*w2+2*y1*v2+2*y2*w1 c2=2*x1*v2+2*x2*w1+2*y1*w2+2*y2*v1 d1=2*x1*w1+2*x2*v2+2*y1*v1+2*y2*w2 d2=2*x1*w2+2*x2*v1+2*y1*w1+2*y2*v2 x1=a1+x,x2=a2-x,y1=b1+y,y2=b2-y, v1=c1+v,v2=c2-v,w1=d1+w,w2=d2-w z=sqrt((a1-a2)^2+(b1-b2)^2+(c1-c2)^2+(d1-d2)^2) z <= 16 } If a symmetrical fractal is desired, one needs to ensure that roots of equal degree rule each half of an axis, as was done here (but while evidently always necessary, this is not sufficient). C4 is a subgroup of C8, and the CP8e frm above generates the Mset. So, progress of a sort, apparently, and Ill post some more on this later meantime, is either of these MrTs configurable into one of your rotational formulas, the better for us to continue this investigation? Ciao, Russ _________________________________________________________________ Tired of spam? Get advanced junk mail protection with MSN 8. http://join.msn.com/?page=features/junkmail

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FOTD 03-02-03 (On the Inside [6])
by Jim Muth 03 Feb '03

03 Feb '03

FOTD -- February 03, 2003 (Rating 6) Fractal visionaries and enthusiasts: I'm not in much of a mood to write this morning, so I'll keep the talk to a minimum. Today's fractal is yet another of my 'evaporated' images, this one created by subtracting 4 parts of Z^(-9.3) from 7 negative parts of Z^(-1.7), then adding 1/C. I rendered the all-inside fractal with the inside set to bof61, and colored the resulting features so that the dark, gloomy foreground appears to be illuminated from behind, creating an effect rather like finding hope in a time of despair. I named the image "On the Inside" for no particular reason. The render time is 5 minutes -- not too trying. The most convenient way of seeing the image is by downloading it from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather was bland here at F.C. on Sunday. We found our- selves in an area known as a 'col', where nothing much happens. The fractal cats took full advantage of the partly cloudy day with no wind, a temperature of a normal 43F 6C, normal humidity, and everything else average. They spent several hours in the yard, chasing the few shafts of sunlight that filtered through the holly trees, and actually chased each other a short distance a few times. For today, I have the normal amount of work to accomplish, and then I shall likely do a lot of pondering as I search for fractals. Until tomorrow, take care, and the FOTD CD is near, that is as soon as I can pull myself out of the doldrums. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ On_the_Inside { ; time=0:05:16.37--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.704046611622666/+1.29535015518134/45\ 3064.1/1/-57.5/4.70417142739432137e-010 params=-7/-1.7/-4/-9.3/0/1e+100 float=y maxiter=600 inside=bof61 periodicity=10 colors=555d5Xb5Y`5Yr5Nr5Qp5TpAXoF_zpzoOdmTgmYjlbml\ gpjltjpujuuhuuhuuguuguuguuduubuu_uuYuuXupzpzSugOud\ Nu_LtVIpSGoNDlICjDAgA7e55b55`55Y55X55V55T55S55O5zp\ zVL7UK8TIASFCRDCQCDPAFO8GN7GM8FLAFKCFJDDIFDKFDNGCQ\ ICTKCWLAYLA`NAdO8eQ8jS8hT7nT7pV7rX5qY5pV5oV5nW5wb5\ vd5ue5ue5ud5ud5ub5ub5u`5u`5u_5u_5uY5uY5uX7uX7uV7uV\ 7uV7uT8uT8uS8uS8uQ8uQAuOAuOAuNAuNAuLCuLCuKCtKCtKCe\ V5Sd5Dm55u55u55u55u55u55u55r55p55m75jA5hD5eG8bKA`N\ CYODVSFTVIQYKO`LLdNIeOGhSDlTAoV8rX5uY5u`5ub5ud5ue5\ ug5uh5ue5ub5u_5uX5tT5oQ5jN7dK8_GCVFDQCGL8IG5LA5O55\ Q55T55V55Y55_55`55`55`55`55`55b55b55b55b55b55b55d5\ 5d55d55d55d55d55e55e55e55e55e55e55d55d55b55b57b5A`\ 5D`5G_5I_5L_5OY5SY5TX5XX5_X5bV5dV5gT5jT7mT7oS8rS8u\ QAuQAuQAtLDoIGhDKdAN_7QX8NVALSCKQDINFFLGDIICGKADL7\ CN58O57Q55S55T55V55X55Y55_55`55b55d55d55_55X55T55Q\ 55N5AK7FGAKDFNAIS7LX5Q`5T } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 02-02-03 (Spots Before the Eyes [5])
by Jim Muth 02 Feb '03

02 Feb '03

FOTD -- February 02, 2003 (Rating 5) Fractal visionaries and enthusiasts: I'm depressed today. As soon as I posted yesterday's FOTD, I turned on the radio and heard the bad news. This latest space disaster has me down. As the difficulties in the foundering U.S. space program continue to add up, it is becoming ever more apparent that neither I nor anyone else will live to see humanity reach the stars. It is almost as apparent to all but dreamers that humanity will *never* reach the stars. I am not shocked. I never expected to see men actually traveling to other solar systems in my lifetime, but back in the 60's, when I was young and enthusiastic, (i.e. a dreamer), I expected to see, before I left this world, men (and women) regularly traveling to Mars, and humanity actually colonizing the moon. Now I realize that I shall never see men on Mars, and unless a miracle happens, that I shall never see men even on the moon. In fact, I'll consider myself lucky if I live to see the earth- orbiting space station completed and in full operation. As I have realized for the past 15 years or so, earth's resources are limited. The planet simply has too few resources to support both an out-of-control population explosion and a workable space program. We didn't even have the resources to build the super- conducting-supercollider down here on earth. The problem lies in our very nature. We are totally dependent on the environment of earth's biosphere for our continued existence. To venture into space, we will always need to take a bit of that environment with us. And we have underestimated the magnitude of the task of maintaining that environment. We have put too much faith in the ability of technology to overcome our natural biological limitations. The only way humanity could ever reach deep space would be to find a way to change its nature. We would need to find a way to transfer our awareness, complete with senses, to some kind of artificially self-aware machines, (is artificial self-awareness an oxymoron?), and travel to the stars as robust androids with replaceable parts and unlimited life expectancies. But this is pure fantasy. Before it could be done, or even considered, we must determine what a self-awareness is and how it might be transferred. Since this appears to be impossible, perhaps even foolish to consider, the presence of humanity in deep space appears to be unachievable, and no amount of science and technology can change that. One good feature about exploring the fractal world is that it consumes very little of earth's limited resources. Today's image is part of the fractal that comes into being when three parts of Z^(-15) are subtracted from three parts of Z^(-1.5) and 1/C is added. It is another of my 'evaporated' images, this time brought to life by the bof60 inside fill. I named the image "Spots Before the Eyes". One glance will reveal why. If my mood had been brighter, I might have rated it a bit higher than the rating of an average 5. The render time of 16 minutes is trying, but may be overcome by downloading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather was unpleasant here at Fractal Central on Saturday. The sky was too cloudy, too many sprinkles of rain fell, the air was too damp, the wind was too raw, and the temperature of 36F 2C was too chilly. As a result, the fractal cats were too testy, and a spat broke out between them when both Thomas and Tippy wanted the same spot by the heat. But the quarrel soon ended, and the duo finished the day with a conciliatory treat of tuna. Today is starting the same as yesterday. Hopefully, the cats' mood will not be as sour. Until next FOTD, take care, and those stars keep getting farther away, don't they? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ SpotsBeforeTheEyes { ; time=0:16:39.60--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-1.28158038164121200/+0.099152116886171\ 08/17371.64/1/97.5/3.0669491252188763e-010 params=3/-1.5/-3/-15/0/1e+100 float=y maxiter=1200 inside=bof60 logmap=yes periodicity=250 colors=000htYfsYdrZbqZ`pXZoYXnZVmZTl_Rk_Pj`NibLh`K\ fZJdXIaVH_TGYREWPDTNCRLBPJAMH9KF7ID6GB5D94B7395161\ 27427637837A47D47F58H58J68M68O78L78N78P9AOBBPDDPEE\ PGFPHGPIHRJIQKJRLKOMJQMKQMKPMKQMKQZVS_WSaYScZSecNd\ _SdXWcT`cQdcNibJmbGrY4x`9wbDvdHufQuhTtjYslasnfrpjq\ rnptqpvroxvnzznwxmuvmsumqsmnqmlpmjnlhlleklcilagl_f\ lXdkVbkTakR_kOYkMXkKVjITjFSjDQjBOj9NjCMfFLcIK`LJXO\ JURIRUHNXGK_GHbFDeEAhD7mC1kD3jD4iD5hE6gE7fE8eE9dFA\ cFBbFCaFD`GE_GFZGGYGHXHIWHJVHKUILTIMSINRIOQJPPJQOJ\ RNJSMKTLKUKKVKMVJLWJKWIKXIJXHJYHIYHIZGHZGG_FG_FF`E\ F`EEaEEaHD`JD_LCZOCYQBXSBWVAVXAUZ9T`9Sc8Re8Qg7Pj7O\ l6Nn6Ms4Lp6Mm7Mk8NhANfBOcCOaEPZFPXGQUHQSJRPKRNLSKN\ SIOTFPT4UT9STDQTIPTMNTRLTVKTZITcGTgFTlDTpBTt6St8Tt\ ATtCTtETtGTtITtKTtMTtOTtQTtSTtUTtVTtXUtZUt`UtbUtdU\ tfUthUtjUtlUtnUtpUtrUtsUmtXgtZ`t`SzhUweVtbXr_YoX_l\ U`jRbgOceLdfMefMefMffMgfM } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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A Note on Real vs Complex Fields
by MARLENE DOCTOROW 02 Feb '03

02 Feb '03

In reply to the member who seemed upset about my comments about the complex multiplication not reducing to real operations, I have to say a few things. 1. There's no room for indicating that a member is old-fashioned in my opinion. In any case, I won't waste time replying to such a person in the future after two occurrences of that behavior. 2. A positive or neutral orientation is the most easily detected part of reading somebody's internet or email postings, and I don't reply to people with negative orientations after two occurrences of that behavior. 3. The real and complex fields are NOT ISOMORPHIC, and the two- dimensional Euclidean plane regarded as a vector space R2 over the real field is not algebraically isomorphic to the complex plane over the complex field because R2 has no complex multiplication. This is not old-fashioned - it is upper division algebra. 4. The positive part of what I said in my previous posting is the part that is obscured by readers' anger: Rare Event Theory is the only way that I know of to get partially around the difficulty of item 3. Osher Doctorow

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FOTD 01-02-03 (The Cave Entrance [8])
by Jim Muth 01 Feb '03

01 Feb '03

FOTD -- February 01, 2003 (Rating 8) Fractal visionaries and enthusiasts: I tried not to see the entrance of a cave in today's image, it appeared so trite, but there it is, clear as can be, a view from inside a cave, looking out toward an unearthly scene and the alien blue sky beyond. There are even puddles of liquid nitrogen on the cave floor, reflecting bits of the scene beyond. With all this evidence, I had no choice but to name the image "The Cave Entrance". I rated the image at an 8 because of its unusually strong resemblance to an actual 3-D scene. The colors are a bit surreal, but this doesn't detract from the impression of a real scene. The puddles of nitrogen on the cave floor are actually small, foreshortened spiral areas where the iteration count of the surface features becomes greater than the count of the features beneath, and the normally hidden features show through. These areas resemble reflections because the features showing through are extensions of the features directly above. To create today's image, I once again used the C4G almost- triternion formula. While searching the East Valley area of a square Mandeloid, I noticed today's curious feature in the pattern around a sub-midget. A zoom-in, a bit of stretching, a bit of rotation and a bit of skewing produced today's image. Perhaps the most unusual aspect of the image is the criss- crossing elements that appear to go on indefinitely, almost invisibly, in the distant blue of the sky. When enlarged and re-colored, this distant sky area changes and becomes another cave entrance. We literally have a cave whose entrance goes on forever. Luckily, the parameter file runs in far less time than forever. In fact, even on my worn-out machine with the balky fan it runs in 8 minutes, and draws an image well worth the short wait. And even that short wait can be avoided if the completed GIF file of the image is downloaded from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Friday remained cold, damp and dreary all day, with the tempera- ture hovering just above freezing and occasional drizzle. The cats remained gloomy all day, and needed a treat of tuna in the evening to make them fit to live around. Today looks like another repeat. I have no idea how the duo will take three indoor days in a row. With most of the work caught up and not much else to do, I'm going to take today as easy as possible. I'll probably spend a good part of the day somewhere in Fractal Land, searching for tomorrow's FOTD. Until then, take care, and prepare for the imminent release of the long-awaited FOTD CD, which will contain every FOTD image from April 1997 through December 2002, plus every FOTD discussion and a lot of spurious blather. It will also contain a number of my earlier fractal images, some of them created (blasphemy) by programs other than Fractint. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Cave_Entrance { ; time=0:08:07.30--SF5 on a P200 reset=2002 type=formula formulafile=c4gsave.frm formulaname=C4G passes=1 center-mag=-1.74974156125\ 1203/+0.00000002376090472/1.527103e+008/1/128.9/1\ 7.7763268937502694 params=-0.72/-0.53 float=y maxiter=1600 inside=0 logmap=246 periodicity=10 colors=000UJXTJZSJ`QKaPKcNKbMKaKL`JL_ILZGMYFMXDMWC\ NVANU9NTANSBLRCKQDJPEIOFHOGHOHIOIJOJJOKKOLLOMLONNQ\ NPSMRTMTVLVXLXYLY_K_aKabJcdJeeIggIhiIjjHllHnnGpoGr\ qGsrJpsLmtNkuQhuSevUcwW`xZYx`WybTzdRzkYurcpcUkukhc\ Uemobiq_esXauUYwSZrQ_mO_iM`dKa_JaWHbRFLMDNICLJBKJA\ KJAMJAOJAQKARKASLATMAUMAVNAWOAXOAYPAZPA_RA`TAaVCaW\ DbYFc_Gc`IdbJedLeeMfgNgiPgjQhlSinTioVjqWksYktZlv`m\ xamybhwXduR`tLXrFTq9UmDVjGVgJWcMX`PXYSYUVYRYZOa_Kd\ _Hg`EjaAma7pb4sb1va4t`6s_9rZBqYDpYGoXInWLmVNlUPkUS\ jTUiSWhRZgQ`fQcePedOgcNjbMlaMn`PjYSgVVcSX`P_XMbUKe\ QHgNEjJBmG8oD6lH9iLCfOFdSHaWKZZNWbQUeS_oxZnwZnvZnu\ ZmuZmtZmsZlsZlrYlqYkqYkpYkoYjoYjnYjmYjmXfjXcgW`dWY\ aVj_ViXVOUULRUIOTEMTBJS8GS5DS2BTQRTOLTMGVOIXPKZRM`\ SNbTPdVRfWThXUjZWl_Yna_pb`rcbtedvffwggtcaq_XnWRlTM\ iPHfLBcH6aE1bG2bH3bI3cJ4cL5cM5dN6dO7dQ7eR8eS9eT9fV\ AfWBfXBgYCg_Dg`DhaEhbFhcF } frm:C4G {; p1 is (plus or minus) 1 or i x=real(pixel), y=imag(pixel)*p1 a=b=0: a1 = a^2-p1^2*b^2 b1 = 2*a*b a=a1+x, b=b1+y z = sqrt(a^2 + b^2) z < 4 } END 20.0 PAR-FORMULA FILE==================================

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Re: Mandelbrot and Julia Sets Explored by RareEvent Theory
by MARLENE DOCTOROW 01 Feb '03

01 Feb '03

>From Osher Doctorow Morgan and Russell, Thanks for some interesting ideas. We may be coming from at least partly opposite directions, but that's fine. I'm 64 years old and missed the computer boat so to speak, although I can read many programs (somewhat like saying somebody can read some French but it isn't their native language or even a specialty or hobby). Curiously enough, I went into the super-abstract mathematics direction outside computers and only fairly recently have been coming back to the more concrete reality and some of it involves computers. One of the difficulties in reducing computer programs to their real and imaginary components also occurs in non-computer mathematics and quantitative sciences, where one comes up against the fact that MULTIPLICATION of complex numbers doesn't decompose (doesn't correspond to any operation in the reals for Re(z) and Im(z)) according to any known theory accepted by the mainstream. So there are no difficulties as long as one just adds and subtracts complex numbers - then there's a pretty clear correspondence to the real numbers and one could use either a complex or two real programs or a combination of two real programs. When multiplying two complex numbers, if you did manage to somehow incorporate complex multiplication into real programs you'd really be extending the real programs to complex programs because it's a known fact that complex multiplication is NOT APPLICABLE TO THE REALS EXCEPT WHEN THE IMAGINARY PARTS OF BOTH NUMBERS MULTIPLIED ARE 0. So what is surprising about Rare Event Theory (RET) insofar as it relates to complex numbers is that it seems to be able to arrive at similar results to complex numbers INCLUDING complex multiplication - but not identical results in general. In other words, RET has potential for exploring things and arriving at results that may be too complicated at present with complex multiplication - but the results may for example have an inequality in the wrong direction or something like that. RET also is useful to establish CAUSES and EXPLANATIONS which may not be so clear using complex multiplication or even complex numbers, because RET is a literally causal language (one of its forms or representations is in fuzzy multivalued logics in fact, where "a implies b" literally corresponds to 1 + b - a, which you will recognize as 1 + y - x or p1(x, y) with a, b being fuzzy multivalued real number values which are attached to the propositions. The probability- statistics meaning or translation or representation of 1 + y - x is literally: probability that x causes y. Here y < = x (is less than or equal to x). The number 1 + y - x is always between 0 and 1 when x and y are betwen 0 and 1. Thanks also to Guy for starting the comments, and let me know on fractint if you see any further ways to get some of this into computer program form or to even generalize or modify or specialize anything. Osher Doctorow

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One Typo
by MARLENE DOCTOROW 31 Jan '03

31 Jan '03

>From Osher Doctorow In equation (1) of the last posting, the second = should be --> where the arrow indicates converting to p1 representation. Osher Doctorow

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Exponential Chaotic Explosion by Rare Event Theory
by MARLENE DOCTOROW 31 Jan '03

31 Jan '03

>From Osher Doctorow Robert L. Devaney in "A survey of exponential dynamics," 2001 or 2002, http://math.bu.edu/people/bob/paper/augsburg.pdf as well as in various publications including a book has examined the exponential function analog of polynomial Julia/Mandelbrot sets which has an explosion when (c1 + ic2)exp(z) has c2 = 0 and c1 > 1/e. Here z = x + iy. According to Devaney, the appearance of so-called indecomposable continua in the chaotic Julia set for c1 > 1/e (in my notation) accounts for the explosion. In the explosion, the Julia set jumps from being nowhere dense to becoming the whole plane. The Rare Event Theory analysis is quite simple and proceeds as follows. 1) c exp(z) = (c1 + ic2)(x + iy) = c1 (cos u - sin u) = p1(c1 sin u - 1, c1 cos u) = 1 where c2 = 0 and x = cos(u), y = sin(u) because exp(z) = cos(theta) + isin(theta) for angle theta in the usual complex representation and we set u = theta. The equating to 1 optimizes p1. Setting the middle expression of (1) equal to 1 results in the following. 2) c1 cos(u) - c1 sin(u) = 1 and therefore: 3) c1(cos(u) - sin(u) = 1 But dividing both sides of (3) by c1 not equal to 0 results in: 4) cos(u) - sin(u) = 1/c1 This is impossible for u between 0 and pi/2 radians and for c1 = 1/e since both cosine and sine functions are between 0 and 1 there. If 0 < c1 < 1/e, then 1/c1 > 1/e and again (4) is impossible. The only place where (4) is not contradictory is where c1 > = 1 which is most of the interval between 1/e and infinity except for (1/e, 1). The fact that the chaotic and non-chaotic regions have reversed in the Rare Event Theory representation for u between 0 and pi/2 is probably not that dangerous because an entire quarter of the complex plane, where u is between pi/2 and pi, is excluded since cosine is negative there and sine is positive there and thus (4) would be contradictory. The pathology is in the function itself c exp(z) more than in its domain or range. Osher Doctorow

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FOTD 31-01-03 (UnNamed Fractal-V [7])
by Jim Muth 31 Jan '03

31 Jan '03

FOTD -- January 31, 2003 (Rating 7) Fractal visionaries and enthusiasts: It looks like it's going to be a good day here at F.C. My luck appears to have finally turned for the better. A few minutes ago I received a phone call. Expecting a customer, I answered the phone on the second ring. But instead of a customer, I heard a near-hysterical voice informing me that I had just won a free three-day trip for two to Orlando in Florida. Unfortunately, I am too busy to take a trip at this time, so I told the voice to simply send the cash equivalent of a three-day trip to Orlando. I am now eagerly waiting for the money to arrive, but it certainly would ease my mind if I could remember entering a contest where the prize was a free trip to Orlando. My fractal luck also appears to be on the upswing. The latest formulas in the undefined triternion series were posted to the Fractint list on Thursday. Instead of complex numbers, these formulas use real numbers, but the result is the same. While noodling around with one of the formulas, I stumbled upon today's image. I could have given the image many names. I see feathered wings quite clearly. But to keep a good thing going, I decided to end the month with another nameless fractal. (Who said fractals must be named?) Since it is the fifth such image, I attached the identifier "UnNamed Fractal-V". But, as a glance at the image will show, the lack of a name does not imply a lack of quality. The parent fractal resembles a square Mandelbrot set. And since parents give birth to similar offspring, the midgets tend to be square also. The squared-off midget at the center of today's image lies in the East Valley of the large midget on the main stem of its parent. Because of the unusually vividly defined square area surrounding the mis-shapen midget at the center, today's fractal effort rates a 7. The render time of only 2 minutes is another good feature of the image. As always, the image may also be seen by downloading it from one of the FOTD web sites: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Thursday was cloudy with occasional flurries of snow and a temperature that hung around freezing. The fractal cats spent the day by the heat, occasionally demanding food. Their mood was barely acceptable. Today's weather promises to be a repeat, so the cats' attitude will likely be a repeat also. My mood will improve markedly when I finish the modicum of work now waiting to be done, and start searching for the next FOTD. Until tomorrow, take care, and is infinity an odd or even number? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Un-Named_Fractal-V { ; time=0:02:30.99--SF5 on a P200 reset=2002 type=formula formulafile=c4gsave.frm formulaname=C4G passes=1 center-mag=-1.74967514907\ 1832/0/1.409911e+007 params=0.5/1 float=y maxiter=1500 logmap=151 inside=0 symmetry=xaxis periodicity=10 colors=000IHMKBQM6SO5UQ4WS3YU3ZW2`Z1b`0db0ee1gg2hi\ 3jk3lm4mo5oqAqsAsuAuwAwzAz6cU5bR4bO8BV6`j5yzwMIuPG\ tSErVCqYBo`9nc7me6y_ZjjRWtJSnMOhPKcSGYVCTY8N`5IcEF\ bNDaVA`c8_k6ZlDblJemPhmWlnaongr`f5Tb8MZBFWE8SH1PJ6\ UOBXTGaYKdaPhfUlkZppbrrYomUkgQg`MaVHYODUI9QB5N54I4\ 3D3292141KA0KAGD88tzPpuNlqLhmKdiIaeGY`FUXDQTBPS2SR\ 8VRDXRJ_QOaQTdQZfQciPhkPnnPspPxnOulNskNpiMnhLkfLie\ KfcJdaJa`I_ZHXYHVWGSVFQTFNRELQDIODGNCDLBBKB9MACNAE\ OAGQAIRAKSAMUAPVARWATYAVZAX_AZa9ab9cc9ee9gf9ig9ki9\ nj9pk9rm9tn9vo9xjHjePX`XJYUHVRGSPEPMDMKBJHAHF8EC71\ 12BA5874552221dlfaic_gaYd_WbYU_WSYUQVROTPMQNKOLIMJ\ GJHEHFCECACA898676444222_72Y61W61V61T51S51Q51P41N4\ 1L41K31I31H30F30E20C20A20910710610400300100YH6WG5U\ F5WE5YD4_C4bB4eA3h93k83nC2qF2tI2wK1zM1zO1zQ0zS0zUT\ zWQzYOz_MzaKzcIzeGzgEziCzkAzm8zm6zm4zm2zm0zm0zm0zm\ 0zm0zm0zm0zm0zm0zm0zm0zm0 } frm:C4G {; p1 is (plus or minus) 1 or i x=real(pixel), y=imag(pixel)*p1 a=b=0: a1 = a^2-p1^2*b^2 b1 = 2*a*b a=a1+x, b=b1+y z = sqrt(a^2 + b^2) z < 4 } END 20.0 PAR-FORMULA FILE==================================

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Probability distribution functions and the Triangle Map
by Morgan L. Owens 31 Jan '03

31 Jan '03

Just spent a couple of hours with a statistics text. Looked at Kerry Mitchell's tent map formulae. Went hnnnnnnnnnn...... pdfs. My initial idea was to iterate the usual nonlinear transformation with one hump that lead to Feigenbaum's discovery of his number. Traditionally, a parabola is used, with its height governed by a parameter lambda that runs from 0 to 4. But a piecewise linear curve - a triangle, in fact, could be used instead and (among other things) leads to exactly the same Feigenbaum constant. I thought, hnnnn, what about a Gaussian curve? Okay, it's not exactly confined to the interval (0,1), but why should that be any hindrance to me? I mean, I'm not even going to be confining myself to the reals, let alone a particular finite interval of them. I mean, some of these distributions are even supposed to be _discrete_! Kerry Mitchell had chucked in a user-definable "c" parameter to adjust the size of the triangle, and to provide a parameter for selecting elements of its Julia space. I left it in for the latter reason, but also tossed in the various parameters that are used to describe the various distributions (I could have used one of these instead of leaving in "c", but which one?). I also put in an offset parameter "o", since many of these distributions are centred on the origin, and they're probably more useful at, say o=1. I haven't done any massaging of these parameters - they still have their statistical significance - so some hunting around may be needed to find something interesting (I found a few things during my initial explorations, including the ubiquitous almond bread man). The bailout is also user-definable, but if none is supplied it defaults to 100. Generally speaking, a full zoom-out may be a good start. Starting with values like 1 or 2 may be beneficial (note, of course, that for some values the resulting distribution may be undefined - a look at the formula should be enough in most cases to pick the bad choices). There are Julia and Mandelbrot sets for each distribution. The Mandelbrot sets for some proved tricky - for those, like the exponential distribution, with a critical point at infinity, I've arbitrarily initialised z to 100. Some I'm not yet convinced have anything to offer. The Laplace distribution may even be buggy - I used a hacked version of Sylvie Gallett's Graph formula to check that the formulae I'd written had the right shape, but despite this laplace_distro_m just doesn't seem to want to deliver. Morgan L. Owens "Now on to more important matters. Whoopdy-doo." gaussian_distj { if(real(p4)==0) bailout=100 else bailout=real(p4) endif sigma = real(p1) o = imag(p1) c1 = 2*sqr(sigma) z = pixel, c = p3/sqrt(pi*c1): z = c*exp(-sqr(z-o)/c1) |z|<bailout } gaussian_distm (XAxis) { if(real(p4)==0) bailout=100 else bailout=real(p4) endif sigma = real(p1) o = imag(p1) c1 = 2*sqr(sigma) z = o, c = pixel/sqrt(pi*c1) : z = c*exp(-sqr(z-o)/c1) |z|<bailout } exponential_distj { if(real(p4)==0) bailout=100 else bailout=real(p4) endif mu = real(p1) o = imag(p1) c1 = mu z = pixel, c = p3/c1: z = c*exp((o-z)/c1) |z|<bailout } exponential_distm (XAxis) { if(real(p4)==0) bailout=100 else bailout=real(p4) endif mu = real(p1) o = imag(p1) c1 = mu z = 100, c = pixel/c1: z = c*exp((o-z)/c1) |z|<bailout } laplace_distj { if(real(p4)==0) bailout=100 else bailout=real(p4) endif a = real(p1) o = imag(p1) z = pixel, c = p3*a/2: z = c*exp(-abs((z-o)/a)) |z|<bailout } laplace_distm (XAxis) { if(real(p4)==0) bailout=100 else bailout=real(p4) endif a = real(p1) o = imag(p1) z = o, c = pixel*a/2: z = c*exp(-abs((z-o)/a)) |z|<bailout } cauchy_distj { if(real(p4)==0) bailout=100 else bailout=real(p4) endif a = real(p1) o = imag(p1) z = pixel, c = p3/(a*pi): z = c/(1+sqr((z-o)/a)) |z|<bailout } cauchy_distm (XAxis) { if(real(p4)==0) bailout=100 else bailout=real(p4) endif a = real(p1) o = imag(p1) z = o, c = pixel/(a*pi): z = c/(1+sqr((z-o)/a)) |z|<bailout } rayleigh_distj { if(real(p4)==0) bailout=100 else bailout=real(p4) endif sigma = real(p1) o = imag(p1) c1 = sqr(sigma) c2 = -2*c1 z = pixel, c = p3/c1: z = z-o z = c*z*exp(sqr(z)/c2) |z|<bailout } rayleigh_distm (XAxis) { if(real(p4)==0) bailout=100 else bailout=real(p4) endif sigma = real(p1) o = imag(p1) c1 = sqr(sigma) c2 = -2*c1 z = o, c = pixel/c1: z = z-o z = c*z*exp(sqr(z)/c2) |z|<bailout } rayleightail_distj { if(real(p4)==0) bailout=100 else bailout=real(p4) endif sigma = real(p1) a = imag(p1) o = real(p2) c1 = sqr(sigma) c2 = 2*c1 c3 = sqr(a) z = pixel, c = p3/c1: z = z - o z = c*z*exp((c3-sqr(z))/c2) |z|<bailout } rayleightail_distm (XAxis) { if(real(p4)==0) bailout=100 else bailout=real(p4) endif sigma = real(p1) a = imag(p1) o = real(p2) c1 = sqr(sigma) c2 = 2*c1 c3 = sqr(a) z = o, c = pixel/c1: z = z-o z = c*z*exp((c3-sqr(z))/c2) |z|<bailout } lognormal_distj { if(real(p4)==0) bailout=100 else bailout=real(p4) endif sigma = real(p1) zeta = imag(p1) o = real(p2) c1 = 2*sqr(sigma) z = pixel, c = p3/sqrt(pi*c1): z = z-o z = c*exp(-sqr(log(z) - zeta)/c1)/z |z|<bailout } lognormal_distm (XAxis) { if(real(p4)==0) bailout=100 else bailout=real(p4) endif sigma = real(p1) zeta = imag(p1) o = real(p2) c1 = sqr(sigma) c2 = 2*c1 z = exp(zeta-c1)+o, c = pixel/sqrt(pi*c2): z = z-o z = c*exp(-sqr(log(z) - zeta)/c2)/z |z|<bailout } logistic_distj { if(real(p4)==0) bailout=100 else bailout=real(p4) endif a = real(p1) o = imag(p1) z=pixel, c=p3: z = z-o z = c*exp(-z/a)/(z*sqr(1+exp(-z/a))) |z|<bailout } logistic_distm (XAxis) { if(real(p4)==0) bailout=100 else bailout=real(p4) endif a = real(p1) o = imag(p1) z=100, c=pixel: z = z-o z = c*exp(-z/a)/(z*sqr(1+exp(-z/a))) |z|<bailout } pareto_jul { if(real(p4)==0) bailout=100 else bailout=real(p4) endif a = real(p1) b = imag(p1) o = real(p2) c1 = a+1 z = pixel, c = p3*a/b: z = z-o z = c/((z/b)^c1) |z|<bailout } pareto_man (XAxis) { if(real(p4)==0) bailout=100 else bailout=real(p4) endif a = real(p1) b = imag(p1) o = real(p2) c1 = a+1 z = 100, c = pixel*a/b: z = z-o z = c/((z/b)^c1) |z|<bailout } weibull_distj { if(real(p4)==0) bailout=100 else bailout=real(p4) endif a = real(p1) b = imag(p1) o = real(p2) c1 = b-1 z = pixel, c = p3*b/a^b: z = z-o z = c * z^c1 * exp(-(z/a)^b) |z|<bailout } weibull_distm (XAxis) { if(real(p4)==0) bailout=100 else bailout=real(p4) endif a = real(p1) b = imag(p1) o = real(p2) c1 = b-1 z = o, c = pixel*b/a^b: z = z-o z = c * z^c1 * exp(-(z/a)^b) |z|<bailout } gumbel_1_distj { if(real(p4)==0) bailout=100 else bailout=real(p4) endif a = real(p1) b = imag(p1) o = real(p2) z = pixel, c = p3*a*b: z = a*(z-o) z = c/exp(b/exp(z)+z) |z|<bailout } gumbel_1_distm (XAxis) { if(real(p4)==0) bailout=100 else bailout=real(p4) endif a = real(p1) b = imag(p1) o = real(p2) z = 100, c = pixel*a*b: z = a*(z-o) z = c/exp(b/exp(z)+z) |z|<bailout } gumbel_2_distj { if(real(p4)==0) bailout=100 else bailout=real(p4) endif a = real(p1) b = imag(p1) o = real(p2) c1 = a+1 z = pixel, c = p3*a*b: z = z-o z = c/(z^c1*exp(b/z^a)) |z|<bailout } gumbel_2_distm (XAxis) { if(real(p4)==0) bailout=100 else bailout=real(p4) endif a = real(p1) b = imag(p1) o = real(p2) c1 = a+1 z = 100, c = pixel*a*b: z = z-o z = c/(z^c1*exp(b/z^a)) |z|<bailout } geometric_distj { if(real(p4)==0) bailout=100 else bailout=real(p4) endif p = real(p1) o = imag(p1) c1 = 1-p z = pixel, c = p3*p: z = c*c1^(z-o-1) |z|<bailout } geometric_distm (XAxis) { if(real(p4)==0) bailout=100 else bailout=real(p4) endif p = real(p1) o = imag(p1) c1 = 1-p z = o+1, c = pixel*p: z = c*c1^(z-o-1) |z|<bailout }

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Re: [Fractint] Mandelbrot and Julia Sets Explored by RareEvent Theory
by Russell Walsmith 31 Jan '03

31 Jan '03

I believe that I can clarify the first part of this statement (and Osher Doctorow can correct me if it's wrong): What is being said here is that the Mset can be generated as easily from real numbers as from complex. E.g., in the form of an frm: C4 { x=real(pixel), y=imag(pixel) a=b=0: a1 = a^2-b^2 b1 = 2*a*b a=a1+x, b=b1+y z = sqrt(a^2 + b^2) z < 4 } Recall that y=imag(pixel) is a real number (u da man Gerald) and so imaginary numbers don't come into play in this formula. One virtue of this approach is that it leads to interesting generalizations. A somewhat trivial example is offered in the formula below; C4G {; p1 is (plus or minus) 1 or i x=real(pixel), y=imag(pixel)*p1 a=b=0: a1 = a^2-p1^2*b^2 b1 = 2*a*b a=a1+x, b=b1+y z = sqrt(a^2 + b^2) z < 4 } -- On Fri, 31 Jan 2003 02:07:12 Guy Marson wrote: >At 12:20 29/01/03 -0800, you wrote: >>From Osher Doctorow (user in mdoctorow(a)comcast.net network). >> >>Let's examine the expression z^2 + c (where z^2 means z-squared) for z, >>c complex (c constant), that is to say z = x + iy, c = c1 + ic2, i = >>square root of -1. For the Mandelbrot set (M for short), we want /c/ < >>2 where /c/ = sqrt(c1^2 + c2^2), sqrt( ) meaning square root of >>whatever's inside ( ). We'll rewrite this in terms of x and y as >>follows. >> >>1) z^2 = (x + iy)(x + iy) = x^2 + iyx + ixy + (iy)^2 = [(x^2) - y^2] + >>2ixy >> >>2) z^2 + c = [x^2 - y^2 + c1] + i[2xy + c2] >> >>In Rare Event Theory (RET), the expression u + iv changes to real >>variables as follows. >> >>3) u + iv --> u - v >> >>where the arrow indicates the result of the change or transformation. >>So from (2) bove, z^ + c changes as follows. >> >>4) z^2 + c --> [x^2 - y^2 + c1] - [2xy + c2] >> >>Now we get a strange result. J. C. Sprott of Dept. Physics U. >>Wisconsin Madison, in "Mandelbrot Set Chaos," July 3, 1997, >>http://sprott.physics.wisc.edu/chaos/manchaos.htm computes the >>Mandelbrot set orbits in the c1-c2 plane, which he calls the a-b plane, >>respectively by the following where xn+1 means x with subscript n+1, >>etc. >> >>5) xn+1 = xn^2 - yn^2 + a >>6) yn+1 = 2xnyn + b >> >>These are precisely the right hand side expressions in the respective >>brackets in (4) with a = c1 and b = c2. >> >>Now, p1 is optimized at p1(x, y) = 1, where p1(x, y) = 1 + y - x. How >>do we write the right hand side of (4) in terms of p1? The right hand >>side of (4) has the form y - x for some y, x, so it is p1 - 1 for some >>p1. In fact, we have: >> >>7) x^2 - y^2 + c1 - [2xy + c2] = p1(2xy + c2, x^2 - y^2 + c1) - 1 >> >>Let's incorporate the -1 into c1 and call the result c1', so we can >>write (7) as follows. >> >>8) x^2 - y^2 + c1 - [2xy + c2] = p1(2xy + c2, x^2 - y^2 + c1') >> >>Now we can set p1 = 1, which says the following. >> >>9) x^2 - y^2 -(2xy + c2) + (c1' + 1) = 1 >> >>and therefore we have the following. >> >>10) x^2 - y^2 -(2xy + c2) + c1 = 0 >> >>or, expanding: >> >>11) x^2 - y^2 - 2xy + (c1 - c2) = 0 >> >>Except for possibly degenerate cases, it is proved in analytic geometry >>that this is part of a hyperbola (by proper rotation of axes and >>translations). >> >>We therefore can study the Mandelbrot set M as a part of a hyperbola in >>Rare Event Theory, which simplifies it considerably. We have c1^2 + >>c2^2 < = 4 from before. >> >>Osher Doctorow >> >> > > >ooooh, big stuffff..... please put it into a .frm (for 'normal people'), so >we pass it through the evolver and will see what happens.. > >thanks, > >Guy > > > > >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint > _____________________________________________________________ Get 25MB, POP3, Spam Filtering with LYCOS MAIL PLUS for $19.95/year. http://login.mail.lycos.com/brandPage.shtml?pageId=plus&ref=lmtplus

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Re: [Fractint] FOTD 28-01-03)
by Jim Muth 31 Jan '03

31 Jan '03

The Programmer Dude wrote: <much cut> >Do you really doubt the, um, reality of reality? It all depends on how the word 'reality' is defined. And, yes, I sometimes do question the reality of at least the physical world, which in the world of science is considered the basis of reality. >As for answering your question, please re-read all of >philosophical and scientific readings from all of human history. It would be great fun, but unfortunately I haven't got the time. >After you finish that you'll realize that no one else knows, >either. I knew this even before you stated it. I myself stated that the answers to the questions are mysteries. >Not everyone feels [that consciousness is generated by the >brain]. The field of AI has a big division between those who >feel (human-like) consciousness is merely a matter of >sufficient complexity (If you build it, it will think.), while >others feel that the *mind* (opposed to the brain) is much more >than a big wet switchboard. A 'hard-AI' machine might behave as though it is thinking, but will it be aware that it is thinking? This is another debate that will never be settled, unless, that is, someone can devise a repeatable experiment that would objectively demonstrate consciousness itself rather than mere mechanistic behavior. Obviously, before this can be done, the field of metaphysics will need to be taken far more seriously. >(FWIW, I fall firmly into the latter category--I believe in the >soul.) I will take you at your word, but please describe this soul you believe in, and state a few of its attributes. I assume the soul of your belief is a bit more than an amorphous and undetect- able bit of vapor. If it is not, then what you have is hope rather than belief. >I recall a long ago short SF story about the world-wide phone >system achieving consciousness...I believe the last line was >about the phones starting to ring... everywhere at once! :-) I also recall the story. I think it was written by Ray Bradbury. >What you MEAN is that matter like rocks and tables [lack >consciousness]. It's not the presumably unconscious brain matter itself that is supposed to generate consciousness. It is the activity of the intricately connected material of the brain that creates, or some would say, *IS* consciousness. When a person is conscious, his brain matter is assumed to be doing the 'consciousness' activity; when that person is unconscious, the matter is doing something else. Here I wonder if the far more complex behavior of the entire universe might also be an aspect of a conscious- ness -- a far greater consciousness. >I take it you don't at all subscribe to the theories of hard AI? I'm actually neutral about the possibility. What I doubt is that we will ever devise an unambiguous way of determining whether hard (or strong) AI is present. Even the existence of human consciousness is a puzzling thing to determine. If you suppose that recognizing the existence of human consciousness is a simple task, ask a neurologist who has experience with patients in a deep coma. >NOTHING remains the same from day to day. NOTHING. Your >location is moving at huge speeds every second (relative to the >frame of the universe). Your cells are constantly changing. >The atoms in your body are constantly changing. So is your >mind and consciousness. Apparently, you wrote this without too much thought. Though the material and appearance of my body is changing slowly, and my thoughts are changing more rapidly; my individual identity, my particular awareness, most certainly has stayed the same. I am the same person today as I have been through my entire life. I assume this is also true with you. >I, for one, surely hope MY spirit evolves in step with the rest >of the universe. So do I. A spirit stagnated for all eternity would be one of the worst hells. >You continue to make what I consider a fundamental error in >thought: you think the immaterial can be illuminated by the >material. How can it? Are they not completely different >domains? You continue to mis-understand my view. I do not claim that the immaterial (spiritual) can be known through objective material means; I claim that it can be glimpsed through subjective means such as meditation. The problem is that knowledge gained through subjective means cannot be demonstrated scientifically, and therefore is not considered valid by those who put their faith in science. If there were no way at all of gaining knowledge of the immaterial, or if it did not exist, how would all the stories of its reality have come into being? (I am aware that primitive men are supposed to have invented the immaterial realm in an effort to escape the fear of death.) >**IF** what controls the brain and body is non-material, then >the universe is not, in fact, a closed system. And those who assume it is a closed system are mistaken. >How many of us really have an "intuition" of how DNA works? >Or, for that matter, a modern jet engine. Or any of a myriad >*physical* things. An important point. Everything I know about most scientific things I have learned by reading books written by the 'high priests' of science. And I must accept these things on faith, because I have personally observed very few of the experiments that demonstrate the truth of what is in the books. Science is like religion, where only the chosen few have had the mystical experience, (observed the experiment), that validates the belief (hypothesis). >As far as we know so far, these [quantum] phenomena are quite >material. They're just a bit beyond our ken. I would say they are quite far beyond our ken. Ten dimensions, time that flows backward, quantum entanglement, etc. are not things we observe every day. And if subatomic particles actually are tiny bits of materialized energy zipping around in an imaginary Hilbert space, is this not an interaction of the material and immaterial such as we have been discussing? Jim (now back to fractals) Muth

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Mandelbrot and Julia Sets Explored by Rare Event Theory
by MARLENE DOCTOROW 31 Jan '03

31 Jan '03

>From Osher Doctorow (user in mdoctorow(a)comcast.net network). Let's examine the expression z^2 + c (where z^2 means z-squared) for z, c complex (c constant), that is to say z = x + iy, c = c1 + ic2, i = square root of -1. For the Mandelbrot set (M for short), we want /c/ < 2 where /c/ = sqrt(c1^2 + c2^2), sqrt( ) meaning square root of whatever's inside ( ). We'll rewrite this in terms of x and y as follows. 1) z^2 = (x + iy)(x + iy) = x^2 + iyx + ixy + (iy)^2 = [(x^2) - y^2] + 2ixy 2) z^2 + c = [x^2 - y^2 + c1] + i[2xy + c2] In Rare Event Theory (RET), the expression u + iv changes to real variables as follows. 3) u + iv --> u - v where the arrow indicates the result of the change or transformation. So from (2) bove, z^ + c changes as follows. 4) z^2 + c --> [x^2 - y^2 + c1] - [2xy + c2] Now we get a strange result. J. C. Sprott of Dept. Physics U. Wisconsin Madison, in "Mandelbrot Set Chaos," July 3, 1997, http://sprott.physics.wisc.edu/chaos/manchaos.htm computes the Mandelbrot set orbits in the c1-c2 plane, which he calls the a-b plane, respectively by the following where xn+1 means x with subscript n+1, etc. 5) xn+1 = xn^2 - yn^2 + a 6) yn+1 = 2xnyn + b These are precisely the right hand side expressions in the respective brackets in (4) with a = c1 and b = c2. Now, p1 is optimized at p1(x, y) = 1, where p1(x, y) = 1 + y - x. How do we write the right hand side of (4) in terms of p1? The right hand side of (4) has the form y - x for some y, x, so it is p1 - 1 for some p1. In fact, we have: 7) x^2 - y^2 + c1 - [2xy + c2] = p1(2xy + c2, x^2 - y^2 + c1) - 1 Let's incorporate the -1 into c1 and call the result c1', so we can write (7) as follows. 8) x^2 - y^2 + c1 - [2xy + c2] = p1(2xy + c2, x^2 - y^2 + c1') Now we can set p1 = 1, which says the following. 9) x^2 - y^2 -(2xy + c2) + (c1' + 1) = 1 and therefore we have the following. 10) x^2 - y^2 -(2xy + c2) + c1 = 0 or, expanding: 11) x^2 - y^2 - 2xy + (c1 - c2) = 0 Except for possibly degenerate cases, it is proved in analytic geometry that this is part of a hyperbola (by proper rotation of axes and translations). We therefore can study the Mandelbrot set M as a part of a hyperbola in Rare Event Theory, which simplifies it considerably. We have c1^2 + c2^2 < = 4 from before. Osher Doctorow

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Re: [Fractint] Triternions
by Russ Walsmith 31 Jan '03

31 Jan '03

>From: "Gerald K. Dobiasovsky" <gerald.dob(a)aon.at> >Reply-To: fractint(a)mailman.xmission.com >To: <fractint(a)mailman.xmission.com> >Subject: Re: [Fractint] Triternions >Date: Wed, 29 Jan 2003 01:29:59 +0100 > >Russ Walsmith wrote: > > > In the following > > frm files, the default imaginary values for Y are changed by > > imag(pixel)*(0,-1) to real. > > > > CP4 (XAXIS){ > > x=real(pixel), y=imag(pixel)*(0,-1), a=b=0: > >Russ, >this seems to be a small misunderstanding regarding >Fractint's parser. The imag()-function returns the >imaginary component of a number already as a real! >That is, from a + i*b you get b + i*0, not 0 + i*b. > >Regards, >Gerald > > Thanks Gerald for calling that to my attention... but I admit that I had to run about six versions of TEST { y=imag(pixel): y^2 > 1 } before I became convinced. Good thing I didn't realize that, I guess, else I never would have rectified the imagined imaginary value in Mr T's formula, and TMan would not have come to life. Then Jim Muth couldn't have turned him sideways to create the fraternal twin, TMan1, and if TMan1 didn't exist, he could not have been so swiftly dissected, his strange internal organs expertly laid bare in front of God and everybody on the Fractint list. And if that hadn't happened, from whence would have come the inspiration for the haunting, surreal video 'Mandelbrot Rising', now playing at http://www.sonic.net/~jot/ufvp.html So hey, it's all good, and to quote Morgan Owens, "...the important thing here are the visual results..." Indeed, those and other happy outcomes are accruing to the bottom line. But if the imag(pixel) theory doesn't hang, then what is going on? I must say that the situation is way more curious than I initally supposed. There is much to ponder in this realm; e.g., I've noticed that CP8 { c1=real(pixel),c2=imag(pixel)*p3,c3=p1,c4=p2 z1=z2=z3=z4=0: t1=z1*z1-z3*z3-2*z2*z4 t2=2*z1*z2-2*z3*z4 t3=2*z1*z3+z2*z2-z4*z4 t4=2*z1*z4+2*z2*z3 z1=t1+c1,z2=t2+c2,z3=t3+p1,z4=t4+p2 z=sqrt(t1^2+t2^2+t3^2+t4^2) z < 4 } seems to be completely indifferent as to whether the value chosen for p3 is real or imaginary. Do you have any insights here? Regards, Russell _________________________________________________________________ Tired of spam? Get advanced junk mail protection with MSN 8. http://join.msn.com/?page=features/junkmail

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Rare Event Theory 'Replaces' Composition by Addition-Subtraction
by MARLENE DOCTOROW 30 Jan '03

30 Jan '03

>From Osher Doctorow Category Theory uses composition of morphisms as its main operation, while Rare Event Theory (RET) uses addition-subtraction as its main operation although multiplication-division are shown to be secondary. See my postings at http://www.mathforum.org/math-history-list. This does not mean that composition does not exist in RET, but it does mean that when examining an iterated function in fractals it is enough in the RET representation to examine the original function ordinarily. If a pathology is found in the original function, that is usually enough, and vice versa. I will simply add here that in my opinion an enormous weight of evidence indicates that RET plays the key role in GROWTH (expansion- contraction) processes in the mathematical and physical universes, and the superstringtheory.com site as well as my paper in B. N. Kursunuglu et al. (Eds.) "Quantum Gravity, Generalized Theory of Gravitation, and Superstring Theory-Based Unification," Kluwer: N.Y. 2000 89-97 should be looked at for this. Radiation from a source is also a growth process, by the way. I respect opposite or different views and encourage competition between them, since in my opinion there are many pictures and many theories that lead to knowledge, and competition is extremely valuable for quantitative sciences/mathematics and philosophy and engineering and medicine. Osher Doctorow

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FOTD 30-01-03 (UnNamed Fractal-IV [5])
by Jim Muth 30 Jan '03

30 Jan '03

FOTD -- January 30, 2003 (Rating 5) Fractal visionaries and enthusiasts: Surrounding every Mandel midget is a basin of attraction. The midget behaves as though it wants to hold on to points that start near it. The closer to a midget a point lies, the more iterations will be needed before that point escapes beyond the bailout radius on its ever-accelerating but futile trip to reach infinity. Today's image, with the arms around the midget appearing to descend into the purple haze of the depths, illustrates this basin effect quite clearly. I originally had named today's image "Fractal Basin". Then it struck me that the name raised images of a bathroom. I quickly changed the name to the boring one that the image now bears -- "UnNamed Fractal-IV". And why not. We've been having a lot of nameless images lately. What harm will one more do? When it came time to rate the image, I could attach a rating no higher than an average 5. But the image is really not all that bad. Most likely I have been spoiled by the recent spate of evaporated images in the 7 and 8 range. At one point, I actually tried to 'evaporate' today's image, but much to my surprise, found that it would not evaporate, even though both exponents of Z are negative. I can only assume that this is because the parent fractal is of immense size, with fractal detail extending out at least as far as one-googol. Today's scene lies near the edge of a most curious double-bayed midget that lies near the edge of a larger double-bayed lake that lies near the shore of an immense ocean in the hugely bloated parent fractal. The parent was generated by taking one part of Z^(-1.11) and adding 0.001 part of Z^(-1000) to it, then adding 1/C. The render time of the parameter file is in the 7-minute range, at least on my exhausted old machine, which BTW I have named "Betsy". The wait may be avoided by downloading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The sleet and freezing rain of Wednesday morning changed to light snow by noon, with a temperature that never topped 30F -1C. Only 1/2in 1cm of snow accumulated, but that was enough to convince the dynamic duo that this was not to be a day for a romp in the yard. Realizing the inevitable, they endured their confinement stoically. Today is starting once again cloudy and chilly. And the snow is still around. The duo will likely have another bad day. At least the work is light, which will give me more time to find one of those elusive fractals that rate a 9. Check in 24 hours to see if I succeed. Until then, take care, and all is not lost. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ UnNamed_Fractal-IV { ; time=0:07:43.96--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+15.47911410363785/+71.86947768905489/8\ 190988/1/5/9.87604994590954299e-005 params=0.001/\ -1000/1/-1.11/0/0 float=y maxiter=1350 inside=0 logmap=145 periodicity=100 colors=000WYDWXDXVDYUEYTEZSE_QE_PF`OFaNFaMFeSJiXNl\ aRpfUskYwpaxqdxrfvohtljrilmfnhckc`hZ_cUYZPWUKUPFSK\ BQ1BT1CW1CZ1C`1Dc1Df1Di1El1En1Eq1Ft1Fw1Fy1Lw7QuCWs\ I`qNfoTkmYij_hhagecfcee`gdZicWkbUlaVkaVkaVkaVk`Wj`\ Wj`Wj`Wj`Wj_Xi_Xi_Xi_Xi_XiZYhZYhZYhZYhZYhXWgWVfVTf\ USeTQcSPaRO_QMZPLZOJZNIZMHZKFZJEZICZHBZG9YF8XE7WD5\ UC4UB2VA1W90XC3_F6bH9eKChNFlPIoSLrUOuSQsQSqOToMVmK\ WkIYiG_gE`eCbcAca8e_6gY4hW2jU1kS2iU2hV3gX3fY4e_4d`\ 4ca5bc5`d6_f6Zg6Yh7Xj7Wk8Vm8Un9Sp9Rq9QrAPtAOuBNwBM\ xBLyEMwHMuKMsNMqQMoTMmWMlZMjaMhdMfgMdjMbmN`oOZnPXm\ QVlRTkSRjTPiURhVUgWXfX_eWcdVfcVidUldToeUqcVsaWu_Xv\ YYvWZuU_uS`tQatObsMcsKbrIarG`qE_qCZpBYoAXo9Wn8Vn7U\ m6Tm5Sl4Rl3Qk2Pk1Oj0Nj2Pg3Re5Tc6Va7WZ9YXA_VCaTDbRE\ dOGfMHhKJjIKkFLmDNoBOq9Pr7`sNltamucmvcmwchxccycZzc\ UzcPzcKzcEzc9zc4zc7zdAzeCzfFz_HzTKzNMzGPz9Rz3VzEYz\ PazUdzUezUSzUTzUUzUUzUVzU } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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the use of very complex numbers .......
by Burnett, David 30 Jan '03

30 Jan '03

This got me thinking (a rare occurance and not without its dangers). Our fractals are mostly based on the micro-interactions of the real and imaginary components of a complex number. Has anyone explored using very imaginary numbers (ie n^4 = -1) or where a very complex number has the form ax + biy + cjz (where j^4 = -1). Or further extensions into any power of 2 = -1. too hot here for anything but such meandering musings. db > -----Original Message----- > From: Jim Muth [mailto:jamth@mindspring.com] > > Would fractals exist if there had been no intelligent beings in > the universe to find them? Would the potential for fractals > exist if there had been no intelligent beings to invent numbers? > And what of numbers? Could they exist without having been inven- > ted by a human type of intelligence?

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the use of very complex numbers ............
by Burnett, David 30 Jan '03

30 Jan '03

This got me thinking (a rare occurance and not without its dangers). Our fractals are mostly based on the micro-interactions of the real and imaginary components of a complex number. Has anyone explored using very imaginary numbers (ie n^4 = -1) or where a very complex number has the form ax + biy + cjz (where j^4 = -1). Or further extensions into any power of 2 = -1. probably been done (hasn't it all) - but you never know........ too hot here for anything but such meandering musings. db > -----Original Message----- > From: Jim Muth [mailto:jamth@mindspring.com] > > Would fractals exist if there had been no intelligent beings in > the universe to find them? Would the potential for fractals > exist if there had been no intelligent beings to invent numbers? > And what of numbers? Could they exist without having been inven- > ted by a human type of intelligence?

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The chaotic Mandelbrot region of the real line via Rare Events
by MARLENE DOCTOROW 30 Jan '03

30 Jan '03

For c2 = b = 0, we get the following for optimality: 1) x^2 - y^2 - 2xy + c1 = p1(2xy, x^2 - y^2 + c1 - 1) = 1 and therefore: 2) x^2 - y^2 - 2xy = 1 - c1 But the chaotic Mandelbrot real line region is most of -2 < = c1 < = - 1.4011, from which 1 - c1 > = 2.4011, but x^2 - y^2 - 2xy < = x^2 < = 1. This is a contradiction (recall that x, y are in [0, 1] X [0, 1] as arguments of p1). So the chaotic region is pathological in the sense that optimizing p1 there leads to a contradiction. It might be asked whether there are any non-chaotic regions which are pathological, and if so what does that mean. Formally, for c between 0 and 1, the above contradiction disappears. However, for c in [-1, 0], we still get a contradiction. We already know that there are pathologies other than based on contradictions, from earlier examples, and perhaps there is another explanation for c in [-1, 0]. Osher Doctorow

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Re: [Fractint] FOTD 28-01-03)
by Jim Muth 29 Jan '03

29 Jan '03

John W. wrote: <snipped> >To a certain extent each observer must observe his private >world, although in many/most(?) cases the experience is, no >doubt, similar amongst observers. Since I basically agree with the entire reply, I have little to add. My only comment might be, 'what are the philosophical and scientific consequences of our mere indirect contact with a presumed reality?' and Ricardo F. wrote: <also snipped> >Let me add some other [questions]: What is conscience >[consciousness?] . . . This question is perhaps the second greatest, right behind: Why is there something instead of nothing? The scientific method of addressing the question has been to assume that consciousness is a phenomenon somehow generated by the brain, (What else is there?), and begin searching for the mechanism. But after hundreds of years of searching, countless 'theories', and continuing claims of 'progress' and 'discoveries', we remain no closer to a definitive answer than we were when we first made the assumption. The problem is that consciousness is totally different from the material of the brain, the meat that is assumed to generate it. When we claim that consciousness originates in the brain, we are claiming that something can come from nothing, which is magic. (There is no consciousness in ordinary matter.) I am far more comfortable picturing the brain as a kind of radio receiver that detects a universal field of consciousness and focuses it into the sub-units that we call our individual self-awarenesses. Those who wish to do so may consider the universal field of consciousness to be their God. Another extremely difficult question is: What remains the same from day to day, while the contents of the mind and material of the brain constantly change? The most immediate answer would be to invoke an unchanging soul or spirit. But science does not admit the existence of such entities, and wanting to appear at least moderately scientific, I must state that I have no idea. >. . . If it [consciousness] is inmaterial, how is it that it >controls the body? . . . >From the scientific viewpoint the question is even more perplexing. It is assumed that the brain creates the mind that controls the body by controlling the material of the brain -- a circular argument that goes nowhere. There is also a conflict with causality. The physical universe is assumed to be a closed system. If what controls the brain and body is not physical, there is a physical effect without a physical cause, a clear violation of the principle of causality. >. . . What is matter? This is another puzzling question, made even more puzzling by the discoveries of quantum mechanics. Regardless of which model we use, reality at the quantum level is so alien to our intuition that it is beyond comprehension. By using numbers, we can create models of what goes on down there, and thereby make predictions, but we shall never achieve an intuitive image of things like atoms -- an image which would match the image we have of the physical world. We have discovered that we live in a material classic world composed of immaterial quantum building blocks. This is the same as discovering that we live in a house composed of the idea of a house. It is one massive puzzlement! Jim (the puzzled fractalist) Muth

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Re: searching for stupid... :)
by travelGirl 29 Jan '03

29 Jan '03

a VERY special thank you goes to russ nelson, who found 1 through 1600 in record time... still missing is 1601 through 1700, but i think the loss of those (should it come to that) will be tremendously mitigated by mr nelson's archival find and generosity... again, THANK YOU! travelGirl <carenp(a)yahoo.com> wrote: i know this is a sad and stupid tale, of a woman who made several backups, then promptly lost track of each and every one... trust me, i know this woman intimately... she's me :) would anyone happen to have backups of my PAR files from compuserve? i have at least one copy of my PARs from image #1 to #150, and one or two packets of 25 each somewhere in the 600 range, but i'm basically missing (ie, lost) everything from #s 151 through 1700... and this news, of course, makes me VERY angry... i've got the images, and could go back through them to regenerate the pars, but it would be nice to have the information (titles, creation dates and times, copyrights, notes, etc) of the original pars that were uploaded to compuserve and on those now-ancient fractint CDs... thank you in advance... :) 00 caren park --------------------------------- With Yahoo! Mail you can get a bigger mailbox -- choose a size that fits your needs

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searching for stupid... :)
by Hans-Joachim Metzger 29 Jan '03

29 Jan '03

Caren, maybe this is a sad tale, but it isn't a stupid one. Could happen to everybody. Seems I have almost all of your original par files: Ckp025 to Ckp975 (November 1992 to June 1994) and Cp1000 to Cp1600 (June 1994 to January 1997), complete with headers - must have missed 1700, though. So if you let me know your email adress I will send them to you. All the best, Hans-Joachim

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searching for stupid... :)
by travelGirl 29 Jan '03

29 Jan '03

i know this is a sad and stupid tale, of a woman who made several backups, then promptly lost track of each and every one... trust me, i know this woman intimately... she's me :) would anyone happen to have backups of my PAR files from compuserve? i have at least one copy of my PARs from image #1 to #150, and one or two packets of 25 each somewhere in the 600 range, but i'm basically missing (ie, lost) everything from #s 151 through 1700... and this news, of course, makes me VERY angry... i've got the images, and could go back through them to regenerate the pars, but it would be nice to have the information (titles, creation dates and times, copyrights, notes, etc) of the original pars that were uploaded to compuserve and on those now-ancient fractint CDs... thank you in advance... :) 00 caren park --------------------------------- With Yahoo! Mail you can get a bigger mailbox -- choose a size that fits your needs

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FOTD 29-01-03 (UnNamed Fractal-III [8])
by Jim Muth 29 Jan '03

29 Jan '03

FOTD -- January 29, 2003 (Rating 8) Fractal visionaries and enthusiasts: With today's image we continue investigating the fractals that result when the numbers pi and epsilon are used as exponents of Z. In today's case 200 parts of Z^(pi) are subtracted from 200 parts of Z^(epsilon), then 1/C is added. This operation produces a large open fractal filled with debris. The eastern end of this fractal has Mandel characteristics, with a bud and a stem extending east along the positive X-axis and terminating in a flower-like feature. Smaller lightning-like side-filaments radiate from this flower. Today's image is located on one of these filaments. To be more accurate, I should say today's image is located where the filament used to be, for the image is another one that has been evaporated by an immense bailout radius and made visible by the bof61 inside fill. (In yesterday's discussion I mistakenly wrote that the image was rendered with the bof60 fill. I should have written bof61 fill.) Fans of clever titles will once again be disappointed. I have once again neglected to name the image. The phrase "UnNamed Fractal-III" that appears in the head of the parameter file should be considered more of a catalog entry than a name. But named or not, the image is well above average. The 6-minute render time requires just about the right amount of effort that should be required to see the image. Of course, those who prefer their images 'on sale' will be able as always to download the pre-rendered image from one of the FOTD web sites. Paul's site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's site is at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Tuesday was partly cloudy with a high temperature that just reached freezing, making the dynamic fractal cats partly happy. When they rest on the porch, they prefer sun, especially when the temperature is chilly. Unfortunately, the sun will not rise above the evergreen holly trees for almost a month yet, so I suppose the intrepid ones will be disconsolate for a few more weeks. This morning is cloudy with showers of ice pellets mixed with freezing rain -- certainly not the kind of weather that will make the cats happy. I'll find my consolation when the work is finished and I can tackle the real task of the day -- finding tomorrow's FOTD. Until then, take care, and what could be worse than a day without fractals? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ UnNamedFractal-III { ; time=0:06:05.09--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.25714998352473700/+0.025876131429569\ 72/9.260188e+010/1/-90/3.88578058618804789e-016 params=-200/-3.14159265358979/200/-2.7182818284590\ 5/0/1e+100 float=y maxiter=400 inside=bof61 periodicity=10 colors=000Lc0z60zA0wC0qG0kH0eL0ZN0aA00000z0Ci0aE0z\ 00a2EELW0ek0Zf0Ue0Nc0Ja0EZ08Y02W00006J1EC4J48S0CY0\ 8S04L02H00C00800200000400801002G06J08N0CE0E60G00J0\ 0L00N00P0040A00z00S00W00n00i00i00u00Z00E0000000000\ GJ0er0UZ0ZkUPS0HN0000AG06C048XUCGYHSkLcyPmzUczYUza\ JzcAzf1zk0zm000AziJyiUufcnemkeweczacfJ0cC0a60Y10W0\ 0S00P00N00Z00kA0wS0zf0zW0zJASW10e01L0H20Z00n00m00k\ 04000f0ae0qc0za0ze0zf0uk0im0Wq0Hs46wA0yE0cN4HWSGN6\ EG060G10f20S20C400400400H00W01i0Hw0Yz0nz0z000U0z20\ zE0zN0zY6zfEzqLzzUzzazCzzza0zZ0zY1zWCuWNqUZmSkiSwc\ JnYCfS4ZL0SG0JA0C404000E04U0CiEJwUSsf8qu0nz0Yz0Hs0\ 1k00c10Y60U40S20P10N02L00nz0uu0ym0ze0zW0zN0zG0z80z\ 01w08i0EY0Hc0Ji0Nn0Pu0Sz0Zs0ek0kc0sW0yN2zGAzAGeA0A\ A0z0knAccJWSUPHcH6nA0y40z00z0NZZz0zz0zz0zz0zz0zz0z\ q0ze0yU0uH0q60m00kPzazzL088zk0uY0NE00600A00C00E00G\ 00H00J00L00N00S04U0AY0GZ0 } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 28-01-03 (UnNamed Fractal-II [8])
by Jim Muth 29 Jan '03

29 Jan '03

FOTD -- January 28, 2003 (Rating 8) Fractal visionaries and enthusiasts: Questions, questions, questions . . . a fool can ask more ques- tions than a wise man can answer. I'm feeling a bit foolish this morning, so I shall ask a few questions that the wise men wisely brush aside. I expect no answers, because if questions such as these could be answered in an absolute manner, they would long since have ceased to be asked. Of course there is always the chance that the questions *have* been answered but those who still ask them have failed to recognize or will not accept the answers. Would fractals exist if there had been no intelligent beings in the universe to find them? Would the potential for fractals exist if there had been no intelligent beings to invent numbers? And what of numbers? Could they exist without having been inven- ted by a human type of intelligence? Things grow more complicated. Could intelligence exist without the universe? What if a few physical constants had a different value? Does the universe exist when it is not being observed? Does it exist when it *is* being observed, or is it some kind of consistent illusion. If the universe is an illusion, what is having the illusion? And if the universe is an illusion, is the same illusion common to all observers, or does each observer ob- serve his own private world. Are the observers also part of the illusion? Finally, the ultimate question: Why is there some- thing instead of nothing? No one can give absolute answers to such questions, though many hold opinions so strong that they confuse belief with knowledge and consider their opinions to be fact. And would we even want to answer such questions, when doing so would take so much of the fun and mystery out of life? Regardless of the answers or non-answers to the questions, one thing for certain is that we have another Fractal of the Day to discuss. It is another of my ghostly evaporated images, made visible by the <bof60> inside fill. In today's case, the evap- orated version proves to be better than the normal equal-itera- tion-band version. The parent fractal, which was created by subtracting quite a bit of minus pi from quite a lot of minus epsilon, is an oversized, double-lobed Mandeloid with X-axis symmetry. A meandering fila- ment extends from the northern bud, circles around to the east and joins the southern bud. Today's scene is located on a node of this filament, not far from where it joins the northern bud. I have rated the image at an 8. This rating might be a bit generous, but I'm feeling a bit contemplative this morning, and want to do something to cheer myself. I am unable to find a satisfactory name for the image for the second time in three days, so it enters the world as "UnNamed Fractal-II". Ghosts come and go quickly, and today's image lives up to its ghostly nature. It renders in less than 2 minutes, about the same time needed to download the completed GIF file from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal temperature never made it to 20F -7C here at F.C. on Monday. Combined with biting winds, the outdoor conditions were far too rigorous for the whiskers of the dynamic ones, who passed the day thankful for a warm radiator to huddle close to. Today is starting cloudy and just as cold, with snow threaten- ing. We'll see how the dynamic ones take the harsh cold. Regardless of how the dynamic ones take the cold weather, I shall take it quite well, especially since I expect to be out in it only a few minutes. Until next time, take care, and know that fractals are mystical things that are normally invisible yet can be photographed. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ UnNamed_Fractal-II { ; time=0:01:44.52--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+13.1945886431/+21.1419337772/635.8224/\ 1/150/7.2211701895863456e-011 params=-23.3/-3.1415\ 9265358979/23.3/-2.71828182845905/0/1e+100 float=y maxiter=400 inside=bof61 logmap=20 periodicity=10 colors=000000000000000L9BDK85J64NA4QE3UUSXS3_YWcX2\ febiczz6hwHZtSPrb0m0hzzEnoMogVp_bpTKiL2bD8cIEcNKcS\ QcXWcaacffck``jWZjQWiLUiGSiLSmPSpTSsXSv`Sy`Ut`Wp00\ 0`_g`ac`c_PL8WBMb1_iMYeN`bOc_PfXQiUQlTRjSSiSTgRTfQ\ UeQVcPWbPWaOSbNPcMLdLIeKEfJBfPMbUW__fWdpTizQNw2Os9\ OoFPkLPgRPcXQ_bQWhQTnTUiWUeZVa`VYcWTfWPiXLkXHbVFUU\ DLSBCR94Q8hpZco__n`WnaSmbOmbSa`WQZ_EXb2VkKQt`MmdNg\ hOalPQgxSerUcmWagY_b_YXaWScUMeTHhWLjZPmaTocXrf`tid\ wlhynkdqLbhT`_`_Rh`U``XTa_LaaEQ6tszkpnfnbashXxnTfY\ 6dSFcMObGXdKSfONgRIiVEjY9000md0XVCHMO1DZRfJPbOOZTM\ WYLSbJPgILlHIqREr_Bsi7tr4up6pn8ll9gjBchDZfEVdGQcHM\ MtyMbBQeGUhKXjP`mTdpYgrakufnwjgnlaemWYnPPoJHpD8q70\ r69t6Hu5Pv5Yw4ex4myC64K86S98_BAgCCnDEcHCTKBINA7Q96\ RC5SE4TG4TJ3UL2VN2VPATMHRJPPGWNEcLBjJ8UcUyG3mD7bAB\ S7FH5JKGHNQFQ_DTiBVsAL9VOIVQQVSYVUeVRdXOcYLcZIb_Fa\ `Caa9`b7`c4__2ZWEUOPQH_LA } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

3 2

The Rare Event Real Growth Origin of Chaos and Maybe Fractals
by MARLENE DOCTOROW 29 Jan '03

29 Jan '03

>From Osher Doctorow (Marlene is the network listname owned by my wife Marleen (notice the spellings) and I will eventually get my own user name on this network). Readers might be interested in some of the postings that I've made to http://www.mathforum.org/epigone/geometry-research and other places concerning the relationships among chaos, Rare Event Theory (RET), and pathology for functions with real ranges and real domains. To summarize in more or less ordinary English, chaos appears to derive from "pathologies" in the REAL numbers even though complex numbers are typically used for fractals and chaos. The intuitive idea of a pathology as something "ill" or "sick" or "life-threatening" is pretty close to it. Of course, that is relative to the system that one is considering - to a virus, maybe we look like pathologies. But we usually consider that life is the "non-ill" system, for better or worse, and THINGS WHICH CONTRIBUTE TO THE SYSTEM are non-pathological, while THINGS WHICH DETRACT FROM THE SYSTEM are pathological. People familiar with engineering systems may quickly get this idea. It turns out in Rare Event Theory (RET) that Rare Events (those with probability less than .05 or .01 typically, although .10 is occasionally used and there are arguments for using as much as 1/3 or even .50 in some circumstances) follow the pattern of the function p1 (x, y) = 1 + y - x with y < = x for their "non-pathological" probable influence behavior, with x and y usually taken between 0 and 1. Notice carefully that p1 is 1 if and only if (iff for short) y = x, which includes points like (0, 0), (1, 1), (x, x) for x between 0 and 1. The first number or letter in (0, 0) refers to the x value, the second to the y value, and similarly for the others. Now let's look at the typical chaotic Logistic map or equation (chaotic for certain values and intervals): 1) y = Lx(1 - x) where L is a constant (fixed real number) greater than 0 here. A closely related equation is the logistic function equation: 2) y' = kx(a - x) where a, k are constants with a > 0 and y' is the growth of y or technically rate of change of y at a particular point x which in the case of (2) is usually taken as x = t (time). Equation (2) is often used to model biological/population growth. Let's change a to 1 for simplicity (we can always make a scale change for example, although when the magnitude of a is studied we'd want to change it back). The equation y = Lx(1 - x) contains two variable factors, x and 1 - x. We can fairly easily see that x is non-pathological and 1 - x is pathological by considering that if x is mass divided by the total mass of the galaxy assumed constant or population divided by maximum supportable population (which is a fraction between 0 and 1) for example, then life increases with x but decreases with 1 - x. It also turns out that (0, 0) and (1, 1) are on y = x, but not on y = 1 - x. In fact, if x = 0, then 1 - x = 1, and if x = 1, then 1 - x = 0. So only (1, 0) is on y = 1 - x (remember that y < = x so y can't be bigger than x). That's all there is to it in essence except to note that for certain values of L and for certain ranges of x relative to this value, things get chaotic. Either equation (1) or (2) is a combination of two conflicting influences - non-pathological and pathological. That's where the chaos comes from when it does occur. I didn't say anything about complex numbers of form x + iy here, where i is the square root of -1. It turns out that many ideas in complex numbers including the complex conjugate x - iy of x + iy extend to the real numbers provided that we stick to Rare Events. How much confidence can readers have in these results in view of the fact that I'm just developing them now? Well, take a look at my postings at the above site, which extend back several years, and which refer also to some of my publications, and also my postings at http://www.superstringtheory.com/forum in the String/M Theory/Duality subforum of their Forum section, and if necessary I'll cite some of my publications directly. But pathology is already well known in super- abstract algebra - it's called the Jacobson Radical (look it up as an internet keyword) which has the star product (look that up) x o y = x + y - xy. Osher Doctorow Ph.D. One or More of California State Universities and Community Colleges

1 0

Re: [Fractint] Triternions
by Russ Walsmith 29 Jan '03

29 Jan '03

>On Sat, 25 Jan 2003 00:22:36 +1300 Morgan L. Owens wrote: > >"Does that make me a bridesmaid?" > Yo Morgan, since all of us are god and were making the world out of thoughts, you are that which you choose to be. I perceive this Earth, and in fact the entire cosmos, is a venue where our ideas, beliefs, desires, attitudes and expectations precipitate into physical reality as objects and events. So we are, for practical purposes, figments of our own imagination here, and thus we are free to define ourselves in any way we choose. Of course the dogmas of limitation that are so strongly embraced in the conventional wisdom of common social consciousness, will vehemently contradict this suggestion. But as you have apparently looked long and deep into many mind-blowing fractals, you surely have evolved beyond the herd mentality to some extent. You see, I conceive of fractals as Cosmic Mandalas, objects of such hypnotic intricacy and beauty that they shall ultimately prove to be powerful tools in the service of expanding our consciousness and awakening us to our grander identity So lets get on with it and if were going to move so quickly into the new freedom of generating fractals of any dimensionality whatsoever, it seems important to have at least a small inventory of fundamental forms that can be utilized as references. An attempt to create a few of these follows. In the interest of uniformity, certain simplifications are employed that should help make the transition upwards from 2D to 3D to 4D and so forth an intuitive process. The first thing to do is to forget that imaginary numbers ever existed, or remember that they never existed; i.e., unimagine them if you will Thus the complex plane reverts to the Cartesian plane, and we have two axes, X and Y, both measured by real numbers. Let a point in the Cartesian plane be identified by x,y: Then the Mandelbrot set (M) can be generated by the following formula, where brackets indicate a subscript. a[1] = b[1] = 0 s[n] = a[n]^2 + b[n]^2, t[n] = 2*a[n] *b[n] a[n+1] = s[n] + x, b[n+1] = t[n] + y if sqrt(s[n]) < 2, then the point x,y is in M. Back to the familiar .frm form in a moment, but in order to see more clearly whats going on here, well take a quick refresher course in CP. CP in this context stands for cyclical permutation, and as an example take the sequential set of numbers 1 2 3 4. Call this configuration of these four numbers, c1. Now permute c1 cyclically to c2 = 2 3 4 1, then to c3 = 3 4 1 2 and again to c4 = 4 1 2 3. So it may be said of c2 that it is the operation permute the four numbers to the leftward one slot, and so c2^1 = c2, c2^2 = c3, c2^3 = c4 and c2^4 = c1. Hence, c2 is a 4th root of identity. As c3^2 = c1, then c3 is a 2nd root of identity. These four permutations form the order 4 cyclic group (C4). It is isomorphic (i.e., abstractly identical) to the complex number system: Thus c1 = 1, c2 = (0,1), c3 = -1 and c4 = (0,-1). There is much more exposition on these ideas at http://fibonacci-arrays.com/Triternions.pdf At any rate, the point being made here is that the complex number concept is not at all requisite to the process of generating fractals. In the following frm files, the default imaginary values for Y are changed by imag(pixel)*(0,-1) to real. CP4 (XAXIS){ x=real(pixel), y=imag(pixel)*(0,-1), a=b=0: a1=a^2+b^2, b1=2*a*b a=a1+x, b=b1+y z=sqrt(a^2 + b^2) z < 4 } There are other versions of C4, so this formula is called CP4 to identify it as being based on the group generated by the CP process. This file makes an interesting version of M. E.g., note that the inside orbits no longer exhibit any curvature. Moreover, certain color mappings make visible field lines that suggest extensive connections between M and its satellites and even (by single threads) to several points at infinity. Now take c1 = 1 2 3 4 5 6, c2 = 2 3 4 5 6 1 and etc. These form the order 6 cyclic group (C6), which comprises the roots c2^6 = c6^6 = c3^3 = c5^3 = c4^2 = c1. The formula that follows is based on this group. CP6 (XAXIS){ x=real(pixel),y=imag(pixel)*(0,-1),w=p1, a=b=c=0: a1=a^2-2*b*c b1=-c^2+2*a*b c1=b^2+2*c*a a=a1+x,b=b1+y,c=c1+w z=sqrt(a^2+b^2+c^2) z < 4 } Somehow, Fractint seems to have reserved z for comparison with the bailout value; any other symbol Ive tried distorts the set? The CP6 formula is a close cousin of TMan and TGirl, which are based on a variant of C6, and the familial resemblance is there. There are 58 other variations of C6 that should also generate images, but suffice it to say that, in constructing formulas for many of these, complications mat ensue... On to C8, where c2^8=c4^8=c6^8=c8^8=c3^4=c7^4=c5^2=c1 CP8 (XAXIS){ x=real(pixel),y=imag(pixel)*(0,1),v=p1,w=p2 a=b=c=d=0: a1=a^2-c^2-2*b*d b1=2*a*b-2*c*d c1=2*a*c+b^2-d^2 d1=2*a*d+2*b*c a=a1+x,b=b1+y,c=c1+v,d=d1+w z=sqrt(a^2+b^2+c^2+d^2) z < 4 } There are many, many possible basic variations here, perhaps even thousands. Some interesting results can come of just changing a few signs In closing, well look at C10: c2^10=c4^10=c8^10=c10^10=c3^5=c5^5= c7^5=c9^5=c6^2=c1. Cp10 (XAXIS){ x=real(pixel), y=imag(pixel)*(0,-1), u=p1, v=p2, w=p3 a=b=c=d=e=0: a1=a^2-2*b*e-2*c*d b1=-d^2+2*a*b-2*c*e c1=b^2+2*a*c-2*d*e d1=-e^2+2*a*d+2*b*c e1=c^2+2*a*e+2*b*d a=a1+x,b=b1+y,c=c1+u,d=d1+v,e=e1+w z=sqrt(a^2+b^2+c^2+d^2+e^2) z < 4 } It should be clear from these patterns that imaginary/complex numbers are not inherent to fractals per se. To reintroduce them into any of these formulas, particularly into systems such as CP6 and CP10, where 4th order roots are not already presently, creates a bit of havoc but hey, havoc and chaos may complement one another nicely, e.g., as in Lee Skinners renditions of Jim Muths TMan1. BTW, some of these, such as Fig Tree, are to my eye reminiscent of Japanese watercolors, an impression that fractals dont often convey. Peace, Russell _________________________________________________________________ STOP MORE SPAM with the new MSN 8 and get 2 months FREE* http://join.msn.com/?page=features/junkmail

2 1

Minibrot Chaos
by Raymond Filiatreault 28 Jan '03

28 Jan '03

Occasionally I like to search for interesting minibrots, although I rarely find nice ones such as some of Jim's FOTDs. Recently, I found one which is most unusual. Certainly not in the sense of being nice from an artistic point of view, but because the entire inside of the minibrot was escaping (with no inside fill) as if it was a window opening on another part of the parent fractal. Inside that "window", I even found another part with all the framing of a minibrot but again seemingly opening up on the parent fractal. I was thus wondering if anybody had such experience before. I was using the HyperMandel formula and the parameters were random ones generated by Fractint's evolver. The following .par file is for the higher zoom "minibrot". By zooming out, you can then find the inside of the parent minibrot (turn the logmap OFF if necessary). Numerous other similar minibrots can be found on the filaments of that parent minibrot. Raymond MiniChaos1 { ; Raymond Jan/03 ; Version 2002 Patchlevel 4 reset=2002 type=formula formulafile=fractint.frm formulaname=hypermandel center-mag=+0.31055536680379110/+0.16071949514401270/1.28043\ e+009 params=-0.4605548265022736/-0.05972472304452651 float=y maxiter=2000 inside=0 logmap=585 sound=off colors=000IfmIciH`eGXa<3>CHKBDFABAKEB<3>bTFfWGjZGn`HqcIteIvg\ JxhJyiJziJzjJziJyiJxhJvgIteHqcG<2>fWDbTCYPAUM9PI7EE6FF5<3>GU\ BHYCH`EIcFIfG<2>JmJJoJJpKJqKJrLJrL<2>JpKJoKImKIkK<3>E`IDYHCU\ HBQGAMG8FF7FF8GJ<3>FJaHKeILi<3>NNuONwPOxPOyPOzPOz<2>POxONwON\ u<3>LKiKJeJIa<3>EEJCCFHIJ<3>XZ`_bdcfhfik<2>mrtotvquxrwyswzsx\ zsxzswyrwxquwotu<2>ilmfijcff_bc<3>LNNHIIFED<3>YIRaJUeKXiKZmL\ apMcsMeuNgwNhyNizOizOizOjzOi<2>uNfsMdpLbmK`iJYeJVaHSYGPTFLOE\ IKDDFEE<3>WUL_YMcaNgdPjhQnkR<2>urTwtUyuVzvVzvVzwVzvVzvVyuUwt\ U<2>qmRnkQjhP<3>WUKSQJOMHJIFFEE<3>YGGaGHeGHiHImHIpHI<2>wIJyI\ JzIJ<2>zIJyIJwIJuHJsHIpHI<3>aFGYFFTEFOEEKDDDDDDHKELOFPTGTYHX\ a<2>IfmJipJksKnuKowKqyKqzKrzLrzLqzKqyKowKnuJksJip } frm:HyperMandel {; Chris Green. ; A four dimensional version of the mandelbrot set. ; Use P1 to select which two-dimensional plane of the ; four dimensional set you wish to examine. ; Use floating point. a=(0,0),b=(0,0): z=z+1 anew=sqr(a)-sqr(b)+pixel b=2.0*a*b+p1 a=anew |a|+|b| <= 4 } _________________________________________________________________ The new MSN 8: advanced junk mail protection and 2 months FREE* http://join.msn.com/?page=features/junkmail

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Get me going...
by Charles Druesedow 27 Jan '03

27 Jan '03

1 0

FOTD 27-01-03 (Fractal Geometry [7])
by Jim Muth 27 Jan '03

27 Jan '03

FOTD -- January 27, 2003 (Rating 7) Fractal visionaries and enthusiasts: Today's pale, green-and-lilac image rates a 7. Only its somewhat washed-out appearance prevents a higher rating. I named it "Fractal Geometry" when I noticed the unusually regular geometric pattern of filaments surrounding the central midget, which in today's image takes second place to its surroundings. This pattern looks surprisingly like the arrangement of seeds in a sunflower, and can be brought out even more clearly with other color palettes. The parent fractal is a vaguely Mandel-shaped open-area, narrow on the east and filled with chains of debris. Some of this debris extends in a broad filamentary loop into the solid material west of the open area. Today's scene is located in a sub-loop on this loop. The parent came about when I subtracted 47 parts of minus- epsilon from 47 parts of minus-pi and added 1/C. The scene I found in the parent is fair enough in its normal version, but unlike yesterday's image, it is even better in its evaporated version, which, made visible by the bof61 inside fill, was used as today's FOTD. The render time of 2 minutes is a bargain for such a highly- rated image. Those who are not impressed by bargains may download the completed image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather started good enough here at Fractal Central on Sunday, with sun and a temperature just about freezing. But in the afternoon, clouds moved in and a brief but heavy snow shower passed over, ending the cats' chances of a pleasant time outdoors. They satisfied themselves eating and keeping warm. Today is starting much colder, making it unlikely they will have any time at all outdoors. For me it's another work day, and not surprisingly, I already have some work on the shelf. So until next time, take care, and brace yourselves for the imminent release of the FOTD CD. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Geometry { ; time=0:02:00.34--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-1.51658971637141400/-0.274992933413616\ 80/1.305493e+010/1/112.5/4.03474752740523579e-005 params=-47/-2.71828182845905/47/-3.14159265358979/\ 0/1e+100 float=y maxiter=1200 inside=bof61 periodicity=10 colors=000fG7gD7cJ6_P6XV6T`6Pf6Ml6Ir6Fw6Et9DrCCpEB\ nHBlKAjM9hP8fS7dU7bX6`_5Za4Xd4Vf7Wd9QcBXaDZ`G_ZI`Y\ KaWMaVOZTQWqSIbKNZklpjkpstzzzzXYeVMdTAcMKQPTMIa8G_\ AFYCEXEDVFCUHBSJARL9PM8OO7MQ6LR9NOBOMEPJGQHJRFLTCO\ UAQV8TW5VX3XY1aS7fMDkHIpBOu5Uz0Z2FqMPseYuyfvmdlbcc\ RbUGaL5`CXdcheZteUpdVmcWicXfbYbbZ_a_Xa`T`aQ_bM_cJZ\ dFZeCYf9Yf3_e5Zf7Yf9XfBXgDWgFVgHVgJUhLThNShPSiRRiT\ QiUQiSSgQUeOWcNXaLZ_J`YHbWGcUEeSCgQAiO9jM7lK5nI4oG\ 5mF5lF5kE5iE5hE5gD5fD6dC6cC6bC6aB6_B6ZA6YA6XA5VB5U\ B5TC4SC4RC4QD4PD3ND3ME3LE2KE2JF2IF2HF5O98V3AX5BZ6D\ _7Ea8Gb9HdAJfBKgCMiDNjEPlFQmGPiHOeINaJNZKMVLLRMKNN\ KKOQMSVNV_OYdP`iRdnSgsTjxUmsWkoYjk_ig`hcbgZdfVfeRg\ dNicJkbFlaMibTfc_dcfadl_dmZamZZnYWnYToXQoXNpWKpWHq\ VEqVBrU8rU5rU3dfGSsSRrTQqUPqVPpVOpWNoXMoYMnYLnZKm_\ Km_LoXLpVMqTMrRNsPNtNNuLOvJOwHPxFPyDPzBRvASrAUoAVk\ 9Wh9Yd9Za9_Y8aU8bR8cN7eK7 } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 26-01-03 (Un-Named [3])
by JimMuth＠aol.com 26 Jan '03

26 Jan '03

FOTD -- January 26, 2003 (Rating 3) Fractal visionaries and enthusiasts: Today's image has no name. I studied it for several minutes, trying to find a name for such an unfocused image that rates a lowly 3, but came up with nothing. At one time I thought I saw a design for the cover of a hypothetical vampire novel, and considered naming the image "Dracula". Then I thought I would name it after one of those large but less repulsive fruit bats that inhabit the tropical Asian regions. Since the image has a metallic sheen about it, I also considered several metallic names. Then I remembered the invisible midget at the center, and considered a name such as "Enigma". But ultimately, all the potential names proved unsatisfactory, and I let the picture remain without a name. The generating formula takes Z^(-17), adds 10 times as much Z^(-1.7), then adds (1/C). The rendering was done with the outside set to < atan >, which is not one of my favorite options, though in this case, it works better than the basic equal-iteration bands. (I also tried evaporating the image, but found that this gives little more than chaos.) The render time of 18 minutes is a bit excessive for such a lowly image. But relief can be found on the WWW, which hope- fully is recovering from the latest hack attack. The completed GIF image can be accessed at Paul's site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather was milder on Saturday, but still rather cold, with a high temperature of 34F 1C. Since no one was at home most of the day, the cats passed the time sleeping by the heat. When we arrived at the door later in the evening, a loud scolding was heard from the inside. It was Thomas, who was irate because he had not been fed all afternoon. Today is a bit milder yet, and no unnecessary shopping trips are planned, so the dynamic duo should have a much-improved day. Until next FOTD, which will appear in 23 hours or so, take care, and go with the flow, never forgetting that those who make no waves accomplish nothing. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ An_UnNamed_Fractal { ; time=0:18:03.95--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.204807016015608/-0.01223600675442206\ /1.486447e+009/1/162.5/-1.62304540859345425e-005 params=10/-1.7/1/-17/0/525 float=y maxiter=1200 inside=0 outside=atan periodicity=10 colors=000KIJLIJLIJLHKMHKMHKNHKNHLOHLOHLNFKOGLOHLP\ HMPIMQJNQJNQKNRKORLOSMPSMPSNPTOQTOQUPRUPRVQSVRSVRS\ WSTWSTXTUXUUXUUYVVYWVZWWZXW_XX_YX_ZX`ZY`_Ya_Za`Zaa\ Zba_bb_cc`cc`ddaddadeaefbefbfgcfgcfhcgidgidhjehkei\ kfilfilfjmgjngknhkohlrimrjkohikfggdecbc_`aWZ_SXYOV\ XKSWLTWLTWLTWLTVLTVLTVMTVMTVMTUMTUMTUMTUNUTNUTNUTN\ UTNUTNUSOUSOUSOUSOUROUROURPVRPVRPVQPVQPVQPVQQVQQVP\ QVPQVPQVPQVORWORWORWORWORWNRWNSWNSWNSWMSWMSWMSWMTX\ MTXLTXLTXLTXLTXKUXKUXKUXKUXKUXJUXJVYJVYJVYJVYIVYIV\ YIWYIWYHWYHWYHWYHWYHXZGXZGXZGXZGXZFXZFYZFYZFYZFYZE\ YZEYZEZ_EZ_DZ_DZ_DZ_DZ_D__C__C__C__C__B`ZC__D__E__\ F__GZ`HZ`IZ`JZ`KZ`LYaMYaNYaOYaPYaQXbRXbSXbTXbTXbUW\ cVWcWWcXWcYVdZVd_Vd`VdaVdbUecUedUeeUefUegTfhTfiTfj\ TflUemVdjTffQhcOk_LmWIoTGrPDtLAvG8zI8xJ8vL8uM8sN8r\ P8pQ8oS8mT8kU8jW8hX8gZ8e_8d`8bb8`c8_e8Yf8Xg8Vi8Uj8\ Sl8Qm8Pn8Np8Mq8Kr8Jq9Kq9K } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 25-01-03 (Spinning Off [5-1/2])
by Jim Muth 25 Jan '03

25 Jan '03

FOTD -- January 25, 2003 (Rating 5-1/2) Fractal visionaries and enthusiasts: In this world of multiplying triternion formulae, there is still room for the MandelbrotMix4. Today, this workhorse formula carries us to the virtual world that pops into existence when various portions of Z^(-1.618) and Z^(-11.48) are combined and (1/C) is added. This entire world is an oversized, fragmented fractal that is indescribable in shape, but has a small open area with numerous Mandeloid features. Today's scene is located in a sub-spiral of a spiral in the center of a feature that resembles a multiple Seahorse Valley more than anything else. I named the image "Spinning Off" because with its coppery fringes it reminds me of an old computer animation. (Is there any such thing as an *old* computer animation?) The original animation was of a spinning disk which disintegrates into coppery fractal dust as it spins. Upon seeing the final result of the day's effort, I stepped back and said, "this one deserves a rating of 6." Then I stepped a bit farther back and decided that the image rates only a 5. I finally decided on the rating of 5-1/2, which is infinitesimally above average. Today's image also can be evaporated and colored with the bof61 inside fill, but doing so results in a fractal a bit too chaotic to be a FOTD. The render time of 33 minutes is admittedly a bit excessive, but fractal salvation is at hand, for the completed GIF image may be downloaded from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather remained below freezing all day Friday, while the fractal cats remained by the heat sources all day. A tempera- ture of 30F -1C is too cold for fractal whiskers. The duo finally came to life in the evening, when their empty stomachs reminded them that food exists. Today is only slightly warmer, so I expect they will have a similar day. As for me, I will try to avoid an imminent shopping trip, most likely without success. Luckily, I have the patience to endure, and thoughts of fractals will carry me through. Until next FOTD, take care, and before we can find the answer, we must know the question. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Spinning_Off { ; time=0:33:53.28--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.34451506120471600/-0.107403741819450\ 00/5.433651e+011/1/155/-0.0660300637674467727 params=3.63/-1.618/5.94/-11.48/0/125 float=y maxiter=3600 inside=0 logmap=691 periodicity=10 colors=000UKfUIfTHeTFeSEdSCdRBcRAcUBeXBf_CgbCheDjh\ DkkElnEmmJkmOimTgmYembdnZfnWgoShoPioMjpIkpFlpCmlBj\ hAgdAda9bY8_U8XQ7UN6SJ6PF5MC5KODIZKHjRFzYEy_FxaGwc\ HveHugItiJskKrmKqoLpqMorMnqNmpOlpOkoPkoPjnQinQhmRh\ mRglSflSekTekTWhONaKEbF5YB6aA7cA8e99g9Aj8Bm8Cp7Ds7\ Ev6Ex6AaP6Lg25zB6rK7kT8da9YiARjCUkDXkEZlGamHdmIflL\ blNZkQVkSSkVOjXKj_HiaDid9if6fd5cb5``5YZ5WY5TW5QU5N\ S4KQ4IP4FN4CL49J46H44G4LJIaLWqNirMesLasKYtJUtJRuIN\ uHJvGFvGCnQRg_e`ht`Xo`Mk`BgWAZR9RM9JH8BC83EE7GKAIQ\ DKWHMaKOgNNlNQmQTnSWoVZpXaq_bv_cqadmcehefdgg`ihWki\ SmiLsiOniRiiUdiX`i_WibRieNihIpkDsr7nn9hkBgeDf`F_XG\ dZIoWK`TMbPNaMP`JR_GT_DU_EW_FY_G__Ha_Ic_Je_Jf_K`_L\ j_Mq_Nh_Oz_Pz_PsaUzcZmecjghgimdjrbgk_edXbaUNaHOaMP\ aRQaWVd__fbchehjilllqnouprnjkkkhhmeeobbq__sXYuUWwW\ UyXTzYRzZQz_Oz`NzaUzc`zdgzfnzguzhozbizXiz7czSYzMxz\ GrzHmzHhzHbzHYzHKz1Mz3Nz5 } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] Triternions, dimensions and orbits of configurations
by Jim Muth 25 Jan '03

25 Jan '03

At 09:38 PM 1/24/03 +0100, Jos Hendriks wrote: >Dear reader > >I have read most of the things about triternions. And rendered >some of the frms/pars. A lot of things are coming into my head. >Some of them I try to write down here. I hope I will get some >comment. <snipped> These latest two triternion formulas come the closest yet to the ideal triternion M-set, which would have no foreshortening and skewing. I have a short formula that draws very similar images with far less calculating. Unfortunately, I have never figured exactly what the formula does, but I have included two parameter files for comparison with the triternion formulas. Hyper1 { reset=2002 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot center-mag=0/0/0.666667 params=0/0/2/0/0.001/0 float=y maxiter=1200 inside=0 logmap=yes periodicity=0 colors=00000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzz\ zLzzz000555888BBBEEEHHHKKKOOOSSSWWW___ccchhhmmmsss\ zzz00zG0zV0zj0zz0zz0jz0Vz0Gz00zG0zV0zj0zz0jz0Vz0Gz\ 00z00zG0zV0zj0zz0jz0Vz0GzVVzbVzjVzrVzzVzzVrzVjzVbz\ VVzbVzjVzrVzzVrzVjzVbzVVzVVzbVzjVzrVzzVrzVjzVbzhhz\ lhzqhzuhzzhzzhuzhqzhlzhhzlhzqhzuhzzhuzhqzhlzhhzhhz\ lhzqhzuhzzhuzhqzhlz00S70SE0SL0SS0SS0LS0ES07S00S70S\ E0SL0SS0LS0ES07S00S00S70SE0SL0SS0LS0ES07SEESHESLES\ OESSESSEOSELSEHSEESHESLESOESSEOSELSEHSEESEESHESLES\ OESSEOSELSEHSKKSMKSOKSQKSSKSSKQSKOSKMSKKSMKSOKSQKS\ SKQSKOSKMSKKSKKSMKSOKSQKSSKQSKOSKMS00G40G80GC0GG0G\ G0CG08G04G00G40G80GC0GG0CG08G04G00G00G40G80GC0GG0C\ G08G04G88GA8GC8GE8GG8GG8EG8CG8AG88GA8GC8GE8GG8EG8C\ G8AG88G88GA8GC8GE8GG8EG8CG8AGBBGCBGDBGFBGGBGGBFGBD\ GBCGBBGCBGDBGFBGGBFGBDGBCGBBGBBGCBGDBGFBGGBFGBDGBC\ G000000000000000000000000 } Hyper2 { reset=2002 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot center-mag=0/0/0.666667 params=0/0/0/0/0.25/0.25 float=y maxiter=1200 inside=0 logmap=yes periodicity=0 colors=00000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzz\ zLzzz000555888BBBEEEHHHKKKOOOSSSWWW___ccchhhmmmsss\ zzz00zG0zV0zj0zz0zz0jz0Vz0Gz00zG0zV0zj0zz0jz0Vz0Gz\ 00z00zG0zV0zj0zz0jz0Vz0GzVVzbVzjVzrVzzVzzVrzVjzVbz\ VVzbVzjVzrVzzVrzVjzVbzVVzVVzbVzjVzrVzzVrzVjzVbzhhz\ lhzqhzuhzzhzzhuzhqzhlzhhzlhzqhzuhzzhuzhqzhlzhhzhhz\ lhzqhzuhzzhuzhqzhlz00S70SE0SL0SS0SS0LS0ES07S00S70S\ E0SL0SS0LS0ES07S00S00S70SE0SL0SS0LS0ES07SEESHESLES\ OESSESSEOSELSEHSEESHESLESOESSEOSELSEHSEESEESHESLES\ OESSEOSELSEHSKKSMKSOKSQKSSKSSKQSKOSKMSKKSMKSOKSQKS\ SKQSKOSKMSKKSKKSMKSOKSQKSSKQSKOSKMS00G40G80GC0GG0G\ G0CG08G04G00G40G80GC0GG0CG08G04G00G00G40G80GC0GG0C\ G08G04G88GA8GC8GE8GG8GG8EG8CG8AG88GA8GC8GE8GG8EG8C\ G8AG88G88GA8GC8GE8GG8EG8CG8AGBBGCBGDBGFBGGBGGBFGBD\ GBCGBBGCBGDBGFBGGBFGBDGBCGBBGBBGCBGDBGFBGGBFGBDGBC\ G000000000000000000000000 } frm:HyperMandelbrot {; periodicity must be turned off a=(p1),b=(0,0): q=sqr(a)-sqr(b)+pixel, b=(p2+2)*a*b+p3, a=q, |a|+|b| <= 100 }

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Fracternions
by Russell Walsmith 24 Jan '03

24 Jan '03

Im almost used to the routine by now, which is that every time I believe I have the Tset formula written down properly, I see a way to refine it. With this latest and last little lick though, I think it's done My first efforts to resolve the set in 2D, were mostly to demonstrate its existence, and hopefully inspire someone to render it in 3D. I used an HP SX48 calculator, and it was a simple matter to construct a program with the 3D vectors that are built-in. The skewed, truncated Msets that this method produced seemed a reasonable result, although not quite what Id hoped for. Then, a few weeks ago, Tim Wegner directed my attention to the Fractint list and the Morgan Owens formula posted on 12/11/02. At the time, I was still focused on a full 3D rendering, so I wasnt that excited about seeing a 2D set in Fractint. Besides, the Owens formula looked about right, but it produces images quite distinct from those on the HP, and I thus suspected that the Fractint parser wasnt up to the job. But just for drill I guess, I tweaked the formula to bring it a little closer to the HP version and voila the images Id found earlier were there. Well that must be right, I thought, reckoning that if one machine confirmed the other, how could it be otherwise but in a short while I saw that the imaginary value for c2 (which the HP's vectors had snuck in on me) was not appropriate in this case. The simple reason is that triternions are based on the order six cyclic group, and there are no 4th roots of unity in C6 (or for that matter, in the other order six group, D3). I saw that simply squaring c2 would rectify the imaginary term, and the images that this change produced were far more intricate and fun to work with. Moreover, Jim Muths flip of c1 produced a nice two-fold symmetry (and incidentally z1=t1-c1*c1 works well with that too), so it looked like wed arrived. Upon further reflection, however, it became clear that in c2*c2, the term also acts upon itself as a scalar, and that this disrupts its proportionality with c1. The proper solution then is c2*(0,1) or (better) c2=imag(pixel) *(0,1) in the definition line, to minimize calculations. There it is then: Weve watched the Tset go from embryo to fetus to now a newborn, and guess what Cuzzins, Its A Girl! You can go to p.12 of my paper, where shes posing for a picture, dressed all pretty in pink: http://fibonacci-arrays.com/Triternions.pdf Or you can render her yourself with TGirl { c1=real(pixel),c2=imag(pixel)*(0,-1),c3=p1 z1=z2=z3=0: t1=z1*z1+2*z2*z3, t2=z3*z3+2*z1*z2, t3=z2*z2+2*z3*z1 z1=t1+c1,z2=t2+c2,z3=t3+c3 z=z1+z2+z3 z < 64 } TGirl is easily persuaded to produce Julia sets: TJul { z1=real(pixel),z2=imag(pixel)*(0,1),z3=p3: t1=z1^p1+2*z2*z3, t2=z3^p1+2*z1*z2, t3=z2^p1+2*z3*z1 z1=t1+p1,z2=t2+p2,z3=t3+p3 z=z1*z2+z2*z3+z3*z1 z < 64 } Try, say, z1=-0.75 with z2 and/or z3 at or near 0.1. Looking forward to seeing where this goes Ciao, Russell _____________________________________________________________ Get 25MB, POP3, Spam Filtering with LYCOS MAIL PLUS for $19.95/year. http://login.mail.lycos.com/brandPage.shtml?pageId=plus&ref=lmtplus

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FOTD 24-01-03 (Without Reason [7])
by Jim Muth 24 Jan '03

24 Jan '03

FOTD -- January 24, 2003 (Rating 7) Fractal visionaries and enthusiasts: Having checked the Fractal Central e-mail box and actually read 3 of 53 pieces of junk, I wonder why so many spammers waste their time telling me that I am receiving the information I requested, when I have requested nothing, or pretending that they are secret admirers, or that I have been approved for something I do not want, or that I have signed up to receive such junk, when only a fool would sign up to receive spam. And if I have requested information or signed up to receive spam, why don't I remember doing it? Why must the spammers tell me something I should already know? But it is not all bad. Those computerized pseudo-personalized letters are particularly amusing. I always get a chuckle when I read something like, "hey jamth, you have been specially selected to receive a free password." Maybe I should create a new e-mail address with a particularly offensive name such as "stupidpigeon(a)******.com". Then the subject lines would read, "hey stupidpigeon, you can get rich quick." Why can't e-mailers just be honest and say something such as, "you are receiving this e-mail because your address was on a list of addresses we purchased"? If someone were to say this, and the product was worthwhile, I might actually consider doing business. But now, having sounded off about the spam, I have fractal business to attend to. I named today's image "Without Reason", though I can give no logical reason why I did it. It is another of my 'evaporated' images, showing the ghost of a fractal that once was there. I put a bit of extra energy into the coloring, which earns the image a rating of 7. Why do images evaporate when their generating formulae contain negative powers of Z? They do it because no points will reach infinity when the exponent of Z is negative. But the points will still jump around quite a bit within a limited range, and when the value of the bailout radius is reasonably low, they will temporarily pass beyond it, giving the program the signal that they have escaped permanently, and stopping calculation. When the bailout is excessive, no points will ever reach it in their travels, and will therefore be seen as trapped. The screen will appear flat, consisting entirely of trapped 'inside' points. The bof61 active inside fill option works quite well in today's image. It colors the trapped points according to which iteration comes closest to the origin, and therefore displays the wanderings of the trapped points. The resulting images can be quite impressive. The other active inside fills can also produce interesting images from a normally flat blank inside. The bof60 option colors trapped points according to how close they come to the origin, and produces bubble-like images. Many of the active inside fills have quirks that limit their usefulness, but they are all worth a try. Setting the logmap can be tricky with images that consist totally of inside points. One method is to bypass the problem by setting the logmap option to zero. Another method that works fairly well is to set the logmap to 1, create a totally black palette and give the 001 register a brilliant color. Then rotate the palette forward until the color first appears on the screen. When it does, note the number of the position where the colored register is located and set the logmap to this value. Unfortunately, this method fails when the colored register passes beyond position 128. The rating of 7 for today's image seems logical. It is above average, at least in my opinion. The render time of 12 minutes borders on the excessive. The download from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> is far more reasonable. Thursday was the coldest day in 5 years here at Fractal Central. And the snow showers and high winds didn't help at all. When the 14F -10C air touched the noses of the fractal cats, they turned around and headed straight for the warmest radiator they could find. They slept peacefully until the time arrived for their evening meal. There is not much cat action around F.C. in this kind of weather. It's a little warmer this morning, but still well below freezing. I suppose the duo will be housebound again today. Being housebound is my normal situation, but it most certainly does not mean idleness. Since the time for work has arrived, the time for the FOTD has come to an end. In 24 hours, the next FOTD will appear. Until then, take care, and be faithful to your fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Without_Reason { ; time=0:12:16.44--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.686817713361516/-0.6536317292615328/\ 9.601575e+009/1/-132.5/-5.15785767828125241e-006 params=11/-1.2/4.3/-6/0/1e+100 float=y maxiter=1200 inside=bof61 logmap=128 periodicity=10 colors=000OGRUGWMGNJGJHFLGEMFEODDPCEQBGSAIT8JU7LW6\ MX4MY3M_4N`6Oa8PbAObCN`EM`GLYIKVJJSKIPLHMMGKNFKOEK\ PDKQCKRCKSDHUFHWHHYJH_KHaMHcOHeQHhRHmTHrVHwXHyYHz_\ HzaHzcHzdHzbKyaNx_PxZSxYUyWXyV_yTaySdyRfzPizOlzMnz\ LqzKsxNqvQptTorVnpYmn`llcjjeihhhfkgdlfcmeXo_RmVKkQ\ EiLHgJKeHNcFPaDS_BVY9YW7_W6RUCIUI9TNDSQGRSJQUNOWQP\ YTQ`WRb_TdbUfeVhhWjaYdWZ_Q_UJaPDbJ7cEFcFNcFVcGbcGe\ cKgcNicQkcUmcXoc_pcaqcbrccscdtbeuZfuVgvRhwNixJjyFk\ zBlz7mwBkuEirHgpKfnNdkRbiU`fX_d_YbbW_fUYeTVdRTcPRc\ OQcRQcUPcXPc_OcbObeN`hNYkMUnMSqLPtLMwLKzKMvJNsJOoI\ PlIRhHSeHTaGUZFVVFXSEYOEZLD_HD`EEXKEZ69X0DW4GV8JUB\ MUFQTITSMWSPZRTaQXeP_hPckOfnNjqNmoMlmLlkKljJlhIlfH\ leGlcFlaEk`DkZCkXBkWAkU9kS8kR7kS8eS9`SAVSAQSBKSCFS\ D9SD4XE7`E9eFBiFDmGFrGHvHJzHLrQKjZKbfKefJhgHkhFniD\ qjBsjAtgLudWubfsdcrf`qgYpiWojTnlQmmOloLkpIjrGisDhu\ Agv8doJahU_bdXWoeGfaGbYGZ } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] Triternions
by Russell Walsmith 24 Jan '03

24 Jan '03

-- On Tue, 21 Jan 2003 16:36:20 Morgan L. Owens wrote: >...though I still say TMan and TJul need a little prophylactic code to stop them from spilling out into six dimensions - unless that's desirable; mainly from the line z=z1+z2+z3. Right on, Morgan, you da Man! That statement and your Hilbert space reference of a while back helped me recall that a metric space of n dimensions is defined when (a^2+b^2+...n^2)^.5 measures the distance from a point in that space to the orgin. Clearly, the appropriate statement is z=(z1^2+z2^2+z3^2)^.5 I tried this in the formulas and it sharpens the images nicely... so much so that the so-called 'TGirl' now looks more like the TMan in drag... (Hey, we knew from the git-go that he might be different...) What to do? I guess we can't very well call him/her/it 'TIt', so it's back to TMan (XAXIS) { c1=real(pixel),c2=imag(pixel)*(0,1),c3=p1 z1=z2=z3=0: t1=z1*z1+2*z2*z3 t2=z3*z3+2*z1*z2 t3=z2*z2+2*z3*z1 z1=t1+c1,z2=t2+c2,z3=t3+c3 z=(z1^2+z2^2+z3^2)^.5 z < 16 } TJul (XAXIS) {;Try z1=-0.75 z1=real(pixel),z2=imag(pixel)*(0,1),z3=p3: t1=z1*z1+2*z2*z3 t2=z3*z3+2*z1*z2 t3=z2*z2+2*z3*z1 z1=t1+p1,z2=t2+p2,z3=t3+p3 z=(z1^2+z2^2+z3^2)^.5 z < 64 } Since you've already summoned the Dobiasovsky genie, Morgan, maybe you can wish him on to these formulas too... BTW, I don't mean to diss your D3Man when I tell you this (he was, after all, a sort of midwife/godfather to TMan), but he's not really based on D3. The reason is that D3, and in fact a dihedral group of any order, is non-Abelian: Therefore, for some term(s) in the number triplet, say j, the outcome of j^2 will not be equal to -j^2. A fractal formula based on D3 will thus require conditional statements in the initialization line... Now at the risk of being reviled by the list members (big deal...), I must admit that I've actually been using Winfract for most of the past 10 years. Indeed, it's only been within the last year or so that I even installed a real DOS version of Fractint, within just the past few months that I've tried diligently to work with it, and within this latest week bygone that I find a bit of a feel for it at last. There are still things I like about Winfract; e.g., with an frm file in a small window, the alt/tab toggle puts it over the image for editing. But every time I ever tried to load an imported par file, this relatively liteweight program simply choked. Eventually I despaired of the effort, flat gave it up. But in this venue (the List), par files fly around like cards at a poker table and if you can't read 'em, Maynerd, it's really hard to stay in the game. So far, in Fractint, I've actually gotten these files to render, but in Lee Skinner's "Fiery Pit' for example, the evidently crucial color info was lost in the shuffle somehow. In general, the process is still far from intuitive... Suggestions anyone? Thanks, Russ _____________________________________________________________ Get 25MB, POP3, Spam Filtering with LYCOS MAIL PLUS for $19.95/year. http://login.mail.lycos.com/brandPage.shtml?pageId=plus&ref=lmtplus

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FOTD 23-01-03 (Somber Planet [7])
by Jim Muth 24 Jan '03

24 Jan '03

FOTD -- January 23, 2003 (Rating 7) Fractal visionaries and enthusiasts: The plethora of triternion formulas from various sources continues to increase, though I have yet to see one that draws a perfect M-set as its 0,0 default, as intuition suggests it should. Since posting variation number one of the original formula, I have made four more variations. Today's variation, number five, draws a reasonably perfect default M-set, yet still creates the criss-crossing elements that make these formulae so interesting. I have named today's image, which resembles a nighttime scene at the edge of a fantastic forest on some dreary planet "Somber Planet". The coloring is perhaps the darkest and most somber of any FOTD image, so dark in fact that the image is best viewed in subdued light. Even the reddish clouds in the distance, about to be illuminated by a rising sun, are somber. The rating of 7 is based on the curious resemblance of the image to an actual scene on another planet. A brighter color palette might have earned it a higher rating, but being the type of person who enjoys less-cheerful things such as slow, solemn funeral music, I stuck with the dreary blue tones. The render time of 4-1/2 minutes is not too dreary, but dreary enough to make the download a better choice. The download may be found on the W.W.Web at Paul's site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Unusual cold settled into the Fractal Central area on Wednesday, chilling the cats' whiskers thoroughly. With their whiskers chilled by the 20F -7C temperature when I opened the door, the fractal cats didn't even think of going out. They passed the day huddled thankfully by the heat, behaving like little cat angels. Today will be even colder, so I expect a repeat. My day will also be spent indoors, working rather than sleeping. And when the work is done, I shall take a trip to Fractal Land. Until tomorrow at about this same time, take care, and unless I am mistaken, cat's whiskers were once a part of simple radios. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Somber_Planet { ; time=0:04:26.83--SF5 on a P200 reset=2002 type=formula formulafile=triter.frm formulaname=tman5 passes=1 center-mag=-0.663490902\ 33551570/+0.47769924811431790/22426.46/0.1228/-46.\ 3/-56.3053693362961667 params=0.1/0.15 float=y maxiter=1600 inside=0 logmap=122 periodicity=0 colors=000F0TG0UH0VI0WJ0XK0YL0ZM0_N0`O0aP0bQ0cP0eO\ 0dN0cM0bL0bK0aJ0`I0_H0_G0ZF0XE0VD0UC0SB0QA0PA0PA0O\ A0NG0MH0MH0LH0KH0JH0JH0IH1HH2GH3GH4FH5EH6DH7DH8CH9\ BH8AH6AH59H48H26H37H38H48H49H5AH5AH5BH6CH6CH7DH7EH\ 8JH8FH8QH9QH9RHASHASHKTHNTHOUHCWHHWHQYHKZNQ_OP`HEY\ OPYPO_PN`QJ`QOaQQbHHbHMcHIdHJdHJeGIdHJaHJZHJWHJTHJ\ SHJRIKQIKPIKOIKOIKNIKMJLLJLKJLJJLIJLHJLGKMGLMFMMEO\ MDQMCSMBVNAXN9ZN8`N8bN7dN6gO5XO4WO3VO2UO1TO0SO0RM8\ QKGOINMHVKFzIDz4Dz3Cz3Cz3Cy3Cx3Cw3Cv3Bu3Bz3Bz3Bz3B\ z3Bz3Az3Az3Az3Az3Az3Az39z39y39x39w39v39u38u38t38t3\ 8s38s38r37r37r37r37r37r37r36r36r36r36r36r36r35r35r\ 35r35r35r35r34r34r34r34r34r34r33r33r33r33r33r20r32\ r33r34r45r46r47r58r59r5Ar6Br6Cr6Dr7Er7Fr7Gr8Hr8Ir8\ Jr8Kr9Lr9Mr9NrAOrAPrAQrBRrBSrBTrCUrCVrCWrDXrDYrDZr\ E_rE`rEarEbrFcrFdrFerGfrGgrGkrGkrGkrGkrGlrGlrGlrGl\ rGlrGlrGlrGlrGlrGlrGlrGlr } frm:TMan5 { c1=real(pixel),c2=imag(pixel),c3=p1 z1=z2=z3=0: t1=z1*z1+2*z2*z3 t2=z3*z3+2*z1*z2 t3=z2*z2+2*z3*z1 z1=t1+c1,z2=t2-c2*c2,z3=t3+c3 z=z1-z2+z3 |z| < 8 } END 20.0 PAR-FORMULA FILE==================================

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Testing, testing...
by Russ Walsmith 23 Jan '03

23 Jan '03

Thanks for the advice on the colormaps thing, y'all... much better now, and I appreciate having more insight into the process. The next little anomaly to deal with is the fact that all of my previous letters tend to sprawl all over the page in the archived versions. I didn't see where I had any options to choose from in Mailcity that might affect this result, so I'm using Hotmail for this attempt... Ciao, Russ _________________________________________________________________ The new MSN 8: advanced junk mail protection and 2 months FREE* http://join.msn.com/?page=features/junkmail

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Re: [Fractint] Triternions
by Russell Walsmith 23 Jan '03

23 Jan '03

On Wed, 22 Jan 2003 13:48:31 Lee H. Skinner wrote: >Hi Russ, I don't understand. Were you not able to generate the images from the pars which contain the colors without need of a colormap? Or, if you want, I can e-mail you my completed 1600x1200 images privately to your e-mail address? Lee, When I try to run any of the last five par files that you've posted, I get an error message, "Oops. I couldn't understand the argument: Color=000LBU... Where the color string is whatever was supplied in the par. I'm running version 20.0 of Fractint. The image then renders with the default map. I suppose, if nothing else, you could send me the .map file, which I could then select for the rendered image, but I'd like to be able to go with what I've got; i.e., maybe the color info is just somehow slightly corrupted, and I can perhaps tweak it back into usefulness...? But hey, you could also send an image so that I know I'm trying to accomplish. Just the Cave, if you will, so that my mailbox doesn't overflow. Thanks, Russ _____________________________________________________________ Get 25MB, POP3, Spam Filtering with LYCOS MAIL PLUS for $19.95/year. http://login.mail.lycos.com/brandPage.shtml?pageId=plus&ref=lmtplus

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Triternions
by Russell Walsmith 23 Jan '03

23 Jan '03

Hola, Fellow Phractophiles, There was a brief murmur of interest in triternions when Tim Wegner broached the subject on 12/9/02, which was about as much as the concept, then embryonic, warranted at the time. Its evolved some since then, and the Tsets now offer more opportunity for exploration; so I thought I put the latest formulas out there and see what happens next. TMan { c1=real(pixel),c2=imag(pixel),c3=p1 z1=z2=z3=0: t1=z1*z1+2*z2*z3 t2=z3*z3+2*z1*z2 t3=z2*z2+2*z3*z1 z1=t1+c1,z2=t2-c2*c2,z3=t3+c3 z=z1+z2+z3 |z| < 8 } There is, I believe, a rather nice rendition of this set on page 12 of http://fibonacci-arrays.com/Triternions.pdf The formula is a 2-D slice (in the X,Y plane) of a 3-D object at whatever value is chosen for p1. In appendix #2 of the paper, some variations are explored. Ive also noticed that sign changes may have nice effects. E.g., z1=-t1+c1,z2=t2+c2*c2,z3=t3+c3, t3=-z2*z2+2*z3*z1, and so forth. It seems a bit challenging to define a Julia set version of the TMan; Maybe someone can see a way to go with that. I'm looking forward, eventually, to seeing these objects in full-on 3-D. Ciao, Russell Russ Walsmith russw(a)lycos.com _____________________________________________________________ Get 25MB, POP3, Spam Filtering with LYCOS MAIL PLUS for $19.95/year. http://login.mail.lycos.com/brandPage.shtml?pageId=plus&ref=lmtplus

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Running fractint
by Fr. Jim Lacasse 23 Jan '03

23 Jan '03

This may be a question answered many time, however, when Jim Muth and/or others put the long set of parameters for the given fractal at the bottom of their posting, Where or how is that to be entered into Fractint so I can make and or explore the same fractal. Thanks Jim LaCasse

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Re: [Fractint] Triternions
by Russell Walsmith 22 Jan '03

22 Jan '03

-- On Wed, 22 Jan 2003 10:27:11 Lee H. Skinner wrote: >Hi Russell, Morgan, et al, I would like to request whenever anyone makes revisions or improvements to a formula, that a revision number be included in the formula name. Otherwise there may be confusion among the list members as to which version to use in any posted pars. Sounds like a reasonable course of action, Lee. If you are to send me the colormap or whatever other info I need in order to behold 'The Cave of the Fire Pit' in all of its blazing glory (wait... throw in the 'Fractal Forest too...) then I guess I will be persuaded to your cause. Thanks, Russ russw(a)lycos.com _____________________________________________________________ Get 25MB, POP3, Spam Filtering with LYCOS MAIL PLUS for $19.95/year. http://login.mail.lycos.com/brandPage.shtml?pageId=plus&ref=lmtplus

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FOTD 22-01-03 (Antibrot [6])
by JimMuth＠aol.com 22 Jan '03

22 Jan '03

FOTD -- January 22, 2003 (Rating 6) Fractal visionaries and enthusiasts: Today's image is named "Antibrot". I named it when I noticed the almost-Mandelbrot shapes surrounding the obvious Mandelbrot shape at the center. It is another of my evaporated scenes consisting totally of trapped inside points made visible by the < fmod > inside option. The scene was created by combining Z^(-0.7), Z^(-6.4) and (1/C). The rating of a 6 might be a bit generous for an image that uses so few colors of the palette, but those colors create a good impression of fractal objects floating in space, so the rating could be considered appropriate. The render time of 59 minutes is quite slow. The download from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> A fresh dusting of snow and a temperature of 26F -3C kept the dynamic fractal cats confined to the indoors all day Tuesday. But they endured their hardship intrepidly, and slept most of the time by the heat. Today is starting sunny but even colder. I hope they can maintain their intrepidness. As for me, I'm ready to have an intrepid day at the work desk. When I finish, I'll take a trip to Fractal Land. The best thing I find there will appear as tomorrow's FOTD. Until then, take care, and when drowning, strap on a fractal. They weigh almost nothing and will keep you afloat indefinitely. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Anti_Mandelbrot { ; time=0:59:10.93--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=t center-mag=+1.7148895301837/-0.0375140875302/29702\ .9/1/57.5/-2.1386011017643369e-010 params=0.6/-0.7\ /0.7/-6.4/0/1e+100 float=y maxiter=1800 inside=fmod proximity=0.45 logmap=yes periodicity=10 colors=000Kgj`UWCjbXVUF7FKyoWidfVV4GITGKhJJkIKmHKo\ GLQySXmQcbOjRMRl0dWBk9maLhcSfdZcfeahlZisXai`V`dOSh\ GIl99p20s43p66m88jABgCEdEGaFJ_HLXJOULRRNTOPWLQYJZS\ KhMLS28d9F9NLnOooMgpK_qISoQRpNPpLOqIMUmhJjj8hkBmjE\ riHwhAV`lmhqn_uoRypJCyIDoWEeiFXvpaNhOIqUMqNLfRlJvz\ ``efXViSSlOQoKNmaYoUTpNP7VGMhnU`faU_iNSD0wVHQfGNcZ\ ZeQEgujl`Y6EsIFjUFaeGTXOS`9aiDTbPbjKUT3tIz9RnC_bFh\ RIlw`nlXoaTpRPQkrSDqdF`7TeJP_VMVfJQebQpKlNqubZbDo8\ RcDdSHneLoZLpTLqMLMHwaGcKkX`WR7tGNfIbTKC8yNAnXCdgE\ VW`jfQYaCaEFbjShlPbnMXpJRKpa`YT2k3SWC0y5YL3bJ8gICl\ HH`9QeBOiDNmFMOH6YGBgGGUcDeSHLi0aVBNzwYjjgVYehbiZX\ mPRY8YgCRzmUz_RqMOA7A`ADpCGhEJcxaglXjaTnRPMX58f_qQ\ e3oRky_miVoVQ1k3Fc8SWCdOH1lxSWd7kLVWL_avS6idBXQyx_\ ijhVYptiqf`qTT0IbRHUm_geZGiSImMKNpZVfVbYSjPO4gyMSr\ aMawe_uXVsOQSUk`PbiKUtzerbVcHGE13S69dBFgzZ7ozknQnX\ NfejjXanOT4epJ8G`CJpnh3us } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Re: [fractint] FOTD 19-01-03 (Maximum Spirals [5])
by Lee H. Skinner 22 Jan '03

22 Jan '03

The TMan1 formula can really produce some incredible images. Here's one deep in the parent of Jim's FOTD of Maximum Spirals. I think it's one of the most beautiful images that I've ever created, but well worth the wait to calculate at the highest resolution you can. It reminds me of some of the images I created with the Carr2821 PHC formula, but the TMan1 formula is not a PHC formula. 60119015 { ; Fractal Forest t= 0:40:10.96 ; on a P4 2Gh at 1600x1200 Jan 21, 2003 22:06:37 ; Image Copyright 2003 by Lee H. Skinner ver=2002 ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=fractint.frm formulaname=tman1 passes=1 center-mag=-0.00595484452179773/+0.74507406570897650/2.889005e+008/1/-44\ .9999986561148546/-1.7144370605542969e-006 params=0/0 float=y maxiter=4200 inside=0 symmetry=none periodicity=0 colors=000ah0<3>`g0`f0`f0<31>DSCDRDCRDBQEAQE9PF<5>CNBDMBDMA<3>GK9HK9JJ9<\ 22>j73l63m63<2>q42r42r72<3>tM1uP1uT1vW1v_1wc0<4>xmPxoUxqZ<2>ywmzzsyzs<12\ >_pvYpvWov<2>QmwOlwOlu<17>MiGMiEMiC<2>Mi5Lh2Mh3<24>prkqrmssn<2>vttxuvxuv\ yvv<6>ypSyoNynJ<2>yk5zj0xh0<8>ZP1XN2UK2<3>IB3<38>`g1 } frm:TMan1 { c1=flip(real(pixel)),c2=imag(pixel),c3=p1 z1=z2=z3=0: t1=z1*z1+2*z2*z3 t2=z3*z3+2*z1*z2 t3=z2*z2+2*z3*z1 z1=t1+c1,z2=t2-c2*c2,z3=t3+c3 z=z1+z2+z3 |z| < 8 }

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Re: Fractint digest, Vol 1 #368 - 7 msgs
by JackOTradez 21 Jan '03

21 Jan '03

In recent fractint mailing lists there were postings about the TMan1 (Russ Wallsmith, tweaked by Jim Muth), and Sylvie Gallet's "rising lake" effect. I have figured how to animate them both; they are currently rendering right now and should be posted on my site in a few days or so. They look 2B seriously cool. Lee Skinner also posted 4 PAR formulas in the last mailing, one of them, "Cave of the Fire Pit" is awesome! If you didn't check it out, do it! I rendered it at 1600x1200, printed out a hardcopy, and hung it up on my wall - I don't often do that. I really see a view from the air of a shallow Carribean sea dotted with little islands. In the middle is a gaping black hole, as if an asteroid had just impacted, with a definite 3D appearance and a wall/cliff (tidal wave?) next to it. And fire spewing out of it like there would be. Now if I could animate the fire w/o affecting the rest of it ... ...

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FOTD 21-01-03 (Sub-Marine Scene [6])
by Jim Muth 21 Jan '03

21 Jan '03

FOTD -- January 21, 2003 (Rating 6) Fractal visionaries and enthusiasts: As the extended fractional value of the real p1 and p2 para- meters of today's image shows, the coefficients were found by Fractint's evolver feature, the robot fractal explorer that can go intrepidly where men would dare not venture. The exponents however were chosen by the man, who had no time to dare to venture intrepidly. The image itself is another of those ghostly ones created by finding an interesting scene in a fractal which contains negative exponents, then raising the bailout until every point is trapped and the image consists of nothing but the infinite fractal ocean. At this point, if an inside fill such as bof60 is applied, a reflection of the original image almost magically reappears, sometimes looking even better than the original itself. I named the image "Sub-Marine Scene", though it has little resem- blance to the underwater world. I rated it at a 6, which might be a bit optimistic considering the hasty and somewhat muddy coloring. The render time of 12 minutes (on my tired machine) can be avoided by downloading the completed image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> With a warm sun, the temperature reached 37F 3C here at Fractal Central on Monday, but the winds were over 40mph 64kph, which made the intrepid duo quite skittish, and cut their outdoor time to a few minutes. They must be getting used to being house- bound, because they were actually quite happy with themselves through the long afternoon. At dinner time I rewarded their patience with a treat of tuna. But today is much colder, and light snow is falling. Their patience will be tried far more severely. Looking at the clock on the wall over my desk, I see that it is time to get busy on the unexpectedly tall pile of tasks on the shelf beside me. Until next time, take care, and be sure to try the fractal diet. Eat only fractals for a month and watch those pounds and ounces (kilograms and grams) vanish like magic. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Sub-Marine_Scene { ; time=0:12:16.60--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+2.27593538850584600/+0.293765268933583\ 40/3.698853e+008/1/57.5/-8.49740486379493842e-005 params=-11.49790215765862/-1.3/-10.61464473403119/\ -9.4/0/1e+100 float=y maxiter=1200 inside=bof61 symmetry=none periodicity=10 colors=000zlJzmJznKzoKzpKzqLzrMzsOztQzuSzvUNBWQCZR\ C`SCbAcaAc`9b_8bZ8bY7bX6aW6aV5aU5aT6bV6bX7cY0007da\ 8db8ed9ef9fg9fiUYVSXXQVZOU`MTcKReIQgGPiENlCMnALp5G\ q9KrDOrGSrKWrNZrRbrVfrYjranr`wsdqrhlqkgqoapsXoxQpv\ SotUnrWmqYlo_km`jkbijdhhfgfhfeiedjdckcclcbmbambana\ `oa_p`_p`Zq_Zr_YsZXtYXtYWuXVvX000UwWTxVTyVSzUSzUUw\ WWuXYsY_pZan_cl`ejaggbieckcdmaeoZfqXgsVhvRguTitVjs\ XkrZmq`nt`pqaoq`pp_qpZroYsoXtnWumUvuWDrYGo_JlbNidQ\ ffUbiX_k_XmcUpfRrjOtmKwqKwpKwpLwnMwmNwkOwiOwhPwfQw\ eRwcSwaTw`TwZUwY000WwUXwTYwRYwQZwO_wM`wLawJbwHdrHg\ lGjgFmaEpXDsRCvLBrSEqTGpUIoVKnWMmXOlYQkZSj_Ui`Wgxz\ fzzevzduzctzbszarz`qy_pxZowYnvWmuYjqYioXhmXgkWfjWe\ hWdfVcdVbbU`aU__TZYTXWTVUSTTSRRRPPRNNQKLQLLROMRPMS\ SNSTPRWRQYTP`VObXNdZMf`LibKkdJnfIpiOndTobYo`bpZgpX\ lqVrrTsmQthNufNvdNwbNx`NyZMzXMzYMzZMz_Mz`LzaLzbLzc\ LzdLzeKzfKzgKzhKziKzjJzkJ } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] Re: Fractint digest, Vol 1 #366 - 3 msgs
by Franktal Gallery 21 Jan '03

21 Jan '03

Check out my Mandelbrot SunSet (animated GIF) on : http://www.geocities.com/franktal2002/gal2.html it's a bit crude but uses the cool "lake" fractint feature. regards, Miguel Fliguer Franktal Gallery - SHUT UP 'N' DRAW YER FRACTALS http://www.geocities.com/franktal2002 (I know, no updates on 2002....) >From: "JackOTradez" <JackOTradez(a)email.msn.com> >Reply-To: fractint(a)mailman.xmission.com >To: <fractint(a)mailman.xmission.com> >Subject: [Fractint] Re: Fractint digest, Vol 1 #366 - 3 msgs >Date: Sun, 19 Jan 2003 12:25:23 -0500 > >Most Intriguing. The Russ-Dude strikes again! The rising Mandelbrot is way >cool. Now I must figure out a way to animate it and make a viddie - like a >Mandelbrot "sunrise" from an ocean horizon....... > _________________________________________________________________ The new MSN 8 is here: Try it free* for 2 months http://join.msn.com/?page=dept/dialup

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An afternoon visiting an old friend.
by Morgan L. Owens 21 Jan '03

21 Jan '03

Guess I should have seen it coming... Finished an article earlier than expected today. Had a few email inquiries to get through and just finished the last one (someone wanting to know what exactly Hilbert spaces are), made some posts of my own, found myself with a whole afternoon with (just for a moment) no idea what to do in it. Brief moment of panic: what had I forgotten? Nope, just no active contracts right now. Nothing needing writing, nothing needing coding, nothing needing expediting, and my friend's nephew is still on holiday, so he won't be in for his tutorial. Halfway through January and things are still quiet. Thought of a few things to do, but I'd already planned trips to the art gallery to see the new Chinese exhibit and the museum for a bit of digging through its archives for Thursday ... wasn't keen on the beach at all ... seen the movies I've been planning to see ... read a book? (glance at the shelves - nope, nothing saying "READ me! Read ME!") ... take a nap? ... could go to the pub ... the usual suspects seemed strangely boring. The proveribal drawing board was as metaphorically quiet as the literal bookshelves. Ended up spending the afternoon messing 'round on Fractint. Well, you should have been able to guess that - otherwise this post about my day and psychological state would have been entirely off-topic; it's not as though any of you would actually be interested in my psychological state while I munched lunch. It's just that I don't play with Fractint as much as I did ... good thing I didn't pay for it, I suppose (Would I use it more if I _had_ paid for it? Judging from past form, no. It would just sit there with its cost/benefit ratio steadily climbing.) I figured twenty pars worth keeping would be a convenient figure; to make things more interesting for myself, I resolved to use only those formulae that I'd coded myself. WFA, here are the final score: Morgan L. Owens "Now, to the theatre." --*--*-- Ypres_Dawn { ; De l'autre extremite du monde. ; Version 2001 Patchlevel 8 reset=2001 type=formula formulafile=dynamics.frm formulaname=distortpendulummg function=log passes=1 center-mag=-0.319069/0.0272592/24.6537 params=0.1/1 float=y maxiter=255 inside=255 periodicity=0 colors=000<82>K00L00L00<90>gY0gY0gZ0gZ0hZ0<74>zzz } Asymptotic_Freedom { ; Version 2001 Patchlevel 8 reset=2001 type=formula formulafile=dynamics.frm formulaname=HenonQuadmapJulGen function=cotanh/recip passes=1 center-mag=-1.36335/0.187656/1.572327/1/-90 params=0/0/0/0 float=y maxiter=255 inside=epsiloncross proximity=-0.001 outside=0 periodicity=0 colors=653<9>cb`fecjig<3>xwu<9>qYXpVVoSS<2>mKLlHIjII<8>QRLOSLMTL<3>CXN<9\ >ekKhmKknK<3>wuI<9>VUOSRPPOQ<3>DCT<9>YCS_CSaCS<3>jCR<9>OMcMNeKOf<3>ATl<9\ >8EL8DI7BF<3>653<9>cb`fecjig<3>xwu<9>qYXpVVoSS<2>mKLlHIjII<8>QRLOSLMTL<3\ >CXN<9>ekKhmKknK<3>wuI<9>VUOSRPPOQ<3>DCT<9>YCS_CSaCS<3>jCR<9>OMcMNeKOf<3\ >ATl<14>AA9 } Grand_Unification { ; Version 2001 Patchlevel 8 reset=2001 type=formula formulafile=dynamics.frm formulaname=distortpendulummg function=zero passes=d corners=-0.0475/0.285/0.15865385/-0.03365385 params=0.5/0.5 float=y maxiter=255 inside=epsiloncross proximity=-0.00025 outside=0 periodicity=0 viewwindows=1/0.526/yes/0/0 colors=000ccc<3>nnnqqqtttwwwzzz<4>IIz99z00z<9>bbOffKjjG<3>zz0<9>zO0zK0zG\ 0<3>z00<9>O0bK0fG0j<3>00z<9>0bO0fK0jG<3>0z0<9>bObfKfjGj<3>z0z<9>`0`Y0YV0\ V<2>N0NK0KJ1L<8>8Ia7Kc5Me<2>2Sk0Um0Vm<8>0em0fm0hm<2>0km0mm0mm<8>0gu0gu0f\ v<3>0cz<9>bqzfrzjtz<3>zzz<25>zhCzgAzf8<2>zd2zc0zd0<8>zq0zr0zt0<3>zz0<9>z\ O0zK0zG0<3>z00<14>ZZZ } Not_a_Nice_Doggy { ; 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Version 2001 Patchlevel 8 reset=2001 type=formula formulafile=more.frm formulaname=PokornyJul center-mag=0.200125/0.776177/2.506266 params=0.25/0.9 float=y maxiter=1023 inside=255 logmap=yes periodicity=0 colors=@altern } Puffer_Train { ; Version 2001 Patchlevel 8 reset=2001 type=formula formulafile=evenmore.frm formulaname=Rossler2Man center-mag=+0.87099255681842290/+0.45740250376426910/5.001221e+012/1.000\ 1 params=0/0/12/0 float=y maxiter=1023 inside=255 logmap=57 periodicity=0 colors=653<9>cb`fecjig<3>xwu<9>qYXpVVoSS<2>mKLlHIjII<8>QRLOSLMTL<3>CXN<9\ >ekKhmKknK<3>wuI<9>VUOSRPPOQ<3>DCT<9>YCS_CSaCS<3>jCR<9>OMcMNeKOf<3>ATl<9\ >8EL8DI7BF<3>653<9>cb`fecjig<3>xwu<9>qYXpVVoSS<2>mKLlHIjII<8>QRLOSLMTL<3\ >CXN<9>ekKhmKknK<3>wuI<9>VUOSRPPOQ<3>DCT<9>YCS_CSaCS<3>jCR<9>OMcMNeKOf<3\ >ATl<14>AA9 } FriendlyBiological { ; Version 2001 Patchlevel 8 reset=2001 type=formula formulafile=evenmore.frm formulaname=Rossler2Man passes=1 center-mag=+0.80768598348989470/+1.07767747322206200/622.4066/1/28 params=0/0/12/0 float=y maxiter=1023 inside=255 logmap=9 periodicity=0 colors=tuu<3>tvvtvvtvvtvvuww<6>lwwkwwjwwiwwgww<3>ctvbtvasu<3>XosVnsUmr<1\ 8>AXh9Wg8Vg7Uf6Te<4>5Pc5Oc5Ob4Na<18>17R17Q16Q<2>13O02N14O02N<8>16Q27Q27Q\ <3>3AT3BU3CV<6>4Ka4Lb5Mc<5>4Si4Tj4Uk3Vl3Wm<4>2_o1_p1`p<2>0cr0cr0br<3>1_q\ 1Zp1Yp<8>3Qg3Pf3Oe<2>4La4K`3IZ<3>4GS4FQ5FO<3>6CG7BD7BD<70>oqqpqqqrrqrrrs\ s<8>suu } Corrosion { ; Kerry Mitchell colour map ; Version 2001 Patchlevel 8 reset=2001 type=formula formulafile=chby17.frm formulaname=H04-17 function=ident/log passes=1 center-mag=-0.405748/-0.631308/5.253812/1/-34.999 params=0/0/1/0 float=y maxiter=1023 inside=255 periodicity=0 colors=222qU6yaEqaMyiUeYQYQIaaaiiiqiayqiqqqyyyemuYemQeuIYmAYu2QmAQe2IYMU\ aUaiQQQIIIAIQ2AIAAA642IC6UKAYK6iSAqS2u_Eq_IugUi_QYSMY_aigeqgYuoiqomuwyio\ uYgqUguI_qA_y6SmASi6KYISaU_eUSQIKMAKU6CIACEA62IEAUI6YMAiQ6uU2qYEuaIqeUiY\ MYUQYaeieauiYqmiuqmquyimqYiuUeqIau6YyAUm6QiAMYIUeUYaUQMIMQ6IUAEI6AEA86IG\ EQG6YOEeO6yW2qWAycIqcQiWIaWQYciecaykYqkeysmqsuikmakuUcmMcu2WyAWq2OiAOaIW\ iQWaUOIMOQ2GUAGM28EEA6MIEQE2aQEeM2yY6mUAyeMmaQeUIaYUaeieaYymamieyuqmquei\ mamyQamMey2UuEYq2MeEQaMYiQUYQMIMQU2EQEIM26AE82MGAUG2aOAiO2uW6mWEucMmcUeW\ MYWUaceicYukamkiusqmsyekqYkyQcqIcy6WuEWm6OeEOYMWeUWYQOMIOU6GQEGI68AIA2QI\ AYI2eQAmQ2uYAmYIueQiaUaUMYYYeeemeYumemmmuuuiqyaiqUiyMaqEay6UqEUi6MaIQYQY\ eUUUMMMEMU6EMEEE666MC2QKEaK2eSEmS6y_Am_MygQe_UaSIa_Yegimgayoemoqywueoyag\ mQgyM_mE_u2SqESe2KaMSYQ_iQSUMKIEKQ2CMECA246ME6UMEaM6iUE } Mitrocoma { ; Version 2001 Patchlevel 8 reset=2001 type=formula formulafile=chby26.frm formulaname=T03-26 function=abs/ident/ident passes=1 center-mag=-0.833021/0.838198/7.751938 params=2/0.2/0/0/8/1 float=y maxiter=1023 inside=255 periodicity=0 colors=(a)blues.map } Six_OClock { ; Version 2001 Patchlevel 8 reset=2001 type=formula formulafile=twodne~1.frm formulaname=twodnewton_o passes=t center-mag=+17.61898205646764000/+11.36059478637080000/109.2896/1/-22.49\ 9 params=0.1/-1 float=y maxiter=1023 inside=255 periodicity=0 colors=000e0_e0be0e<9>eDGeEEeFB<3>eL0<9>eYQeZSe_V<3>eee<9>TTTSSSRRR<2>NN\ NLLLLLN<8>LLjLLlLLo<2>LLwLLzLNx<3>LYm<21>MruMsvMtv<3>Nxx<8>j``lZZoWW<3>z\ LLzLNzLQzLS<18>zgVzhVzjV<2>zmVzoWzrTztRzwOzzL<9>zzjzzlzzo<3>zzz<3>kkkggg\ ccd__`<31>__`<4>__`0_60b30e0<9>0eQ0eS0eV<2>0eb0ee2cc<8>QGGSEEVBB<3>e00<1\ 2>e0Y } frm:distortpendulumMG{ bailout=4 dt=real(p1) a=imag(p1) b=real(pixel) c=imag(pixel) time=0 z=pixel: x=real(z) y=imag(z) z=x+dt*y+flip(y+(dt*fn1(b*x-c*time)-x)*a) time=time+dt |z|<=bailout} frm:HenonQuadmapJulGen{ bailout=real(p2)+4 c=p1 d=1-c z=pixel: x=real(z) nx=c*x-imag(z)-d*fn1(x) z=nx+flip(x-c*nx+d*fn2(nx)) |z|<=bailout} frm:Ca03-19 {; V.1.1 - earlier versions may be discarded ; Copyright (c)1998,1999 Morgan L. Owens ; = (2(a+2)xCa(2)-(2a+1)Ca(1))/3 a=p2, b=(a+a)*(a+1), c=(a+a+4)/3 t=p1, bailout=4, z=pixel: x=real(z), y=imag(z) y=y+t*(b*x*(c*x*x-1)) x=x-t*(b*y*(c*y*y-1)) z=x+flip(y) |z|<=bailout } frm:C03-15 {; V.1.1 - earlier versions may be discarded ; Copyright (c)1998,1999 Morgan L. Owens ; = zC02-C01 r=p1, bailout=real(p2)/10000, z=pixel: zz=z*z f=z*(zz-3) fd=3*zz-3 oz=z z=z-r*f/fd bailout<=sqrt(|(|z|)-(|oz|)|) } frm:P07-07 (XYAxis) {; V.1.1 - earlier versions may be discarded ; Copyright (c)1998,1999 Morgan L. Owens ; = (13zP06-6P05)/7 bailout=real(p2)/10000, z=pixel: zz=z*z f=z*(3*zz*(11*zz*(13*zz-21)+105)-35)/16 fd=(21*zz*(11*zz*(13*zz-15)+45)-35)/16 oz=z w=z-f/fd ww=w*w fw=w*(3*ww*(11*ww*(13*ww-21)+105)-35)/16 z=w-fw/fd bailout<=|z-oz| } frm:quarterblend_iJJJJ{ z=pixel: if(imag(z)>0) if(real(z)<0) c=p1 else c=p2 endif else if(real(z)>0) c=p3 else c=p4 endif endif z=sqr(z)+c |z|<=4} frm:threecircles2 { ; three circles located at the cube roots of 1 ; real(p1) specifies their common radius - note that they're tangent to ; each other when real(p1)=sqrt(3)/2. ; ; p2 specifies a point (the "radiant") from which test particles are ; launched. More precisely, every point in the complex plane emits a ; test particle, which travels directly away from p2 ; ; First, we need to establish the centres of the three circles. centre1=1 centre2=exp(flip(2*pi/3)) centre3=sqr(centre2) ; Reckon this is faster than another exp()? rho=real(p1) direction=pixel-p2 z = pixel trapped=(|z-centre1|<sqr(rho) || |z-centre2|<sqr(rho) || |z-centre3|<sqr(rho)) ; For efficiency, we see if z is _inside_ a circle. If it is, we can ; predict how long it will take to escape :-) ; Note also that since Fractint's || operator is nonstandard, we use ; sqr(rho) instead of rho. : ; End of initialisation section. Now beginning the loop. if(trapped) escaped=0 ; We'll continue to iterate, though - so that the insides of ; the circles really are classified as "inside" else ; Let's get dangerous ; Right, we have a ray that passes through the point z in the direction ; theta. Finding the intersections (if any) of this ray with a circle ; involves finding the solutions of a certain quadratic with real ; coefficients. If the quadratic has two real roots, then the ray cuts the ; circle. If it has one real root (necessarily of multiplicity two) then ; the ray is tangent to the circle. And if both roots are complex, then ; the ray misses the circle completely. escaped=1 ; As far as we know at the moment. hit=9999 ; Meaningless when escaped==1 ;Examining circle 1 coefA = |direction| coefB = real(z-centre1)*real(direction)+imag(z-centre1)*imag(direction) coefC = |z-centre1|-sqr(rho) discriminant=coefB*coefB-coefA*coefC ; If discriminant==0, then the ray is tangent to circle 1 - we won't ; count this as a "reflection" ; If discriminant<0, then the ray misses circle 1 completely. if(discriminant>0) ; Two solutions t1=(-coefB-sqrt(discriminant))/coefA t2=(-coefB+sqrt(discriminant))/coefA if(t1>0) ; If t1<0 then this hit is actually behind us escaped=0 ; Sorry, not this time. hit=t1 target=1 ; The first circle endif if(t2>0 && t2<t1) ; Hits t2 before hitting t1 escaped=0 hit=t2 target=1 endif endif ; Circle 2 ; coefA = |direction| is already known coefB = real(z-centre2)*real(direction)+imag(z-centre2)*imag(direction) coefC = |z-centre2|-sqr(rho) discriminant=coefB*coefB-coefA*coefC if(discriminant>0) t1=(-coefB-sqrt(discriminant))/coefA t2=(-coefB+sqrt(discriminant))/coefA if(t1>0 && t1<hit) escaped=0 hit=t1 target=2 endif if(t2>0 && t2<t1 && t2<hit) escaped=0 hit=t2 target=2 endif endif ; Circle 3 coefB = real(z-centre3)*real(direction)+imag(z-centre3)*imag(direction) coefC = |z-centre3|-sqr(rho) discriminant=coefB*coefB-coefA*coefC if(discriminant>0) t1=(-coefB-sqrt(discriminant))/coefA t2=(-coefB+sqrt(discriminant))/coefA if(t1>0 && t1<hit) escaped=0 hit=t1 target=3 endif if(t2>0 && t2<t1 && t2<hit) escaped=0 hit=t2 target=3 endif endif ; We now know when we hit a circle (hit) and which circle it is (target) ; The hit point is z+direction*hit, the normal at this point is ; z-centre?, which we normalise to a unit vector (un). ; ; We set z to the hit point, and the reflected vector is ; direction-2(direction.un)un if(target==1) un=(z-centre1)/cabs(z-centre1) elseif(target==2) un=(z-centre2)/cabs(z-centre2) else un=(z-centre3)/cabs(z-centre3) endif r=direction-2*(real(direction)*real(un)+imag(direction)*imag(un))*un z=z+direction*hit direction=r endif ;bailout continue until we escape escaped==0 } frm:newton_elliptics_4{ x=real(pixel) y=imag(pixel) A=real(p1) B=imag(p1) phi=tan(real(p2)) t=imag(p2) z=x+flip(y) : oz=z x=real(z) y=imag(z) d=2*y*phi-(3*sqr(x)+A) f=(sqr(x)+A)*x+B-sqr(y) g=phi*x+t-y nx=x-f+2*y*g ny=y-phi*f+(3*x^2+A)*g z=nx+flip(ny) |z-oz|>0.0001 } frm:Mandelbar(Xaxis){ z=pixel: z=sqr(conj(z))+pixel |z|<=4} Julibar(Origin){ z=pixel: z=sqr(conj(z))+p1 |z|<=4} frm:A4Page(XYAxis){ s=-sqrt(2) z=pixel: x=real(z) y=imag(z) if(x>0) z=s*(flip(conj(z)-1)) else z=s*(flip(conj(z)+1)) endif |z|<=300} frm:Sc06-05 {; V.1.1 - earlier versions may be discarded ; Copyright (c)1998,1999 Morgan L. Owens ; = Sc[6]=2(zO[5]-cos(5*pi/2)^2)/5 r=p1, bailout=real(p2)/10000, z=pixel: z2=z*z, z4=z2*z2 f=((((((72-8*z)*z-192)*z+384)*z-704)*z+768)/(z4*z)) fd=((((384-72*z)*z-1152)*z+2816)*z-3840)/(z4*z2) oz=z z=z-r*f/fd bailout<=|z-oz| } frm:twodnewton_o{ h = real(p1) m = imag(p1) z=pixel: oz=z x=real(z),y=imag(z) f=2*x-y-m*(x-x*x) g=2*y-x-m*(y-y*y) fx=2-m*(1-2*x) gy=2-m*(1-2*y) delta =(-g-f*gy)/(fx*gy-1) epsilon=(-f-g*fx)/(fx*gy-1) nx=x+h*delta ny=y+h*epsilon z=nx+flip(ny) |oz-z|>.001 } frm:Rossler2Man(XAxis){ bailout=real(p2)+4 z=p=pixel: x=real(z) y=imag(z) z=abs(sqr(x)-sqr(y))-real(p)+flip((x+x)*y-imag(p)) |z|<=bailout} frm:PokornyJul(Origin){ bailout=4 c=p1 z=pixel: z=1/(sqr(z)+c) |z|<=bailout} frm:P03-24 {; V.1.1 - earlier versions may be discarded ; Copyright (c)1998,1999 Morgan L. Owens ; = ( 5zP02-2P01)/3 t=p1, bailout=4, z=fn3(pixel): x=real(z), y=imag(z) y=y+t*(fn1(x*(5*x*x-3)/2)) x=x-t*(fn2(y*(5*y*y-3)/2)) z=x+flip(y) |z|<=bailout } frm:T03-26 {; V.1.1 - earlier versions may be discarded ; Copyright (c)1998,1999 Morgan L. Owens ; = 2zT02-T01 t=p1, bailout=real(p3), z=pixel, v=imag(p3): x=real(z), y=imag(z) Tx=(fn1(x*(4*x*x-3))) Ty=(fn1(y*(4*y*y-3))) x=x-t*Ty, y=y+t*Tx w=fn1(x+flip(y)) z=fn3(v/fn2(w*w))+p2 |z|<=bailout } frm:H04-17 {; V.1.1 - earlier versions may be discarded ; Copyright (c)1998,1999 Morgan L. Owens ; = 2(xH(3)-3H(2)) z=pixel, oz=0 fz=12 zt=fn1(z)+p1: foz=fz zz=z*z fz=4*(4*zz*(zz-3)+3) z=z-p2*fz*(z-oz)/(fz-foz) oz=zt zt=fn2(z) |fz|>=0.0001 } frm:Ca10-05 {; V.1.1.1 - earlier versions may be discarded ; Copyright (c)1998,1999 Morgan L. Owens ; = ((a+9)xCa(9)-(a+4)Ca(8))/5 a=p1 b1=a*(a*(a*(a*(a+10)+35)+50)+24)/382860 c1=15*(a+5) d1=2*(a+6) e1=a*(a+15)+56 f1=2*(a+9)/45 g1=14*(2*a+13)/5 b2=a*(a*(a*(a*(a*(a+15)+85)+225)+274)+120)/12762 e2=(a+9)/9 f2=21*(2*a+13)/5 bailout=real(p2)/10000, z=pixel: zz=z*z f=b1*(c1*zz*(d1*zz*(81*zz*(e1*zz*(f1*zz-1)+g1)-1418)+2127)-31903) fd=b2*z*(d1*zz*(162*zz*(e1*zz*(e2*zz-2)+f2)-2881)+2127) oz=z z=z-f/fd bailout<=|z-oz| }

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Oops, belay that earlier Tjul formula
by Russell Walsmith 20 Jan '03

20 Jan '03

I've noticed that cutting and pasting doesn't always save time. TJul { z1=real(pixel),z2=imag(pixel)*(0,1),z3=p3: t1=z1*z1+2*z2*z3 t2=z3*z3+2*z1*z2 t3=z2*z2+2*z3*z1 z1=t1+p1,z2=t2+p2,z3=t3+p3 z=z1*z2+z2*z3+z3*z1 z < 64 } _____________________________________________________________ Get 25MB, POP3, Spam Filtering with LYCOS MAIL PLUS for $19.95/year. http://login.mail.lycos.com/brandPage.shtml?pageId=plus&ref=lmtplus

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Re: Fractint digest, Vol 1 #367 - 5 msgs
by JackOTradez 20 Jan '03

20 Jan '03

It worx! Yeah-Right! I have figured how to animate the TMan1 Rising 3D Mandelbrot. The program is writ and the images are rendering as I write this. They are slow. It will take a few days at this rate; possibly due to all that extra complex math my poor little CPU has to deal with. I also changed the color palette. It will look like a flaming 3D Mandelbrot arising and forming out of a lake of frothing lava - way cool! Soon as it's done I will post on my web site for download. Mean time, let me check out those Lee Skinner / Guy Marson formulas ... ... ... (one of the nice things about being unemployed is you have lotsa time for these things <g> )

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FOTD 20-01-03 (Bad Boy [6])
by Jim Muth 20 Jan '03

20 Jan '03

FOTD -- January 20 2003 (Rating 6) Fractal visionaries and enthusiasts: Today's image is titled "Bad Boy". This name does not allude to a reggae song; it refers to the fact that at one point there are 12 elements surrounding the central midget, which is quadratic in nature and therefore not expected to have rings that consist of a number of elements that is a non-integral power of 2. The image might also be considered bad because it is unstable. The slightest change in the real(p2) parameter causes the entire scene to vanish. Finally, the two satellites in the northeast and southwest corners have six elements surrounding them, which is another wrong number. This image certainly earns its bad reputation. I don't know what it's going to do when they come for it. The generating formula is unusually simple. It takes Z^3 and adds somewhat more than half as much Z^5 before adding C. The resulting parent fractal is rather routine, except when the value of the parameters is near today's, at which point the area of the fractal where today's image lies becomes unstable. Like everything else in the world of fractals, this localized instability happens because of the things numbers do. Given the nature of complex numbers, it could not be otherwise. I rated the image at a 6, a rating that might be considered generous. The coloring is only moderately impressive, and the math interest is worth only slightly more. But then, a 6 is only slightly above average, so the rating will remain. The attached parameter file renders in under 6 minutes on my tired old P200 machine, which might soon be replaced as my fractal-dedicated unit. Those who would rather not wait 6 minutes to see the image may download it, already completed, from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> I continue to find interesting things in variations I am creating of the recently posted Tman formula. Regardless of the number of dimensions, the images are out of this world. In fact, they're in the fractal world. Some unusual images could be coming in the near-future FOTD's. The Fractal Central weather turned milder, but remained too cold on Sunday for the dynamic cats to venture outdoors. There was some sun, but also flurries of snow, and a temperature that never reached freezing. The dynamic ones were surprisingly pleasant in the midst of their confinement. Today is starting milder yet. Could this be the day when the cats' paws reach the turf of the yard? Check in 24 hours to see. Until then, take care, and go where the fractals take you. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Bad-Boy { ; time=0:05:40.20--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+1.09529517003905100/+0.003871516957443\ 89/856841.9/1/155/2.75135829397310516e-009 params=1/3/-0.599/5/0/0 float=y maxiter=1200 inside=0 logmap=112 periodicity=10 colors=0004EO4FS3GX3H`2Ie2Ji2Jm6HmAGmEFmHEmLDmPBmT\ AmW9m_8mc7mg5mj4mn3mr2mv1my0mw6cvCUpCPkCLfCHaCCXC8\ SC4NC0ME2MF4MG5MH7MI9LJALKCLLELMFLNHLOIJPKIQLHQNGR\ OFSQESRDTSCUUEXVG_XIbYKeZMhYOk`QldUmhYmkcmnhmpnmrs\ mtrhprclrZhrUdrP`qKXqFTqAPq5Lq0HsAEtKCuU9vc7reDofI\ kgNhhTdjYakbYlhVmmSnrRonRokQohQodPoaPoZXbbcRfjEjq2\ np7npCnoHnoLnoQnnVnn_nncnmhnmmnmqninhfkcbiZ_fUWcPT\ aKPZFMWAJU5PT9UTCZTFdSJiSMnSPsSSi3uj5qj7mk9ikBfkCb\ lEZlGVmISmKOmLKnNGnPDoR9oT5oU2nW6nX9nYCmZFm_Im`Lma\ OibPfbPbbQ_bQWcRTcRPcSMcSIdTFdTBdU8dU7bV7`W7ZW7XX6\ VY6TY6RZ6P_6N_6N_7O_7O_7O`7O`7O`7O`7OaKOaLOaMOaNOa\ OObPObQObRObSOcTOcUOcVOcWOdXPdYQfZPd_Pd`PdaPebPecP\ ecPecPfcPfcPfcPfcPfcPgcPgcPgdPgePhfPhgPhhQhiQhjQik\ QilQimQioRjqSjsTjuUjwVjyWkzXkzYkzZkz_lz`lzalzblzcm\ zcnzcozcpzcqzcrzcszctzcuzcvzcxzcyzczzczzczzczzczzc\ zzczzczzczzczzczzczzczzcz } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Re: Fractint digest, Vol 1 #366 - 3 msgs
by JackOTradez 20 Jan '03

20 Jan '03

Most Intriguing. The Russ-Dude strikes again! The rising Mandelbrot is way cool. Now I must figure out a way to animate it and make a viddie - like a Mandelbrot "sunrise" from an ocean horizon.......

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Re: [fractint] FOTD 18-01-03 (Rising mandelbrot [6])
by Lee H. Skinner 20 Jan '03

20 Jan '03

This TMan1 formula can produce some amazing looking 3D-like images. frm:TMan1 { c1=flip(real(pixel)),c2=imag(pixel),c3=p1 z1=z2=z3=0: t1=z1*z1+2*z2*z3 t2=z3*z3+2*z1*z2 t3=z2*z2+2*z3*z1 z1=t1+c1,z2=t2-c2*c2,z3=t3+c3 z=z1+z2+z3 |z| < 8 } The following par produces what looks like midgets intersecting in 3 perpendicular planes: 60118025 { ; 3-Plane Midget t= 0:33:48.68 ; on a P4 2Gh at 1600x1200 Jan 19, 2003 22:43:12 ; Image Copyright 2003 by Lee H. Skinner ver=2002 ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=fractint.frm formulaname=tman1 passes=1 center-mag=-0.14086254709453280/+0.63267349162819330/12556.45/1/-137.500\ 000000003013/1.74807113229036304e-011 params=-0.4/0 float=y maxiter=18000 inside=0 logmap=108 symmetry=none periodicity=10 colors=000d6fX7`Q8U<2>AHV<2>4A9<3>BONCRQEVT<2>JdbLhfOig<12>mttouuqvv<3>z\ zzxzz<16>UcOTaLR`J<3>JV9LY4<11>OG4OF4OD4<2>P94Q74Q86<21>EVmDWoDXq<3>Aaz<\ 2>`Lz<5>lcZnfUpiP<2>vsBxv6xvH<3>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8KJ8<3>MD6N\ C5NA5O94P73<3>aI8eLAhMBiODjQF<3>qeBriAtm9vq8xu7zz5zz4zz3<8>zY4zV5zS5<3>z\ E6<28>jEJiEJiEK<3>fDMhENjFPlLS<3>rdhtilvoqxtuzzz<3>pvzmtzgpz`lzUhz<3>iWz\ mTzrPz<3>z3zs4tk5m } The 3 following images show more 3D-like views: 60118021 { ; Fig Tree Strangling a Mandelbrot t= 0:04:09.58 ; on a P4 2Gh at 1600x1200 Jan 19, 2003 22:43:05 ; Image Copyright 2003 by Lee H. Skinner ver=2002 ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=fractint.frm formulaname=tman1 passes=1 center-mag=-0.14094542272236100/+0.61891532192206370/284916.1/1/-37.4999\ 99999989555/1.37909239583677845e-010 params=-0.4/0 float=y maxiter=18000 inside=0 logmap=63 symmetry=none periodicity=10 colors=000bOvdRqfUlhXgj`c<2>piQrmLsnQ<3>wujxvoyxtzzz<3>jqdfo_blU<3>Mb8<3\ >LQ8KM8KJ8<3>MD6NC5NA5O94P73<3>aI8eLAhMBiODjQF<3>qeBriAtm9vq8xu7zz5zz4zz\ 3<8>zY4zV5zS5<3>zE6<4>xE8wE8wE9<3>tEAsEArE9<11>eE3dE3cE2<2>`E1ZE0_G4<5>j\ YTl`Xnc`<2>tllvoqxtuzzz<3>pvzmtzgpz`lzUhzUhzUhz<44>wxzwxzxyzyyzzzz<33>ai\ s`ir_hr<3>Xfqzsz<24>LezJdzHdz<3>Aaz<2>`Lz } 60118007 { ; Cave of the Fire Pit t= 0:21:46.41 ; on a P4 2Gh at 1600x1200 Jan 19, 2003 22:42:41 ; Image Copyright 2003 by Lee H. Skinner ver=2002 ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=fractint.frm formulaname=tman1 passes=1 center-mag=-0.14109239066731250/+0.63265570738880520/95831.26/1/-44.9999\ 999998383586/-5.38782074510635312e-011 params=-0.4/0 float=y maxiter=18000 inside=0 logmap=139 symmetry=none periodicity=10 colors=000LBUFEVAHV<2>4A9<3>BONCRQEVT<2>JdbLhfOig<12>mttouuqvv<3>zzzxzz<\ 16>UcOTaLR`J<3>JV9LY4<11>OG4OF4OD4<2>P94Q74Q86<21>EVmDWoDXq<3>Aaz<2>`Lz<\ 5>lcZnfUpiP<2>vsBxv6xvH<3>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8KJ8<3>MD6NC5NA5O\ 94P73<3>aI8eLAhMBiODjQF<3>qeBriAtm9vq8xu7zz5zz4zz3<8>zY4zV5zS5<3>zE6<28>\ jEJiEJiEK<3>fDMhENjFPlLS<3>rdhtilvoqxtuzzz<3>pvzmtzgpz`lzUhz<3>iWzmTzrPz\ <3>z3z<4>Q8U } 60118013 { ; Fiery Forest t= 0:07:39.35 ; on a P4 2Gh at 1600x1200 Jan 19, 2003 22:42:51 ; Image Copyright 2003 by Lee H. Skinner ver=2002 ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=fractint.frm formulaname=tman1 passes=1 center-mag=-0.14072100474163920/+0.63232110386355890/380133.7/1/-142.500\ 000001225942/7.55598403290314025e-010 params=-0.4/0 float=y maxiter=18000 inside=0 logmap=110 symmetry=none periodicity=10 colors=000JXzSRz`Lz<3>hXgj`clc_nfVpiQrmL<3>vsewujxvoyxtzzz<3>jqdfo_blU<3\ >Mb8<3>LQ8KM8KJ8<3>MD6NC5NA5O94P73<3>aI8eLAhMBiODjQF<3>qeBriAtm9vq8xu7zz\ 5zz4zz3<8>zY4zV5zS5<3>zE6<6>wE9vE9uEA<3>sEBrEBqEA<13>cE3bE3aE2<3>XD0<3>f\ VMiZSlcY<9>LmoJnpGor<3>4sz<41>MgzMgzNgz<2>OfzPeyOex<63>D_vD_vD_vD_vD_vCZ\ uB_wAaz }

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investigations#3.2
by jos hendriks 19 Jan '03

19 Jan '03

Dear reader I'm not really fond of complex complex functions. They are too complicated for me and I can't follow what they are "doing". So I continued with something much simpler the real valued function f(x)=x^2+c. If you choose c between -2 and .25 then the prisoner set of the orbits of x,f(x), f(f(x),..... is an interval. For c>. 25 all orbits escape and there is no prisoner set. For c<-2 the prisoner set is a Cantorlike set (you can figure these things out by drawing the graph of f(x)=x^2+c for some values of c and then tracing back the orbits of intervals (the prisoner set is invariant not only under forward but also under backward tracing)) So making pictures with f(x,y)=(x^2,y^2)+ (c1,c2) what do you expect? Well choosing c1 and c2>.25 nothing, c1 and c2 between -2 and .25 a rectangular prisoner set. The interesting things are when you choose one or both of c1 and c2 smaller then -2. . If you choose only one of them <-2 then you expect a band-like patron. If both <-2 then you expect a patron with smaller and smaller rectangular parts. Below are some pars. Pictures are indeed as expected. The boogie_woogie pars all have the same value for c1 and c2. But the use of different coloring methods give slightly different but interresting/nice pictures. All the pars renders in seconds, so you don't need to spend much time if you decide to look at them. frm:Jh_square {;Jos Hendriks,2002 if (ismand) z = 0 , c = pixel else z = pixel , c = p1 endif : a=real(z),b=imag(z) z=a*a+flip(b*b)+c real(z)<p2 && imag(z)<p2 } Boogie_Woogie_1 { ; Jos Hendriks ,2002 reset=2000 type=formula formulafile=invest~1.par formulaname=jh_square ismand=n passes=1 center-mag=0/0/0.6666667 params=-2.012450635926158/-2.013287548247079/4/0 float=y colors=000zpC<4>zTBzOBzJB<3>z0AzAM<2>z3az0gz0i<3>z0rz0uz0wz0yz2x<14>ziOz\ kMznJ<3>zzA<3>zoEzlFzjGzgHzeJ<8>zUQzSRzRS<3>zLV<19>zVnzWozWp<5>z`uzavzbw\ <2>zeyzfyzgyzhyziy<3>znyzoyzpy<2>zty<3>zoyznyzmx<3>zgpzfnzelzci<19>zrkzs\ kztl<3>zwlztl<3>zbgzZfzUe<2>zHa<4>zHfzGg<3>zAfz8ez7e<19>zkkzmkzok<3>zwl<\ 4>zndzlbzja<2>zeXzcVzcV<5>zZUzYUzXUzXTzWT<8>zRLzQKzQJ<3>zNFzMEzLD<12>zuC } Boogie_Woogie_2 { ; Jos Hendriks ,2002 reset=2000 type=formula formulafile=invest~1.par formulaname=jh_square ismand=n passes=1 center-mag=0/0/0.6666667 params=-2.012450635926158/-2.013287548247079/4/0 float=y outside=mult colors=000aJB<4>iMEjNFlNF<2>qPHsQIwYB<4>wRBwPBwOB<3>wIBwKBwNBwPB<15>cYGb\ ZG`_H__HZ`HXaI<10>RQOQPOPOPPNPOMQNKR<25>RaERbDRcD<2>ReBSfATdC<10>cIYdG_e\ Ea<3>i5i<12>FBYDCXACW<3>0FS<8>RDWUDXXDX<3>hB_<15>shdtjduld<2>wrexufxuc<3\ >uuRuuOtuLsuH<14>GfJEeJBdJ<3>0_K<9>XSK`SKcRK<3>qNL<5>WMWTMXPLZ<3>AKf<3>E\ WdF_dGbc<2>JlaETK991<16>_IA } Boogie_Woogie_3 { ; Jos Hendriks ,2002 reset=2000 type=formula formulafile=invest~1.par formulaname=jh_square ismand=n passes=1 center-mag=-0.00113141/0.401369/9.887676 params=-2.012450635926158/-2.013287548247079/4/0 float=y outside=mult colors=0000jR<2>0eM0cK0cK<5>0ZJ0YJ0XJ0XI0WI<8>0RA0Q90Q8<3>0N40M30L2<6>0d\ 10g10j1<3>0u1<5>0T00O00J0<3>0000AB<2>03R00X00Z<3>00g00j00l00o<3>0Bf0s1<1\ 1>0O80M80J9<3>08C<22>0ad0be0dg<5>0jn0ko0lp<3>0qu<3>0ZR<2>0lQ<6>0Qd0Mf0Jh\ <3>05q<3>0El0Gk0Ij0Lh0NgFPf<9>FlTFnSFpR<3>EzL<3>Sb9WX6_Q2LUC5YM0aW0ef06f\ <5>0_J<3>0s31x01w0<2>0s00r10p10o20m2<16>0RA0PA0OB<3>0ID<2>0PN0RY<9>0k`0m\ `0o`<3>0wa<5>0lS } Boogie_Woogie_4 { ; Jos Hendriks ,2002 reset=2000 type=formula formulafile=invest~1.par formulaname=jh_square ismand=n passes=1 center-mag=0/0/0.6666667 params=-2.012450635926158/-2.013287548247079/4/0 float=y outside=summ colors=0000SA<3>0NC0LD0KD0IE<2>0PO0RZ<9>0ka0ma0oa<3>0wb<4>0nV0lT0jS<2>0e\ N0cL0cL<5>0ZK0YK0XK0XJ0WJ<8>0RB0QA0Q9<3>0N50M40L3<6>0d20g20j2<3>0u2<5>0T\ 10O10J1<3>0000AC<2>03S00Y00_<3>00h00k00m00p<3>0Bg0s2<11>0O90M90JA<3>08D<\ 22>0ae0bf0dh<5>0jo0kp0lq<3>0qv<3>0ZS<2>0lR<6>0Qe0Mg0Ji<3>05r<3>0Em0Gl0Ik\ 0Li0NhFPg<9>FlUFnTFpS<3>EzM<3>SbAWX7_Q3LUD5YN0aX0eg06g<5>0_K<3>0s41x01w0\ <21>0UA } Boogie_Woogie_5 { ; Jos Hendriks ,2002 reset=2000 type=formula formulafile=invest~1.par formulaname=jh_square ismand=n passes=1 center-mag=0/0/0.6666667 params=-2.012450635926158/-2.013287548247079/4/0 float=y outside=atan colors=000SG9<10>iMFjNGlNG<2>qPIsQJwYC<4>wRCwPCwOC<3>wICwKCwNCwPC<15>cYH\ bZH`_I__IZ`IXaJ<10>RQPQPPPOQPNQOMRNKS<25>RaFRbERcE<2>ReCSfBTdD<10>cIZdG`\ eEb<3>i5j<12>FBZDCYACX<3>0FT<8>RDXUDYXDY<3>hB`<15>shetjeule<2>wrfxugxud<\ 3>uuSuuPtuMsuI<14>GfKEeKBdK<3>0_L<9>XSL`SLcRL<3>qNM<5>WMXTMYPL_<3>AKg<3>\ EWeF_eGbd<2>JlbETL992<10>QF8 } Boogie_Woogie_6 { ; Jos Hendriks ,2002 reset=2000 type=formula formulafile=invest~1.par formulaname=jh_square ismand=n passes=1 center-mag=0.00500626/-0.0250417/4.901961 params=-2.012450635926158/-2.013287548247079/4/0 float=y outside=atan colors=000ISEDSD9RC<3>5P84P73O6<2>0L3<6>Xd2ag2ej2<3>xu2<5>VT1PO1KJ1<3>00\ 0AAC<2>J3SM0YN0_<3>T0hV0kW0mY0p<2>`8iaBg`Cg<17>DXjCYkBZk<3>5cl<17>QGnSFn\ TEnUCnVBnX9o<24>LENLEMKFL<2>JFIIGGKHG<4>ZOGaPGdRG<3>pXGnXJPmn<3>DgfBfdAe\ b8c_<19>mraosartb<3>zwbwtb<3>ibYeZXbUW<2>SHS<3>bHWeHXhGY<3>rAXt8Wv7W<19>\ xkaymayoa<3>ywb<4>tnVtlTsjS<2>peNocLncL<4>i_KgZKfYK<3>bVJ<3>MTF } Boogie_Woogie_7 { ; Jos Hendriks ,2002 reset=2000 type=formula formulafile=alle.frm formulaname=Jh_square ismand=n passes=1 center-mag=0/0/0.6666667 params=-2.012450635926158/-2.013287548247079/4/0 float=y outside=imag colors=000<8>000000000<3>000zzz<88>zzz<4>zzzccc<143>ccc } Beach_Tent_Stuff { ; Jos Hendriks ,2002 reset=2000 type=formula formulafile=alle.frm formulaname=Jh_square ismand=n passes=1 center-mag=-1.12092/0.549035/5.495472 params=-2.074165287254229/-0.1060234799935393/4/0 float=y maxiter=30 colors=(a)goodega.map } More_Stuff { ; Jos Hendriks ,2002 reset=2000 type=formula formulafile=alle.frm formulaname=Jh_square ismand=n passes=1 center-mag=0/0/0.6666667 params=-1.266704348177156/-2.115420862728206/4/0 float=y maxiter=30 colors=000Pmm<3>DgeBfcAea8cZ<19>mr`os`rta<3>zwawta<3>ibXeZWbUV<2>SHR<3>b\ HVeHWhGX<3>rAWt8Vv7V<19>xk`ym`yo`<3>ywa<4>tnUtlSsjR<2>peMocKncK<4>i_JgZJ\ fYJ<3>bVI<3>MTEISDDSC9RB<3>5P74P63O5<2>0L2<6>Xd1ag1ej1<3>xu1<5>VT0PO0KJ0\ <3>000AAB<2>J3RM0XN0Z<3>T0gV0jW0lY0o<2>`8haBf`Cf<17>DXiCYjBZj<3>5ck<17>Q\ GmSFmTEmUCmVBmX9n<24>LEMLELKFK<2>JFHIGFKHF<4>ZOFaPFdRF<3>pXFnXI }

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FOTD 19-01-03 (Maximum Spirals [5])
by Jim Muth 19 Jan '03

19 Jan '03

FOTD -- January 19, 2003 (Rating 5) Fractal visionaries and enthusiasts: Since yesterday's FOTD I have continued to work with a variation of the Tman formula that was posted on Friday. Working with this formula gives the impression that more than three dimen- sions are involved. I can get no clear mental image of slicing through a single 3-D object. And if there is only one dimension in addition to the two on the screen, why are the two variable parameters needed to fully explore it?. Morgan has also commen- ted on this, but for now, we'll assume that we're dealing with a three-dimensional M-set (and a six-dimensional Julibrot?). Today's image lies in the default fractal created by the TMan1 variation, near the point at the northern edge, where the two straight stretched arms criss-cross. I named the image "Maximum Spirals". I have rarely seen an image with so many spirals surrounding a midget. In the parent fractal, the scene is stretched, (foreshortened actually), and skewed. So in order to have a normal image I needed to unstretch and unskew the scene. When this was done, I was left with an image that rates a 5. I could rate the image no higher than a 5 because it duplicates scenes that lie in spirals in many valleys of the classic M-set. I don't expect to find any totally new Mandelbrot features in this formula or its variations. The interest lies in discover- ing which parts of the classic M-set are reflected in which parts of the new-shaped Mandelbrot fractals. I'll continue working with these fractals of ambiguous dimension for a few days, then it will be back to the ever-fruitful M-Mix4 formula. The render time of 9 minutes can be avoided by downloading the GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather was sunny but very cold and breezy all day here at Fractal Central. The temperature in the teens F, around -9C, kept the dynamic cats glued to the warmest spots they could find. They moved around enough to ask for food and eat, but retired as soon as their meal was done. It's cold again this morning, with clouds and a few flakes of snow in the air. But it is not as cold as yesterday. Only time will tell if the snow will turn heavier and if the intrepid cats will venture outdoors. I find myself with nothing to do again today. If I play my cards right, I'll get through the entire day without doing anything that can be considered work. Until next FOTD, take care, and one must work hard to be truly lazy. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Maximum_Spirals { ; time=0:09:08.43--SF5 on a P200 reset=2002 type=formula formulafile=triter.frm formulaname=TMan1 passes=1 center-mag=-0.003218524\ 4524517/+0.7498998373975185/2.623604e+007/4.125/-4\ 6.9647077347951267/-9.94802466789319162 params=0/0 float=y maxiter=4200 inside=0 periodicity=0 colors=000kRElLInRFoXDqaBrg8tm6tt1ur4uq6up9uoBunDu\ mGulIukLujNuiPuhSvgUvfXveZvd`vccvbevahv`jv_lvZovYq\ vXsuWruWquWpuVouVnuVmuUluUkuUjtTitThtTgtSftSetSdtR\ ctRbtRasQasQ`sQ_sPZsPYsPXsOWsOVsOUrNTrNSrNRrMQrMPr\ MOrLNrLMrLLvJJrLLoNMkOOhQPeRRaTSZVUVWVSYXOYXPZYQZZ\ QZZRZ_SZ_SZ`TZaUZaU_bV_bW_cW_dX_dY_eY_eZ_fZ_f_`g_`\ g_ah`ah`ai`bi`biacjacjackbdkbdkbdlbelcemcfmcfmdfnd\ gndgodgoehoehpeipfiqfiqfjqfkrgkrgksglshlshlthlvhlu\ ikwikuikvjkxjkyjkwjjwijuhjsgjsfiqehodgmcflbejadi`c\ g_afZ`dY_bXZaWY_VWZUVXTUWTTUSSTRRRQPQPOOONNNMLMLJL\ JIKIGJHFIGDHFCGDAFC9EB7DA6C94B71C83D95EA7FA9GBBHCD\ IDFJDGKEILFKMGMNGOOHQPISQJUQJVRKXSLZTM`UMbVNdWOfXP\ hYPiZQk_Rm`SoaSqbTscUudVwcWwdVxdVxeVxeVxeUyfUyfUyg\ UygTzgTzhTzhTzhTziUwiVuiWsiXqiYojZmjZkj_ij`gjaekbc\ kcakc_kdYkeWlfUlgSlhQlhOliMmjKmkImlGmmEnoBmmCmlClk\ CljCkiCkhCjgDjfDidDicDhbD } frm:TMan1 { c1=flip(real(pixel)),c2=imag(pixel),c3=p1 z1=z2=z3=0: t1=z1*z1+2*z2*z3 t2=z3*z3+2*z1*z2 t3=z2*z2+2*z3*z1 z1=t1+c1,z2=t2-c2*c2,z3=t3+c3 z=z1+z2+z3 |z| < 8 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 18-01-03 (Rising mandelbrot [6])
by Jim Muth 18 Jan '03

18 Jan '03

FOTD -- January 18, 2003 (Rating 6) Fractal visionaries and enthusiasts: A formula that draws the 3-D triternion Mandelbrot set was posted yesterday to the Fractint list by Russell Walsmith. As posted, the formula draws slices in the XY orientation of the 3-D M-set. After seeing what the formula would do, and being unable to resist experimentation, I made a slight modification to it. I flipped the value of initial c1 from real to imaginary, and named the modified formula TMan1. The change enables the formula to draw what I assume is the YZ orientation. Of course, it could be the XZ orientation, or something in between. I have no idea how triternions work. But regardless of the orientation, the revised formula draws slices with intact midgets. Many of these midgets duplicate scenes in the classic M-set, but some midgets are entirely different, doing strange things even while we watch. Today's image illustrates one of these new and unusual midgets. The midget (or half-midget) appears to be rising above a horizon that consists of part of another, larger midget. The fragment of a larger midget is stretched, most likely because the larger midget lies in a different plane. In the 2-D M-set, midgets are oriented in every possible direction. I assume the same thing happens with an even greater degree of freedom in the 3-D M-set. Overlapping features such as those pictured in today's scene are common in the hypercomplex M-set, but I have never seen both stretched and unstretched Mandelbrot features overlapping. I need to do much more experimenting with this three-dimensional Mandelbrot set. For now however, I'll settle for a FOTD image that rates a 6. The rating reflects the mathematical worth of the image. The artistic worth barely rates a 4. The name "Rising Mandelbrot" was inspired by the impression of one Mandelbrot midget rising above the horizon-like edge of another. The render time of 10 minutes can be avoided by down- loading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather was cold here at Fractal Central on Friday. With a temperature of 25F -4C, brisk winds, and occasional showers of snow waiting for them, the cats didn't even think of going out. They were quite contented lying by their radiators. Today is even colder, (the 8am temperature was 7F -14C), so they will be housebound for at least another day. As for me, I've got a bit of work to wrap up, then a day with little to do but wander through FractalLand. If I find anything worthwhile, it will appear as tomorrow's FOTD. Until then, take care, and when the going gets tough, get a fractal going. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Rising_Mandelbrot { ; time=0:10:14.45--SF5 on a P200 reset=2002 type=formula formulafile=triter.frm formulaname=TMan1 center-mag=-0.33019260452431920/\ +0.53369254258170410/2256.431/3.3373/149.75/-15.93\ 32167459564502 params=-0.4/0 float=y maxiter=18000 inside=0 logmap=94 periodicity=10 colors=000UKATKASKARKAQKAPKAOKANKAMKBLJCKKDJKEIKGH\ KHGLIFLKELLDLNCMODMPDMREMSFNUGNVHNWINYJOZKO`LOaMOb\ NPdNPeOPgPPhQQiRQkSQlTQnURoVRpWRrXRsXRtWSsWSsWSsWT\ sWTsWTsWTsWUsVUsVUsVVsVVsVVsVVsVWsVWsUWsUWsUXsUXsU\ XrUYrUYrUYrTYrTZrTZrTZrTZrT_rT_rT_rS`rS`rS`rS`rSar\ SarSarVbvTatSarR`pQ`nP_lO_jN_hMZfLZdKYbJY`IYZHXXGX\ VFWUEWSDVQCVOBVMAUK9UI8TG7TE6TC5SA4S83R62R41R33Q55\ Q77P89PAAOBCODENFGNGHMIJMJLLLNLMOLOQKQSKRUJTWJUXIW\ ZIX`HZbH`cGaeGcgFdiFflDhjFgiGfhHegIdfJcdKbcLabM`aO\ _`PZZQYYRXXSXWTWVUVTVUSWTRYSQZRP_QN`PMaOLbNKcMJdLH\ dKIeLIeLJeLJeMKeMKfMKfMLfNLfNMfNMfNMgONgONgOOgPOgP\ OhPPhPPhQQhQQhQUfPQhQNiRJjRGkSCmT9nT2oU4qS6pT8pUAp\ VCpVEpWGpXIpYKp_MpaOpcQpeSpgUpiWpjYpk_plapmcpnepog\ pphpqiprjpskptlpumpvmpwmpxmpympzmpzmpzmpzmpzmpzmpz\ mpzmpzmpzmozmozmozmozmozmozmnzmnzmnzmnzmnzmnzmmzmm\ zmmzmmzmmzmmzmlzmlzmlzmlz } frm:TMan1 { c1=flip(real(pixel)),c2=imag(pixel),c3=p1 z1=z2=z3=0: t1=z1*z1+2*z2*z3 t2=z3*z3+2*z1*z2 t3=z2*z2+2*z3*z1 z1=t1+c1,z2=t2-c2*c2,z3=t3+c3 z=z1+z2+z3 |z| < 8 } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] xfractint questions and quirks
by Natalie 18 Jan '03

18 Jan '03

On Wed, 13 Nov 2002 21:14:49 -0600 Jonathan Osuch <osuchj(a)avalon.net> wrote > > 1. ---------- passes=b does not work, it freezes up xfractint. > Yes, it's broke. ?It is on my list of bugs to fix. Good luck! >?> 2. ---------- Why is the initial colormap different from the > Put map=default.map in an sstools.ini file. ?Now, where to > put the sstools.ini file, I don't have a clue. I'll try to figure out where to put it. >?> 3. ---------- Is there no way to use multiple directories in > > xfractint? > Use sstools.ini to define your subdirectories. As soon as I've found out where to put it ;-) > > 4. ---------- In DOS I could move to another dir or to another ?> > drive, xfractint doesn't seem to know there are subdirs in the ?> > default dir. > Hmm, somebody should fix that. ?8-)) Would be great. ?> > 5. ---------- Is it possible to create an xfractint.rc file > Yes, use sstools.ini. Yes, as soon as ... ;-) ?> > 6. ---------- When I use <Page-Up> to call up a zoombox it is not ?> > always visible. I tried <Ctrl-Ins> and <Ctrl-Del> to change the ?> > colors, no effect whatsoever. I tried <Ctrl-I> and <Ctrl-D> too, ?> > still no change of color. When using the mouse, the zoombox is ?> > visible. It makes no difference if I use the left or the right ?> > button. Manipulating the zoombox while using the mouse seems ?> > impossible. As soon as I release the button, the zoom-in is drawn. > Mouse support is not what it should be, yet. ?One of these days > someone will get to working on it. Thank you. And what about the invisible zoombox? And the color changing? ?> > 7. ---------- Sound doesn't work always. Sometimes it beeps > Sound is not implemented in Xfractint. Doesn't really matter. ?> > 8. ---------- In the Helpscreens: Backspace to get to the Last > > Topic dooesn't work. The Helpscreens get scrambled > Other than the top line being scrambled (it's on the list), the help > screens work fine for me. ?Even the backspace works. I've tried another xterm and yes, the Backspace works and the screen does not get scrambled. It seems that the various xterms behave differently. In this xterm the 'image-is-completed' beep uses the internal speaker. In the one I previously used the sound came via the soundcard. Natalie -- Stolen tagline: Linux is like a wigwam, no windows, no gates, apache inside. [ Linux Counter: user 230952 machine: 111180 ]

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FOTD 17-01-03 (Four_Esses [5])
by Jim Muth 17 Jan '03

17 Jan '03

FOTD -- January 17, 2003 (Rating 5) Fractal visionaries and enthusiasts: Though it appears quite weird, today's image was not created with the M-Mix4 formula. It is actually part of the Z^1.93+C fractal, which, when the multi-valued nature of the complex logarithm is taken into account, is infinite in surface area. In today's case, we have examined the fractal as it appears 57 levels down the log spiral. In fractals like today's, the strangest and most interesting things are found along the negative X-axis, where the major split usually exists. This is especially true in the parent of today's image, where things that I would never expect are happening along the X-axis split. There is a fairly normal almost-quadratic midget at the center of today's image, though it lies beyond the limit of resolution. In fact the image itself is so close to the break-up point that I included a mathtolerance=/1 entry in the parameter file to be sure the image renders at the correct magnitude. The image consists of a mixture of inside and outside material. It was rendered with the inside set to < fmod >. It is this inside coloring that creates the effect of concentric rings. I named the image "Four Eesses". There are four almost-perfect letter 'S's in the image. I rated it at a 5. It takes more than a few embedded letters to make an above-average image. The render time of 17 minutes can be avoided by downloading the pre-rendered GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Now let's get to constructing that 4-dimensional 24-cell. To keep things simple, we'll start at the two-dimensional level. It's best to have a glass-topped light table, straight edge, and X-acto knife for this kind of dissection and construction. I did a lot of this kind of play stuff back in the slow times of the good old days of the 70's and early 80's, when I worked at a light table, cutting and pasting by hand. But since light tables are expensive and not everyone has one, the same thing can be done with paper and scissors. As I said in yesterday's FOTD, the 24-cell is the only regular 4-dimensional polytope that has no analog in 3-space. It does however have a corresponding figure in 3-space that is similarly constructed -- the rhombic dodecahedron. To understand the construction of the rhombic dodecahedron we can start in 2-space, with two equal paper squares. Lay the two squares side by side on the table top. Then take one square and cut it along its diagonals, resulting in four right triangles, whose bases are the edges of the square and apexes the center. Now take the four triangles and attach their bases to the four edges of the other square. The result is a larger square, rotated 45 degrees, with twice the area and 1.4142 times the width. Not a very impressive construction, but it is a start. The next step will be a three-dimensional one -- more difficult to perform, but relatively simple to visualize. Lay two equal cubes on the table. Take one cube and slice it into six square pyramids, whose bases are the faces of the cube and apexes the center. Then take the six pyramids and attach their bases to the six faces of the other cube. The resulting polyhedron is a rhombic dodecahedron. It is not a regular figure because its rhombic faces are not regular, and more importantly, because it has two different kinds of vertices -- those where 3 edges meet and those where 4 edges meet. The final step -- the construction of the 24-cell -- cannot be visualized, but the analogy is so clear that it can be followed. To begin, we need an extra dimension. Assuming we have found the extra dimension, we can get started. Lay two equal 4-D hypercubes on the hypertable. Take one hypercube and slice it into eight cubical hyperpyramids, whose bases are the cells of the hypercube and apexes the center. Then take the eight hyper- pyramids and attach their bases to the eight cells of the other hypercube. The resulting figure is the 24-cell. 4-space is the only space higher than 2 in which this construction produces a regular figure. In the higher spaces, there are too many lower- dimensional parts to the figure, which must be shaped and fit together just right. It appears I'm getting so involved in hyperspace that I almost forgot about the Fractal Central weather. The weather was cold again here at Fractal Central on Thursday, with a temperature of 28F -2C and only a hazy sun. The cats chose comfort over adventure. They decided to spend the day indoors. This morning is once again cold, and to make matters worse, about 3cm of fresh snow fell overnight. The cats, who dislike cold wet paws, will not be happy about this. I have a minor pile of work sitting on the shelf to my right, but unlike the fractal duo, I can do more than be unhappy about the situation. So until the next FOTD appears almost by magic in 24 hours, take care, and be moderately happy. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Four_Esses { ; time=0:17:30.18--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-0.4282456346546068/+0.0113573879900267\ 6/5.48016e+012/1/-132.5/0.00936043190115933704 params=1.93/0/-57/0 float=y mathtolerance=/1 maxiter=1200 inside=fmod periodicity=10 colors=000_U2bS2cR2eP2hR2gP2eN2eM2cM2cL2bJ2bI2`I2_\ G2_F2YD2YD2XC2XB2VB2U92U83S74S74R56R47P28N28N1AM0B\ M0BL0CL0EJ0FI0FI0HG0IG0KF0KF0LD0MD0MD0TD5ZF9fDCdDD\ bCGbCIaBLaBM_BPZ9RZ9UX8VX8YW7_W7bU7cT5gT5hR4kR4mQ2\ qQ2rO2vM1wM1zL0zL0zK0zK0zK7z25z25w25t25r25o25k24j2\ 4g24c24b24_24X22V22S22P22N32L42I62G71G70F70F60D60D\ 60C60C20C20C600A00B00C00E00F00F00H01I01K01L02K02K0\ 2L04M04M04L05M05M05N05M07N07P07Q08S08S08T19V19X19Y\ 2BY2B_2BY4CW4CY4Cd5Df5Dg5Di5Di4Ck4Ck4Ck2Ck2Au2Ak2C\ k1Ck1Bl1Bl1Bl0Bl0Bl0Bl0Bl0Ba0Bl09n09n0Sn09n0Sv0Qn0\ 9n09n09n08d08k08o08o08o08o08o08o07o08p09n09n0Bk0Ck\ 1Ch4Dg5Fe7Fe8GbBIaCIZDJXGLUILTJMQMNMNNLV14U24S44R5\ 4P54N73M83L93J93IB3IC2GD2FD2DF2CT27E29I28J27L25M20\ M25T2S`FSlWbqUloUqmTrkTtjTthRvgRveQwcQybQy`Oz_OzYO\ zXMzVMzULzSLzRLzPKzNKzLMzMKzMIzNHzNEwNCtPBqP8oP7kR\ 6hR4eR2cS2RY3SY2VX2XV2YU2 } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-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 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] FOTD 15-01-03 (Nest of Tachyons [8])
by Jim Muth 16 Jan '03

16 Jan '03

At 06:49 PM 1/15/03 +0000, John lewis wrote: >And if you could persuade one [tachyon] to travel in a >circle -- it would never overtake itself? Interesting idea. Exactly what would happen? I rather suspect that the tachyon would soon reach infinite speed and disappear from our view, having gone back in time. A tachyon moving faster than light would likely create a shock wave, which would cause it to lose energy and therefore increase its velocity to infinite. At infinite speed, a tachyon would travel backward in time at the same rate we are traveling forward. >>Until next time, take care, and never forget that we >>are made of tardyons. >Especially when we feel lazy? Most especially when we are fractal cats. Jim M.

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FOTD 16-01-03 (Negative is Positive [4])
by Jim Muth 16 Jan '03

16 Jan '03

FOTD -- January 16, 2003 (Rating 4) Fractal visionaries and enthusiasts: I am always fascinated by polytopes of higher dimensions, particularly the regular polytopes of the fourth dimension. In 4-space, six regular polytopes exist. The 5-cell corresponds to the tetrahedron of 3-space; the 8-cell, to the cube; the 16-cell, to the octahedron; the 120 cell, to the dodecahedron; and the 600-cell, to the icosahedron. But in 4-space there also exists a polytope known as the 24-cell, which would appear to have no corresponding figure in 3-space. This appearance is not totally true. The 24-cell has no corresponding regular figure in 3-space, but it does have a similarly constructed figure -- the rhombic dodecahedron, which consists of 12 rhombic faces, 24 edges and 14 vertices. Curiously, the rhombic dodecahedron is a space-filling figure. In tomorrow's discussion, we shall construct a 24-cell polytope from the ground up, but before then, we have today's fractal to examine. Today's image is named "Negative is Positive". I gave it this name for two reasons -- first: many of my images result from combining negative powers of Z, which is a positive thing, and second: I received a junk e-mail this morning from a spammer, which is nothing unusual. But this letter was intended to sell an anti-spam program to me. It began by saying "If you had our product, you would not have received this letter." My mental reply was, "It's always best to start the day with a laugh." Then, after a moment's consideration, I deleted the e-mail and named today's image. Though its name was given in jest, today's image has perhaps a bit more of the negative than the positive about it. The rating of 4 is quite a comedown from yesterday's, but then, we can't be above average on every day. And yes, the image was created by combining two negative powers of Z, in this case -3 and -5. The parent of today's scene is a rather comical figure resembling a lobster sitting on its blunted tail. Today's image is located at the tip of an irregular filament near the point where the lobster's right claw joins its body. The image renders from the attached parameter file in just over 3 minutes. The GIF file of the completed image downloads in even less time. The download may be found at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> With a temperature of 25F -4C, Wednesday was very cold and windy here at F.C. Occasional flurries of snow made things even worse. The F.C. cats spent the entire day indoors, checking the outside conditions several times, but turning around as soon as their sensitive noses felt the chill. Today is starting just as cold, and more snow is threatening. The cats will have another unsatisfactory day. My day will be satisfactory if I find a perfect fractal, which is unlikely. Until next time, take care, and remember that no one is perfect. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ NegativeIsPositive { ; time=0:03:15.26--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.23970545929533/-1.269509193680854/9.\ 148861e+009/1/170/7.41674007990883455e-005 params=1/-3/0.5/-5/0/0 float=y maxiter=1200 inside=0 logmap=60 periodicity=10 colors=000OCVPCYQAaT9gV7jW5iX3n`2qd1ph1nl0mp0kt0ix\ 0hz0fz0ez0dx0ct2aq5`m8_iAYfCYcGX_IWWMVTOTPSSMVQJXQ\ I_PH`PHaPGdOGeOFfODhODjNClNCmNBoNAqMAsM9tM9vMDtLIt\ JNtIStHXtGatFftDltCqtBwtAztAxpBvlCthDqdFo`GmXHjTIh\ PJfMLdIMaFN`BOY8PW5QV2QQ8TNDWJJYHP`DWcAae8ffBhhDhi\ GijIilLjmNjoQloTlpWmqYms`otcoveovcisaep_aoYYlXViVQ\ hTNeSJcPGaOC_N9Y1DD1AG08I05L03M52TB1_H0eN0lT0sS2tQ\ 5tP9tOCvNGvMJvLNwLQwJVwIYxHaxGexFizDmzCqzCvzVpqmjj\ hihdhe`fcXeaTd_OcXLaVHaTD`QA_O5YM2XL0WI0VG0VF0`P0f\ _0li0st0xz1mz8cvFVqMLmTCizpHzoFzmCzmBzl9zl7xj5wj3v\ i1th0sh0qf0pf0oe0oe0WJ5D0LI5MNANSGOXMP`QQeXSjcTpiV\ toVvmNvoGvq9vs3su5pw5my5jz5hz7ez7cz8az8_zAYzCXzDWz\ GVzITzJSzMQzNOzPNzSMzTLzWJzYIz_HzaGzcJzWMzOPzHSzBW\ zLYzV`zcczmezwazq_zlXzhVzcSzYPzVSzWVzWXzW_zXazXdzX\ fzXizYlzYozYqz_tz_wz_zz_xzYxzYxzXxzXwzWwzWwzWwzVwz\ VvzTCz5FzAGzDHzHJzMLzPMzT } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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inside=atan
by Guy Marson 16 Jan '03

16 Jan '03

Dear Jonathan, Stone-Soupers, Fractinters, high magnifications of midgets with 'inside=atan' are highly maxiter-sensitive, thus pretty difficult to manage. Is there a trick to find the right value for maxiter? After a time consuming 'try ad error' periode, I found a way to get appropriate maxiter=nnn values. Here are examples for 5 orders of maxiter. Low mag's as 'startman' are easy to manage.. No value for maxiter below the value for the first order leeds to a nice pic and the value for the first order is no easy to find.. So it would be great to implement 'maxiter' to the evolver, and, if it's possible, the 'proximity value for inside=epscross and fmod' (x-screen) too.. Try to change the values for maxiter and see the results.. startman { ; time: 0h15' on a K7/600 ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=d center-mag=-0.538232/0.00782014/0.929296/1/-90/3.88578058618804789e-016 params=0/0 float=y maxiter=8000 inside=atan symmetry=none periodicity=0 cyclerange=1/1 colors=000<3>321421031642<51>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000\ 001<56>Q_tQ`uR`v<2>SbyTczSby<61>000 } ataniter { ; 1th order =12033 ; time: 0h26 on a K7/600 reset=2002 type=mandel passes=d center-mag=-0.74896255201844790/+0.05435555412152205/7.927134e+011/1/-4.\ 99675937785410795/-0.0902709561915964742 params=0/0 float=y maxiter=12033 inside=atan logmap=yes symmetry=none periodicity=0 colors=00000T<24>005004003<2>000000222<4>DCEFEGIGI<3>QORSQTUSW<4>c`ddaff\ ch<3>lhnmjonkq<3>soutovtpw<3>wrywszwsz<2>xszxszwry<6>sousnurnt<3>okqnjpl\ in<2>hejgciebgc`e<3>XVZWTXURV<5>HGIFEGDCD<3>444<39>ma1na1pb1<2>se1se1re1\ <3>pc0ob0ma0<27>860750540430220000<34>00`00a00b00c00d00f<13>00U } atannumb { ; 2th order =24066 ; time: 1h26 on a K7/600 reset=2002 type=mandel passes=d center-mag=-0.74896255201845010/+0.05435555412154748/2.119379e+012/0.999\ 9/-4.99548275077093162/-0.086997345982712887 params=0/0 float=y maxiter=24066 inside=atan outside=0 symmetry=none periodicity=0 colors=000000<57>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`\ uR`v<2>SbyTczSby<61>000 } atanfmod { ; 3th order =36099 ; time: 0h46 on a K7/600 reset=2002 type=mandel passes=d center-mag=-0.74896255201844790/+0.05435555412152205/6.97086e+011/1/-4.9\ 9687607663320321/-0.0914427337369515397 params=0/0 float=y maxiter=36099 inside=atan proximity=0.007 outside=fmod symmetry=none periodicity=0 colors=000000<57>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`\ uR`v<2>SbyTczSby<61>000 } atansumm { ; 4th order =48132 ; time: 0h55 on a K7/600 reset=2002 type=mandel passes=d center-mag=-0.74896255201844790/+0.05435555412152205/1.113368e+012/1/-4.\ 99670916040466828/-0.0879347820503879468 params=0/0 float=y maxiter=48132 inside=atan outside=summ logmap=yes symmetry=none periodicity=0 colors=000A81<3>431320110000000<29>4hg4ji4kj<3>5qp6sq6ts<3>6zy<30>2IH2GF\ 2FE<3>198077065<2>011000001<34>HNqHOsIPt<2>JRyKRzJRy<34>349237226<2>0010\ 00110<29>hZ7j_7k`7<3>qe8sg8th8<3>zl9<33>C92 } atanatan { ; 5th order =60165 ; time: 1h22 on a K7/600 reset=2002 type=mandel passes=d center-mag=-0.74896255201845010/+0.05435555412154748/1.356392e+012/1/-4.\ 98344032497560363/-0.100894378737287849 params=0/0 float=y maxiter=60165 inside=atan outside=atan symmetry=none periodicity=0 colors=000<58>ARtASuBSv<2>BUyBUzBUy<55>136125024<2>001000110<56>tr9us9vt\ 9<2>ywAzxAywA<61>000 } have fun, Guy

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FOTD 15-01-03 (Nest of Tachyons [8])
by Jim Muth 15 Jan '03

15 Jan '03

FOTD -- January 15, 2003 (Rating 8) Fractal visionaries and enthusiasts: Today's image is a lot like yesterday's, though I spent a bit more time on it and worked the coloring up to where the image earns a somewhat liberal 8. When I was finished, I named the image "Nest of Tachyons". Like the name I gave yesterday's FOTD, the name of today's image has little to do with the image's actual appearance. In fact, certain colorations that I tried and then discarded resulted in an image resembling rings of shark's teeth. Tachyons are hypothetical particles that travel faster than light. Perhaps it would be best to call such particles imaginary, for there is no evidence that they do exist and good reasons why they cannot exist. But if such particles did exist, they would travel backward in time. They would reach their destination before they left their point of departure. This attribute of tachyons might raise thoughts of backward time travel. We might latch on to a tachyon and go back in time to warn our earlier selves of all the mistakes we have made. If we could go back in time only a few hours, we could give ourselves the winning lottery numbers in time to buy a winning ticket. It's a good dream, but it will never happen. The natural world seems to treat backward travel in time as a taboo. Every time we discover a way we might do it, we soon find a reason why the way we have discovered will not work. No matter how clever our schemes, we are frustrated by some ineluctable law of nature. It reminds me of the situation we face with the uncertainty principle. If we try to determine both the position and momentum of an electron at the same time, we find the task impossible. The more accurately we know one, the vaguer the other becomes. Something always gets in our way. In this case, it is our assumption of the nature of the unmeasured electron that has led us to mistakenly look for something that does not exist. An electron is a wave of probability, with no definite attributes until we pin it down by our measurement. We naturally cannot measure what does not exist. I strongly suspect that when we contemplate the possibility of backward time travel, we make another wrong assumption. We assume time itself to be something that it is not. That 'grandfather' paradox could be trying to tell us something important. We often see black holes presented as possible means of time travel and faster-than-light travel. The problem with this method is that we could not survive the tidal forces as we pass the singularity. We also see multiple universes optimistically mentioned as a possible means of going backward in time. We have dark matter and dark energy which some say could be the gravity of these alternate worlds bleeding into our own universe. We have a cosmic repulsive force, which is said to result from the energy of the vacuum. We have many signs and theories that other worlds might exist, but no possible way of reaching them. We must face the fact that our one-way trip into the future, which actually is time travel, cannot be escaped. And I must face the fact that I have again wandered from the topic of fractals. I can see no way in which fractals could be a means of time travel, but stranger things have happened. With its 5-minute render time, today's image is mercifully fast. But even faster is the download from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> It was quite cold here at Fractal Central Tuesday, remaining just below freezing despite the strong sun. At this time of year the earth is about as close to the sun as it ever comes, yet the temperature is about as cold as it ever gets. Not concerned with astronomical trivialities, the dynamic ones (cats, that is) remained outside only a few minutes before getting their whiskers chilled and retiring indoors to their favorite heat sources. Today is starting cold again, and to make things worse, a fresh dusting of snow is on the ground. The fractal cats will not want to hear this. As for me, I always take whatever comes. (I have no other choice.) Until next time, take care, and never forget that we are made of tardyons. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Nest_of_Tachyons { ; time=0:05:43.17--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-1.36800428773697500/+0.557337704952596\ 80/2.390289e+007/1/-37.5/-6.94211269788858054e-008 params=3.7/-0.85/0.1/-8.5/0/1e+100 float=y maxiter=120 inside=fmod proximity=0.5 periodicity=9 colors=0005zA5zA8zD8zD8zGAzGAzGAzIDzIDzLGzLGzOGzOI\ zOIzQIzQLzTLzTLzTOzWOzWQzYQzYQz_Uz_Uz_UzbWzbWzeWze\ YzgYzg`zg`zj`zjczmczmczoezoezoezrgzrgztjztjzvjzvmz\ vmzymzyozzozzmzzozzozzozzozyozyozyozyozvozvozvozto\ ztoztoztozrozrozrozrozoozoozoozmozmozmozmozjozjozj\ ozjozgozgozgozeozerzerzerzbrzbrzbrz_rz_rz_rz_wzYwz\ YwzYwzYwzWwzWwzWwzTwzTwzTwyTwyQwyQwyQwxQxxOyxOzxOz\ xLzxLzxLzxLzxIzxIzwIzwGzwIzxIzxLzxLzxOzxOyyQxyQwyT\ wyTwyWvzWuzYtzYsz_rzbqz_pz_oz_nz_mz_kz_iz_gz_ez_cz\ _az__zYYwYWwYUuYPuYKrYFpYApY5nY2kY2kY2hW2hW2fW2cW2\ bW2aW2`W2_W2YW2WW2UW2SV2RU2QT2PS2OR2NQ5MP5LO5KN5JM\ 5IL5HK5GJ5FI5EH5DG5CF5BE5AD59C58B57A56A55A54A53A82\ A81A80A80A80A80A80A80A80A80A80A80L80L80L80L80L80L8\ 0L80L80LA0OA0OA0QA0QA0TA0TA0WA0WA0YA0YA3_A8_ABaAGc\ AIeAKgAMiAOkAQmASoAUqAWsAYuA_wAaxAcyAezAgzAizAkzAm\ z8oz0qz0sz0uz0wz2xz2yz5zz } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 14-01-03 (Polytope Paradise [6])
by Jim Muth 15 Jan '03

15 Jan '03

FOTD -- January 14, 2003 (Rating 6) Fractal visionaries and enthusiasts: While at least one member of the Fractint list appears to perhaps be losing a bit of enthusiasm for fractals, there is no danger of a similar fate befalling myself. The only thing I regret is that I lack the time to explore more of the infinitely infinite world of fractals. Perhaps the first sign of impending boredom with fractals is the desire to add multiple layers, as if a single-layer fractal needed something to give it more interest. Then again, perhaps my devotion to single-layer fractals is an individual quirk of mine, caused perhaps by my typical male tendency to concentrate on one task at a time. After all, multiple layers works very well in the case of music, which is candy for the ears; why not in the case of fractals, which are candy for the eyes? I named today's image "Polytope Paradise". I can give no logical reason why I chose such a name, since a polytope is a geometrical figure, existing in n-dimensional space and enclosed by a finite number of planes or hyperplanes. The strings of bubbles in today's image are enclosed by curved 2-D surfaces rather than planes, and therefore cannot truthfully be consid- ered polytopes. As a matter of interest, the word 'polytope' was invented by Alicia Boole, the daughter of logician George Boole. In 1-space and 2-space, an infinity of regular polytopes are possible. In our everyday 3-space, only 5 regular polytopes are possible. In 4-space, 6 are possible, but in 5-space and all higher spaces, only 3 regular polytopes can exist. Today's image is another ghostly one, consisting entirely of trapped points whose orbits have been made visible by the bof60 inside fill. The generating formula combines 1/Z and Z^(-2), then adds 1/C. The image itself rates a 6. The render time of 41 minutes for today's image is admittedly slow. The wait can be avoided by downloading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather was actually not too bad on Monday, with warm sun, little wind, and a temperature of 43F 6C. The fractal cats found the outdoors reasonably comfortable. Tippy, the lean lanky tabby, spent nearly two hours in the yard. Thomas, the overweight yellow, returned indoors after one hour. No treats were needed. Today however is much colder, and the dynamic pair will not find it so pleasant out of doors. I will not find it pleasant until the work is finished. The next FOTD will appear in 24 hours, so take care, and see you then. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Polytope_Paradise { ; time=0:41:12.86--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.84049791931695570/+0.257654873112327\ 50/235620.6/1/-65/5.48976843151027794e-010 params=1/-1/1/-2/-32/1e+100 float=y maxiter=900 inside=bof60 logmap=yes periodicity=10 colors=000zzzzwyzuxzswyqvyouymtxlsxksxjrwirwhqwgqv\ fpqepldjgbcb`YYZRTXLNWGOVFPUFPTEQSEQRERQDRPDSODTNC\ TMCULBUKBVJBVIAWHAXH7YGAZFD_FF`EIaELbDNcCQeCTfBVhB\ YiA`i9bhAbgAaeA_cAZaAY_AWXAVUAUSBSPBRNBPLBOJBNGBME\ BKD8KCBJBDI000AIHALG9NG8PF8SE7UE7XD6ZD6aC5cB4eB4hA\ 3j93m92o82q84o96mA7kB9jCAhDCfDEeEFcFHaGI_HKZHMXINV\ JPUKQSLSQMUPMVNNXLOYJP_IQaGQbERdDSeBTg9Uj6Vh8Ug9Uf\ BUeCUdEUcFUbHUaIU`KUZLUYNUXOUWQUVRUUSTTUTSVTRXTPYT\ O_TN`TMbTLcTKeTJfTIhTHiTIqNGjTEcZCXdAQj8Jp5Dx7Cv9C\ uACtCBsEBrFBqHBpJAoKAnMAmNAlMBkMBkMCkLCkLCkLDjLDjK\ EjKEjKEjKFiJFiJGiJGiJGiIHhIHhIIhHIhHIhHJgHJgGKgGKg\ GKgGLfFLfFMfFMfFMfENdEOcDPbDQ`CR_CSZCSYBTWBUVAVUAW\ T9XR9XQ9YP8ZO8_M7`L7aK7aJ6bH6cG5dF5eE4fC4fB4gA3h93\ i72j62k50m22k44j66i88g99fBBeDDcEFbGGaII`JKZLMYNOXO\ PVQRUSTTTVSVWQXYPY_O_aMacLbdKdfJfhHgjGikFkmDloCnqB\ prAqVNIXPLYQN_RP`SRaTTcUV } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 13-01-03 (Mysterious Energies [7])
by Jim Muth 13 Jan '03

13 Jan '03

FOTD -- January 13, 2003 (Rating 7) Fractal visionaries and enthusiasts: Unable to find a good opening for today's FOTD discussion, I shall simply place my mind in idle and let my thoughts ramble where they will. Now let me see . . . Every day for almost the entire life of the FOTD, I have opened the discussion with the line 'Fractal visionaries and enthu- siasts'. I do it without thought of the meaning, since the line is part of my pre-formatted FOTD template file, and is inserted into the text of the discussion automatically. The nature of the fractal enthusiast mentioned in the line is obvious, but what is a fractal visionary? My dictionary defines the word 'visionary' both as an adjective meaning 'existing only in the mind', and as a noun meaning 'a person who sees visions of hidden things'. So a fractal visionary is one who sees visions of the normally hidden things known as fractals, (which BTW are only partly unreal). Those who can see things, real or unreal, that others cannot see are also known as mystics. In times past, mystics were seen as wise people; in our present age of reason run amok, they are looked upon as a little weird, amusing but harmless -- that is unless they start claiming and convincing too many others that their visions are actual glimpses of other real worlds, in which case they must be shown to be deluded. In this age of reason, there is and can be only one real world, the physical world, with which we can be in touch. There is no possibility of interaction with other real worlds, which preferably do not exist. This status quo must be preserved at all costs. Well, I often see things that others cannot see with eyes alone, though I'm not sure if this makes me a mystic. The things I see are called fractals, and must be seen with the aid of a computer and monitor. With my real eyes, I can see fractals on my computer screen whenever I wish, and I sometimes see them in my dreams as real 3-D objects existing and evolving in 3-D space. Since others can at least see my fractal visions on their own computer screens, I guess this makes me a mystic of the second order. I could not be a mystic of the first order unless others could also see the fractals I sometimes dream of in my dreams. Today's image is a fractal of the third order. It is mystical in the sense that it cannot be seen without the aid of a computer and also that it is another of my 'evaporated' images, which consist entirely of the ghost of a fractal that once was there. (To see the fractal that once was there but has vanished, change the imag(p3) parameter from 10^100 to zero.) The parent of today's image consists of a multi-lobed string of bays extending north to south. A filament extends southwest from the southernmost bud, and terminates in a zig-zagging ring. Today's scene lies on this ring, not far from where the filament joins it. I named the image "Mysterious Energies" for no good reason, and rated it a 7 because in my opinion it is above FOTD average. The render time of 9 minutes is a bit beyond the range of reason for those with busy lives to lead. But the already completed GIF image is available for download on the internet at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather Sunday was sunny but cold here at Fractal Central, with a high temperature of 29F -1.5C. The cats endured their indoor confinement with patience, blaming me only twice for the chilly conditions beyond the door. Today has so far been uneventful. Hopefully, it will remain so, as there is a bit more than the average amount of work to be done. Until next time, take care, and is it reasonable to believe that fractals are real? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ MysteriousEnergies { ; time=0:09:16.89--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.80567324593928600/-2.034640713112640\ 00/2.056237e+009/1/-62.5/2.93630749607157182e-005 params=-7.57/-1.5/-0.98/-6.5/0/1e+100 float=y maxiter=900 inside=bof61 periodicity=10 colors=000_QjXSl000STmVXgXYaY`Y_aS`dOcfIdiDfj7gm3i\ o0jp0fo0co4`oAYmFVmLSmQOlXLl`IlfFjlCjr9jvDdxI`xMVx\ QQyVLyYGyX`pXuiXzarz0mz0jz0gy0dv0as0_p0Xm0Tj0Pg0Md\ 0Ja0000DX0AT07Q04P0CV9J`GQdOYjVcoaczfczigzclm_o`Ts\ OPxAJz0Fv1Js4Mp7PmASjDVgGYcJ``McYPfVSiSVlPYoGMv9Cz\ 11z00z0Az0Tz0jzLVTfG0cM0aS0`X1Ya4Xg6Vl7SrA000PzDQz\ GSzITzLVzMXzOYzQ_zS`zTazXczYdz_fzagzcizdgxc000dpac\ m`ci`000`aY__YYVXYSX`VQaXLc_Fd`Agc4id0jg0li0gf0dc0\ ``0YY0TV0QS0MP0JM0FJ0CG07D04A00700410A10730N40F40P\ 60L60S70S70Y90_A0eA0dC0nC0lD0uD4iAGi9T_7dV4rP3zL1y\ Q6uV9r`CmdGiiJfoMasPYxTVzXQz_OzaPzcQzdSzfSzfTzgVzi\ XxiXvjYul_rl`pm`oo00ocjpdirdgrQfpCfo0fo3_f6T_0S_0S\ _0Ma6Gd_QT`Qa`QjgJ`mCQu4Gz07x4MvA_sGlrMypSzmXzl`zj\ dziiz90_DAPIQGMg6Px0Ts1Yo6aj9fgDjcGo_LsXOpTGmQAfMG\ _IMSDSM9YF4c70i10m41f66_7AT9FMAJGCO9DS37`01g0Ai0Ij\ 3Pl7XmCcoGjpLrrPyrTupQpoP } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 12-01-03 (Hidden Flames [5])
by Jim Muth 12 Jan '03

12 Jan '03

FOTD -- January 12, 2003 (Rating 5) Fractal visionaries and enthusiasts: I'll have to keep today's discussion short. It's already past 10am and the Fractal Central support staff is becoming impatient to set out on a trip to search for some old and worn-out objects which she must have. When the parameters of today's image are entered into the MandelbrotMix4 formula, all the excitement lies beyond the right edge of the default image, where a pair of siamese minibrots straddles the X-axis. Today's image lies in a spiral in the shoreline chaos of the bay that connects the pair. I named the image "Hidden Flames" because of the subtle flame- like features that dot the arms swirling toward the center. I rated it at a 5 because, despite my best intentions, it is still only an average image. A bit farther out in this same area lies a row of minibrots unlike any I have seen before. If things work out well, these midgets in a row may appear in a soon-to-come FOTD. The 14-minute render time drags when the fractalist has other things to do. It would be more convenient for most to download the already-rendered image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Though we had brilliant sun all day Saturday, it was quite cold here at Fractal Central, home of the dynamic duo of fractal cats. Brisk winds and a temperature in the 20's F, minus single digits C, kept the dynamic ones indoors, behaving very un-dynam- ically. Since cats of the fractal variety need outdoor warmth to enjoy life, the cats were unhappy, and a treat of tuna only partly lifted their flagging spirits. Today is once again cold, but not quite as cold as yesterday. Maybe the duo can find peace of mind. As for me, I find I have semi-volunteered for a trip to a local antique mall. These 'shopping' trips always raise the question, "if you don't know what you're shopping for, how will you know when you find it?" Until tomorrow, take care and keep your cat warm. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Hidden_Flames { ; time=0:14:24.46--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+2.85671879185512400/+0.016441220570067\ 03/7117130/1/85/7.17137860692385054e-008 params=4/-6.4/-6/-3/0/525 float=y maxiter=12000 inside=0 logmap=220 periodicity=10 colors=000CzzCxz5wz7uz7tx7ru7qr8oq8nn8nk8lh8ke9ic9\ h`9fZ9fa5hS9cVCbWE`ZIZ_LXbNVcSTfVQhXPm`Ml`JoiLybIn\ eGsbDlbAr`8i_7hZ4eK0KW0aV0_T0ZP0`S0XV0TX0Q_0Mb0Je2\ Gh3Dk59n75q93tA0wD0zE0zC0zG0zJ0zN0zS0zW2z_5zc8zhCz\ lEzqHzuLzzNtzQezWoz`0ziize2zb7z_AzWGzTJzQNzNTzJXzH\ bzEfzAlz8qz5xz0uz3tr4rk5ob7nV8tM8lN9fPA`QCWQDPSEJT\ GEVH8XJ9VHATECSCDQAEP8GM5HQ3IJ2JW0LH0M_0IT8GfLCuZ9\ l_Ew_IePN_ESV4P55NP7M88J99IAAHCCEGEGDDHCCI9CJ8AL5A\ M49N29N08P08Q07S07T05V05W04W04Z08`0Ac2Df5HiAJlEMoJ\ QrNTuTWxXZwZWu_TpTQtTNtcLreIreGqfDohAoi8nk5nl3ln0l\ n0if5h`CfWIeQNcLV`G`_AfZ5nX0uW0z_2zb7zfCziIzlNzqTx\ t_xxbxzbxzbxzbzzbzzbzzbzzbzzbzzbzzbzzbzzbzzbzzbzzb\ zzbzzbzzbzzbzzbzzbzzbzzbzzbzzbzzczzczzezzezzfzzfzz\ hzzhzzizzizzkzzkzzlzzlzznzznzzozzozzqzzqzzqzzqzzqz\ zqzzqzzqzzqzzqzzqzzqzzqzzqzzqzzqzzqzzqzzqzzqzzqzzq\ zzqzzqzzqzzqzzqzzqzzqzzqz } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 11-01-03 (Down Down Down [5])
by Jim Muth 11 Jan '03

11 Jan '03

FOTD -- January 11, 2003 (Rating 5) Fractal visionaries and enthusiasts: For today's FOTD fractal I simply changed the 2's of yesterday's formula to 3's. Some adjusting of real(p3) was necessary to produce a promising fractal. The fractal that resulted is an oversized circle filled with debris. Today's scene is located at the bottom edge of this bloated circle. I named the image "Down Down Down" because while studying it for a name, I had the impression of looking down at the burning coals of a fiery pit, maybe not the pit ruled by Hades, god of the underworld, but fiery nonetheless. The image has little going for it other than the effect of a bed of glowing coals toward the center, thus I could rate it no higher than a 5. But, rendering as it does in less than 2 minutes, the image at least will consume little of the time of those who choose to run the parameter file. As always, the completed GIF image is available at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The Friday weather was typical of the season here at Fractal Central, with clouds, sun, wind, flurries of snow, and a high temperature of 38F 3C. Despite the chill, the fractal cats managed over an hour in the outdoors. When they came in, they were both happy and hungry. I have a relatively slow day ahead of me, which should give time for an above average fractal for tomorrow. Until then, take care, and I've found a projective plane, but it's too large to fit on the shelf beside my Klein bottle. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Down_Down_Down { ; time=0:01:55.34--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.07563752269483708/-7.541266062129865\ 00/5.6606e+009/1/-102.5/-0.0246641156100383535 params=3/3.3/-3/-3.33/-0.995/0 float=y maxiter=350 inside=0 logmap=36 periodicity=10 colors=000IHzBSz4Xz0iz2jz9dwEZoKTgQN`SHOaBLj9Bm72r\ 50z40zZ0zc4zhDznAWB7VA5R92Q71Y9AdAIlBRrDZzEgzGpzHx\ zO`rWElNOeGZ`9iV1tO0zL1lI7VGDDDI0Lz0QxATwLWuW`tgcr\ tepzGNm00Z07d5IiEVmLetVrxazzRzoHzc9xR0wG0u40l5Ad5K\ W5TO5aaDjmItzQzzWwzZtz`pzcmwdjrggoidgcaaY`WTYONVIH\ TDDWIGZOIaVLc`OeeRilVjpYelQagIZcDV`5RW0NR0KO0HWAGc\ YEjuGYiGLZG9NG0DzVIzLGmDE`4BN0AZ7EjGHwOKoVLiZLadNW\ iNOoOItOLxZNzgOzpTzeYwWatNepDim4dd9aWBZNGVEIR5NO0Q\ K0KG0EB097022002cr9YoDTlINjNIgTDdY9cc2`g0Zi9ZiIZiT\ ZicZimZ`cLRTAII0A90EB1IDHNEYQGlWHdaIYgKQlGWoDarAew\ 7lz4rz1wxKrtcoowjlzgezi`rjVelOWmIKoDAp70r`RdTKgLEj\ E9m72p2Hj0Wd0i`0xV0zQ0zK0zE2zA7z4Bz0Ez0Iz0Lz0Qz0Vz\ 7ZzHazTezdjzoozzrzzozZmz0iz9dzHazRYz`VziRzaQzVOzNN\ zGLz9Kz1Rz9ZzEezKmzRuzYzzczzizzrzzzzzzzzzzzzzzzzzz\ zzzwzzuzzKz0Hz0Ez0Dz0Gz0Iz0Lz0Oz0Rz0Tz0Wz0Zz0az0dz\ 0ez0az0Zz1WzARzIOzRLz`Qzz } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 10-01-03 (Two Satellites [7])
by Jim Muth 10 Jan '03

10 Jan '03

FOTD -- January 10, 2003 (Rating 7) Fractal visionaries and enthusiasts: To produce today's fractal, I took most of the 1's in the formula of yesterday's fractal and changed them to 2's. I had no mathematical reason for doing this, I did it only for fun. (I could not simply change the 1's in yesterday's real(p3) parameter to 2's because doing so would have produced an inferior fractal.) When all the number-changing was finished, I had created another oversized area of chaos, this one with its main Mandeloid well beyond the borders of the default screen. This Mandeloid resem- bles a nearly perfect M-set. Today's scene is located in one of the rays radiating from a larger midget, which lies just beyond the tip of the main stem of the large Mandeloid. Thanks mostly to the strong coloring, the image rates a 7. I named the image "Two Satellites" when I noticed the two prominent areas in the corners of the image, which obviously hold still smaller midgets that are beyond resolution. The render time of 7 minutes is fast enough, but downloading the finished GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> will leave more time for other things. Thursday was an exceptional day here at Fractal Central. How often does a day come in the middle of winter, with almost hot sunshine and a temperature of 63F 17C? . . . Once every two or three years? The dynamic cats took advantage of the unusual conditions by spending almost the entire afternoon in the yard, trying to ignore the remaining puddles and mud. Needless to say, their moods were as exceptional as the weather. Today is starting sunny but colder. It will be harder for the dynamic ones to stay happy, but they are already eager to get outside and give it a try. And as always, I have a few tasks to finish, so until next FOTD, take care, and I wonder where I could find a Klein bottle. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Two_Satellites { ; time=0:07:21.10--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-7.38358917092518/+20.54585830913693/6.\ 4431e+009/1/-122.5/-0.00244863563439755294 params=2/2.2/-2/-2.22/-1.3/0 float=y maxiter=1200 inside=0 logmap=157 periodicity=10 colors=000D9AC0FA3L99P7FT6L_4Qc3Vg1`l0fr0lv0rz0vz0\ rx0mp0ji1fc3aX4_P6VI7SC6I7474301A34I66P97XC9cFAjJC\ rMDyPFzSGzVIzcAzi4zo0vs0sz0ry0rr0rm0rl0pj0pi0pg0pf\ 0pd0oc0oa0o`0r_0uY0xX1xT0xQ0pO0iL0`I0TF0M70OA0PF0Q\ L4SP9TVFV_JXdOYiT_oY`scaygczmdzrdzv_zuTzuPxsJrsFms\ 9gr3ar0Yp0Sp0Op0Jr3Gr9DrGArM7rT4r`1rf0rm0rs0rl0gd0\ YY0PQ0FJ16C30440A60G60L60Q60X60`60f60l60p60v60z60z\ 60y40s30m16g0Ca0GX0MQ0SL0YF0aM0cS0dY1fc4gi7io9juCl\ zFmzGmxPjpYgifd`maTv_MzXFzVVzTizSyuQzoPmpFPr40s04v\ 07x3Ay6Dz9GzCLzFOzIQzLTzOXzQ_zTXy_VldS`jQOpOCvM0zL\ 0zM0zMAvMMpMYlMifMuaPs`Ss_TsYXsXYsV`rVarTdrSfrQirP\ jrPrdaxSozFzz3zz1zz0zz0zz0zz0xz0ux0pv0mu0js0fr0cp0\ `o0Yg6daMlXasTfpSimPmjOpiMrmMusMxxMyzQxsTvjXuc_sVa\ rOcmPciPddPd`PdXPfSPi1zm0zr0zv0zz0zy0zx1zv6zuAzsFz\ rJzpMzoQzmVzl_yjcxigvijvjmpjpjlsflv`lxXmzQmzLozG9z\ LAzICzFDzAFz7Gz4Iz1Jz0Gz4 } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 09-01-03 (Curlers [8])
by Jim Muth 10 Jan '03

10 Jan '03

FOTD -- January 09, 2003 (Rating 8) Fractal visionaries and enthusiasts: Sometimes I enter parameters into the M-Mix4 formula without thinking, simply letting my fingers go where they may. In today's case my fingers became stuck once again on the '1' key, and tapped out a fractal filled with interesting places to explore. The parent fractal is a hugely bloated crescent-shaped thing filled with chaos, which can be seen in its entirety only after several out-zooms have been made. But despite the overall chaos, a relatively small area of smooth circular bands lies near the origin, with a Mandeloid just to the north. The smooth bands and chaos come together in the East Valley of this Mandeloid, forming the most interesting area of the entire fractal. Today's scene lies in this East Valley, where the smoothness begins breaking down into chaos. I have named the image "Curlers". (Have I used this name before?) The curly things filling the image remind me of those fantastic creatures that appear in certain of Escher's pictures. These curious creatures can curl themselves into balls and quickly roll to wherever they want to go in the impossible worlds conjured up by Escher's imagination. I rated the image at a much-above-average 8. The average in this case is the average worth of the typical hastily constructed FOTD image, not those carefully-crafted images that fractal artists have spent weeks or months in creating. The average FOTD image, by its nature, is a quickie. I rarely spend more than 1 to 2 hours on the entire task of finding and rendering the image, and composing the discussion. Today's image renders in 8 minutes. This is fast enough for those who prefer to render their own images, and slow enough to make the download the more efficient choice. The download may be found at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather was actually quite pleasant here at Fractal Central on Wednesday, as a chinook wind from the west raised the temperature to 48F 9C and melted the remaining snow, permitting the dynamic duo a brief romp in the yard, if sitting and looking around can be considered romping that is. Today will be even warmer, but before I can even think of the pleasant day outdoors, I must get some work finished. So until next time, take care, and whatever is a chinook? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Curlers { ; time=0:08:05.82--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.64012469245893500/+1.044967891978891\ 00/6.066313e+007/1/-130/-3.89582091792489704e-005 params=1/1.1/-1/-1.11/-0.11/0 float=y maxiter=1100 inside=0 logmap=155 periodicity=10 colors=000H0OI0eJ0dK0cL0bM0aN0`O0_O2ZP3YP4XP5WQ5VQ\ 6UQ7TQ7SR8QR9ORAMSAKSBISCGSCFWHEZLEbPDeTDhXCl`CodB\ shBvlAypAwl9vh8ud8t`7sY7rU6qQ6pM5oI4nF4mB3l73k32j0\ 2g48e8DbCJ`GOYKUWOZTSdRWiP_nQblRekShiTkhUnfVqeWtcX\ wbXyaWrcWkeWdgWYiWRkUThTVeRXbQZ`O`YNaVLcSKeQJgNHiK\ GjHElFDnCBp9Ar69s4IrVRrtVonZmibkdfhZjfUndPraJv_EzY\ 9sUFlQKeMPZIUSE_LAdE6i82nG9bNGRUNF`T4YV7WWAUXCRYFP\ ZIN_KL`NIbQGcSEdVCeY9f_7gb5he3ig9dfF`fLXeRTeXPdbLd\ hHcmDcnHboLbpPaqTaqXar``sc`tg_tk_uo_vsZwwZwzZorXhj\ W`bUUVTMNRFFQKHROJRSLSXNS`PTdRThTTiURiUQiVOiVNiVLj\ WKjWIjWHjXGjXEkYDkYBkYAkZ8kZ7kZ6jXAiVDhTGgRJfPMfOP\ eMSdKVcIZbGabFdaDg`Bj_9mZ7pZ6saBtcFtfJthNujRumWuo_\ uqcvtgvvkvxovsnrnnojnleni`neXnbSm_OmXJmTEmQAmN5mK1\ mH2jH2gH2dH2aH2ZH2WH2TH2QH2NH2KH2HH2EH5GK7HMAIPCJR\ EKTHMWJNYLO_OPbQQdSRfTTdTVcUXaUZ`V`ZVbYWdWWfVXhTYR\ 9ZS8_T8`V7aW6bX6`ZBZ_FY`J } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 08-01-03 (Happenings-II [7])
by Jim Muth 08 Jan '03

08 Jan '03

FOTD -- January 08, 2003 (Rating 7) Fractal visionaries and enthusiasts: It's another very busy day here at F.C. But despite the work, I have found a fractal worthy of being honored by being declared Fractal of the Day -- FOTD for short. For today's image we again try the fractal trick that worked so well yesterday. Probably due to the color palette, the trick does not work so well today, but it still earns its FOTD. Most of what I said about yesterday's image also applies to today's. When I entered today's parameters, my finger became stuck on the '1' key, though the end value of real(p3), which is -2, changes the '1' of real(p1) and real(p2) to -2. I rated the image at a 7, which is above average. I named it "Happenings-II" because it is largely a repeat of yesterday's image. The render time of under 6 minutes may be avoided by downloading the completed GIF image from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Despite ample sun, Tuesday was cold and windy here at F.C. With a temperature of 28F -2C and winds of 20mph 30kph, the outdoors held no attraction whatever for the dynamic duo, who passed the day sleeping and eating. Today is starting cloudy and warmer, with enough work to keep me busy until mid-evening at least. But I'll still find time for the Fractal of the Day for 1-9. Until tomorrow, take care, and when a change is needed, make the change. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Happenings-II { ; time=0:05:49.16--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.41337046687929880/-4.168575424427294\ 00/3.249936e+007/1/75/-1.53247584789434343e-006 params=1/-1.1/1/-11.11/-3/1e+100 float=y maxiter=1200 inside=bof61 logmap=yes periodicity=10 colors=0006eQ7dR7dS7cT7bU8bV8aW8aX8`Y9_Z9__9Z`9ZaA\ YbAXcAXdAWeBVeAczAWg9Wh9Xh9Xi8Xj8Xj8Yk7Yl7Ym7Zm6Zn\ 6Zo5_n6Zo6Zo7Zo7Zo8Zo8Zo8Zo9Zo9cpAZpAZpAZpBZpBZpCZ\ pCZpCZpDXmEWjFUhGTeHRbIQ`JOYKNVLLTMKQNINOHLPFIAczQ\ EGUDGZCGbCGgBFkAFp9Fs8Fw7GzPFqAFoBElCEiDDgEDdFDbGC\ _HCXIBVKBSLAA00NNAKN9IP9FQ8CR8AS77T74V65U76U77U77Z\ 78U89T8AT8AX8BT9CT9DT9DZ9ES9000GSAGSAHSAIWBJRBJRBK\ RBLRBMQCMXCNQCOQCPQDPQDQPDRPDSPDSPETPEUPEVOEVOFWOF\ XOFYOFYOFXPGXPGWQHWQHWQIVRIVRJUSJUSJUSKTTKTTLTTLSU\ MSUMRVMRVNRVNQWOQWOQWPPXPPXPOYQOYQOYRNZRNZSNZSM_SM\ _TL`TL`UL`UKaVKaV9bWFaVKaVP`UU`UZ_Td_TiZSnZSsYRyZP\ xYRxYSwXTwXUvXVvWXuWYuWZtV_tV`sVasUcrUdrUeqTfqTgpT\ hpSjoSkoSlnRmnRnnRonQpoQpoPqoPqpOrpNrpNsqMsqMtqLtr\ KurKurJvsJvsIwsHwtHxtGxtGxuIyuJyuKyvLyvMzvNzwOzwPz\ wQzxRzxSzxTzyUzyUzyUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzU\ zzUzzUzzUzzUzzUzzUzzUzzUz } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 07-01-03 (Ghostly Happenings [9])
by Jim Muth 07 Jan '03

07 Jan '03

FOTD -- January 07, 2003 (Rating 9) Fractal visionaries and enthusiasts: The work is quite heavy this morning. With no time for a lengthy discussion, I will let the image speak for itself. This is no problem, for it speaks very well. I really like today's image. The rating of 9 that it was given is no exaggeration. The image earns every bit of its excep- tional rating. I named the picture "Ghostly Happenings", not because there is something spooky about it, but because the image is another of my 'evaporated' images, consisting of all-inside, with the ghost of the vanished material made visible by <bof60> fill. The parent fractal was created by combining negative portions of Z^(-0.75) and Z^(-7.5) before adding (1/C). The fact that one exponent has ten times the value of the other is of no impor- tance. The parent is an indescribable thing that is almost impossible to describe, but it is typical of this class of double-negative fractals. Today's scene is located in a valley in an unlikely area of the northern part of the parent. I call the area unlikely because at first glance it appears to be non-critical and therefore to hold no midgets. But, as today's image shows, the world of fractals, like the real world, sometimes holds the unexpected. The render time of 12 minutes is quite reasonable for such a quality image. And as always, the completed GIF file is available on Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and on Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather here at Fractal Central on Monday was partly cloudy with a temperature of 34F 1C and occasional flurries of snow. The dynamic cats, who dislike snow, spent the day sleeping by the warmest radiators they could find. I don't know what has come over the once truly dynamic pair. The older they get, the more they sleep. It seems like 10 years since they last chased each other up and down the stairs. As for myself, I have a bit of work to chase down and finish before starting my search for a fractal that equals or exceeds today's. I probably will fail to find one -- such images are not easy to find -- but check tomorrow to see how close I come. Until then, take care, and good things sometimes come to those who wait, but if they wait too long, they sometimes miss the fractal boat. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Ghostly_Happenings { ; time=0:12:36.98--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-1.49916201924092700/+2.289316930073352\ 00/1.336895e+007/1/85/-5.98323907294306956e-008 params=-2/-0.75/-9/-7.5/0/1e+100 float=y maxiter=1200 inside=bof61 periodicity=10 colors=0006Qa3Qc5Oe7Mg8LhAJjBIkDGmEFnGDpHCqJAsK9tM\ 7vN6wO9uPCsQFqQIoRLmSOkTRiTUhUXfV_dWbbWe`XhZYkXZnV\ ZpUluMyzFvuJspNpkRmfVjaZgXacWd_WfXVhTVjPVmMUoIUqFU\ sESnEQjEOfDMbDKYDIUCGQCEMCDIUEjPFmLFpGGrCGu7Hx3Hz6\ Jx8LvANtCPsFRqHToJVnLWlOYjQ_iSagUceXedZgb`i`bj__ga\ YecWbdU`fRYhPWiNUkLRmJPnGMpEKrCHsAFu8Dv7Iq6Mm5Qi4U\ e4Za3bY2fU1jQ1nM3kK4hJ6eH7cG9`EAYDCVBDTAFQ8GN7HL6N\ J7SI7YH7bG7gE7mD7rC7wB7dBENBL5BS5BR5CP5CO4DM4DL4EJ\ 4EI3EH3FF3FE3GC2GB2H92H82H73KB4NF5QJ6TN7WQ8ZU8aY9d\ aAgdBjhCmlDppDrsCsrCsqBspBsoAtnAtm9tl9tl9uk8uj8ui7\ uh7vg6vf6ve6ve5ub5t_5tYwsVwsSwrQwrNwqLwpIwpFmzDzzc\ zn7zn5wm2zm0mf6c_CUTHXNNdGSk9Yr3bj2`b2ZV2XN2VG2UK4\ XO6ZS7`W9b_BdcCfgEhjFjhDcgBXe9Rd8Kb6Ea47`31c8FeDTS\ 9ME6G13A77CCAEHDFNGHSJJXMKYNLZOM_PNzQzzRzzSzzTzzUz\ zVzdWUeXVfYWgZXh_Yh_ZeYVcXS`WPZUMWTJUSFRQCPP9MO6KN\ 3JL9JKFJJLJIRIHXIGbIFh9Q_ } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 06-01-03 (Siegel Mandelbrot [4])
by Jim Muth 06 Jan '03

06 Jan '03

FOTD -- November 06, 2003 (Rating 4) Fractal visionaries and enthusiasts: Two days ago I posted a FOTD that illustrates what I assume to be almost-Siegel Disks, or about as close as is possible to come to Siegel Disks this side of infinity. Then, yesterday, I began wondering about the appearance of the Mandelbrot set at a point so close to the Siegel-boundary. The area was extremely easy to find, but its maxiter of over 1-million made the rendering quite slow. What I found was an area of thin, wiry arms, so jagged that it is difficult to determine the direction from which they are coming. The coloring shows that the arm in the upper right part of the image is the lowest-iteration feature in the frame, but the tan-colored arm in the left half of the frame could just as easily be entering from the top as from the bottom. It actually enters from the top. I also noticed that the midgets are very plentiful this deep in the M-set. At least 30 become visible in the frame when the color mode is toggled. I assume that the smaller ones are surrounded by even wirier and more jagged arms in addition to taking even longer to render. Curiously, at this extreme location of the M-set, the normal 2-4-8... pattern has all but vanished. The pattern might be there, but if it is, it is so distorted as to be virtually beyond detection. I am also curious about the appearance of the odd planes and oblique slices of the Julibrot at this point, but without Fractint's fast Mandelbrot formula to speed up the rendering, such images would be extremely slow. Still, I might investigate this aspect in the near future, and if the results show anything unusual, it will appear as a FOTD. Like the Siegel Disk image of two days ago, the interest of today's image lies mostly in the mathematical aspect, and like the earlier image, it also rates a 4. I named the image "Siegel Mandelbrot" as a simple description. With its render time of almost 1-1/2 hours, the image is a very slow one, I recommend downloading it from one of the following two web sites: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> But before going for the download, give Paul and Scott a chance to render and post the image. Snow fell all day Sunday here at Fractal Central, piling up 5in 12cm by nightfall. The snow, combined with a temperature of 30F -1C, kept the dynamic fractal cats housebound. They put on their best pouts to let me know of their unhappiness, but knowing them as I do, I realized that their displeasure was mostly a show. It's another threatening day today, with talk of several more inches of snow by this evening. (We still measure length in inches, and temperature in degrees Fahrenheit here in the best educated ;-) nation in the world.) The cats were saddened by the news of still more snow. As for me, I've got enough supplies stocked and enough graphic work waiting that I have no time to be sad and no need to venture out on treacherous roads. The next glorious fractal will appear in only 24 hours. Until then, take care, and if you lift too much heavy snow, you might hurt a Siegel Disk. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Siegel_Mandelbrot { ; time=1:22:52.63--SF5 on a P200 reset=2002 type=mandel passes=1 center-mag=-0.3905\ 4756291390700/-0.58679532300884950/442757.7/1/102.\ 5/-2.48215537707041634e-009 params=0/0 float=y maxiter=1200000 inside=0 logmap=905 periodicity=10 colors=0008pe5rf7pg8ng9mhAkhBiiChiEfjFdjGckHakI_lJ\ ZlKXmMVmNUnOSnPQoQPoRNpTLpUKqVIqWGrXFrYDsYBuZCs_Cr\ _Cq`Cp`CoaCnaCmbDlbDjcDidDhdDgeDfeDefEdfEcgEagE`hE\ _iEZiEYjFXjFWkFVkFTlFSlFRmFQmGPnGOoGNoGMpGKpGJqGIq\ HHrHGrHFsHEtHDtHBuHAuI9vI8vI7wI6wI5xI4xI3tH7qGAnFD\ kEGgDJdDMaCPZBSVAWS9ZP8aM8dI7gF6jC5m94p53t64s75r86\ q97pA7oB8oC9nDAmEAlEBkFCjGDjHDiIEhJFgKGfLGfMHeNIdN\ JcOJbPKaQLaRM`SM_TNZUOYVPYWQXWQWXRVYSUZTT_TT`USaVR\ bWQcWPdXPdYOeZNfZMg_Lh`KiaKjaJkbIlcHmdGohCmdGk`KiY\ NgUReQVcNYaJa_FeYChW8lV5oU6pT6pS6pS7pR7pQ7pQ7pP8qO\ 8qO8qN8qM9qL9qL9qK9qJArJArIArHArHBrGBrFBrEAsFBrFCr\ FCrFDrFDrGEqGEqGFqGGqGGqHHpHHpHIpHIpHJpIKpIKoILoIL\ oIMoJMoJNnJOnJOnJPnKPnKQnKQmKRmKSmLSmLTmLTlLUlLUlM\ VlMWlMWkMXkMXkNYkNYkNZkN_jN_jO`jO`jOajOaiObiPciPci\ PdiPdiPehQehQfhQghQghQhgRhgRigRigRjgRjgSihThhTghUf\ hUehVehVdhWchWbhXahBpaApc } END PARAMETER FILE=========================================

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FOTD 05-01-03 (The Forest [4])
by Jim Muth 05 Jan '03

05 Jan '03

FOTD -- January 05, 2003 (Rating 4) Fractal visionaries and enthusiasts: Today's image rates a somewhat-below-average 4. As is true with all my ratings, this rating is totally subjective and exists 'in my opinion'. I found the midget easily enough, and decided that its ghost would make a better image soon enough. I determined quickly enough that the <bof61> inside fill would do the best job of revealing the ghost, and the final image rendered fast enough. At that point I was expecting an image worthy of a rating of at least a 6. But then I began coloring the image, and soon found that nothing seemed to work. I ended up with an image that I feel had a rating of at least 6 in it, but which failed to live up to its potential. The disappointment might be due to my clumsy attempts at coloring, or it might be due to an inherent diffi- culty in coloring such images. Regardless, I could rate the final result no higher than a humdrum 4. I named the picture "The Forest" because, with much imagination, one might see an exotic forest in the image. The formula behind the image combines portions of Z^(-1.4) and Z^(-9.6), and adds (1/C) instead of plain C. The parent fractal, before it is evaporated, somewhat resembles a caterpil- lar. Today's scene is located in a tiny valley on the southwest shore of the largest circular bay. As is the case with all fractals of this double-negative class, (indeed with all frac- tals of any nature), other areas of the parent hold an infinity of other scenes that will never be discovered. The 9-minute render time can be avoided by downloading the com- pleted GIF image file from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather Saturday was fractal-like here at F.C. -- some sun, some clouds, some wind, and a temperature of 36F 2C. Being frac- tal in nature, the cats checked the weather, ventured briefly into the yard, then retired to their resting places to pass the day. As one can easily see, the lives of aging fractal cats are not very exciting. And this morning, light snow is falling. The dynamic duo will likely have another less-than-exciting day. The nature of my day is yet to be determined, as is the quality of tomorrow's FOTD. Check back then to see what happens. Until next FOTD, take care, and the FOTD-CD will be coming soon. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Forest { ; time=0:09:15.79 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.37047999988935450/-0.627083448737120\ 20/25184.95/1/42.5000000000153761/6.43986378112693\ 103e-010 params=5.9/-1.4/10.4/-9.6/0/1e+100 float=y maxiter=1600 inside=bof61 logmap=yes colors=0000sJ0q`0mo0kz0iz4gzAezGezJdzPdzVbzZbzd`zi\ ZzoZzsXzxXzzVzzVzxTxoTxeTvXTvNTvETu4Tu0Tu0`k2ed4kX\ 8qPAvHCzAzCqzAmz8iz8ev6bs6Zo4Vk4Rg2Nd2J`0GX0CT08P0\ 4L00J00E6A8EL2LX0Tg0`s0gz0oz0vz0sz0oz0mz8ixGeqNdkX\ `ddXXkVRZLHNEAC42000800G00L00T00`00e02m02u04z04z06\ z06z0Az0Cz0Ez0Gz0Jz0Lz0Nz0Pz0Rz0Vz0Xz0Zz0`z0bz0Vx0\ No0Hd4AVC2JJ0AR00Z00d00`00Z00X00V04T06P0AO0CL0GJ0H\ H0LE0000RA0T82V62`4Ae4Hk2Pq2Xu0bz0iz0qz0xz0zz0zRbs\ zozzkzu8zm2ze0zi0zR0zJ0zC0z40z00z40zC0zJ0zR4zcCzZE\ zZEuZEiZEZZENZEEVJ8TP4PV0N`0Le0Hk0Gq0Eu0Jk0Px0Vx0`\ z0ez0kr0qz0vz0zz0zz0zz0zz0qz0ez0Xz0Lz0Cz00u40z8zXG\ voPubZsVgqVqoVzmVzkVziVzT0zE0iJ0eP0bV0``0Xe0Ti0Re0\ Ld0H`0CZ08V02T00P00N00L00G00CA08K04X00e00q40z60zA0\ zC0zA0zA0zA0x82m86m8Ag8Eb6HX6JR6NL6RG4VA4Z44`04d06\ e08g0Ak0Cm0Co0Eq0Gu0Hv0Jx0Jz0Lz0Nz0Pz0Rz0Rg0zb0xX0\ qR4kLEdHLZCTR4q00u00x00u4 } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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investigations#3.1
by jos hendriks 04 Jan '03

04 Jan '03

Dear reader Intro It was Jim Muth, who gave me the inspiration to contribute now and then to the list. I transport his pars to a file specially called muth.par . About once a week I render some of them. Often I like the pictures. It is also quite funny to compare his rating with the one I should give. Most o the time they differ considerable. For instance the last one I rendered, the one 31-12-2002 named:"so let it be", I would rate an 8 at least. It reminds me of a (intricate) staircase. And because it's never ending I should have call it "staircase to heaven". Ismand In the documentation (helpfile) of fractint you can find under "formula" that it's possible to use the predefined variable ismand to create formulas with witch you can toggle between mandel and Julia frm's. But how? A few weeks ago I run into the demo from Sylvie Gallet, so know I know. But it might be a good idea to put some information about the use of ismand in the documentation itself. The formula frm:Jh_square {;Jos Hendriks,2002 if (ismand) z = 0 , c = pixel else z = pixel , c = p1 endif : a=real(z),b=imag(z) z=a*a+flip(b*b)+c real(z)<p2 && imag(z)<p2 } This time, again, a simple and at first look nothing promising, formula: f(x,y)=(x^2,y^2)+c. I don't think there exist a ( simple) complex equivalent. The Mandelbrotset is a square (not hard to see) with corners (-2,-2) and (0.25,0.25) (witch is more difficult to see). So that gives really nothing. Nevertheless Juliasets can give nice images (although then nothing of the Juliaset itself is to be seen). Sometimes with fractal features. Below are two pars. I called the pictures: "looking at the block of flats at the opposite of the street and "looking out of the window to the windows at the opposite of the street." They render in seconds, even on a slow machine. frm:Jh_square {;Jos Hendriks,2002 if (ismand) z = 0 , c = pixel else z = pixel , c = p1 endif : a=real(z),b=imag(z) z=a*a+flip(b*b)+c real(z)<p2 && imag(z)<p2 } block_of_flats { ; Jos Hendriks ,2002 reset=2000 type=formula formulafile=fractint.frm formulaname=jh_square ismand=n passes=1 center-mag=-0.77118865717993890/+0.78113466887094510/227799/0.6848 params=-2.522474238758866/-2.5106260160601/4/0 float=y 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 } windows { ; Jos Hendriks ,2002 reset=2000 type=formula formulafile=fractint.frm formulaname=jh_square ismand=n passes=1 center-mag=-1.64e-006/2.205e-006/0.5706675 params=-2.016863584518433/0.3288808465003967/3/0 float=y colors=000z0zc0cz00c00zz0cc00z00c000z00c0zz0cc000000zzzccc<238>ccc }

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FOTD 04-01-03 (Siegel Disk Fractal [5])
by Jim Muth 04 Jan '03

04 Jan '03

FOTD -- January 04, 2003 (Rating 5) Fractal visionaries and enthusiasts: For quite some time I have been hearing rumors of the existence of fractal things known as Siegel Disks. When I first started hearing these rumors, I had no idea what Siegel Disks were supposed to be. I supposed they were some type of Julia set, but why were they called disks? I wondered about the problem a day or two, then forgot it. Then, a few months later, I found that a Siegel Disk is a feature that appears in Julia sets with a C-value that lies on the exact boundary of the Mandelbrot set. And there appears to be a particular Julia set, the one with a C-value of -0.390541,-0.586788i, that lies on the boundary and is considered to be the 'Siegel Fractal'. At that point, I lost interest in Siegel Disks, but yesterday, I decided that I would like to see exactly what a Siegel disk looks like, so I calculated the Julia set that corresponds to the above value of C. The result was a Julia set like many I had seen and ignored before. Why, I wondered, was this fractal called a 'disk'. I raised the maxiter from my usual exploration value of 1200 to 500,000 and recalculated the fractal. Other than going somewhat slower, the image remained unchanged. But I did not give up. Doing further investigation, I changed the value of C to -0.390547-0.586796i, a value that corresponds to a point lying a tiny bit inland on the M-set, and recalculated the fractal. To be sure the calculation did not skip over any near-periodic points, I set the periodicity to 12. Now, things started to happen. As the image developed, I saw that the fractal was not empty, but was filled with disk-like rings of extreme maxiter value. Here at last were my Siegel Disks. They are not the true Siegel Disks, which would have a maxiter of infinity and be totally flat and featureless. These would be impossible to draw. My disks are close enough to be called pseudo-siegel-disks however, and they have a huge advantage in that they are possible to calculate within the time that the universe will continue to exist. When all my exploration was finished, I named the resulting image "Siegel Disk Fractal" and rated it at a 5. The rating is mostly for the mathematical interest of the image. Artistically, it rates no more than a 3 or 4. Despite its extreme maxiter, the image draws in only 15 minutes on my tired old Pentium 200mhz machine. Most machines, being faster, will draw it faster. And as always, the completed GIF image is available on the internet at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Now that I have a way of controlling the flood of spam that could result, I also might soon resume posting the FOTD images to: <alt.binaries.pictures.fractals> But don't go there yet. I have not yet made the decision. It rained and rained Friday here at F.C. -- a 34F 1C ice-cold rain that did good to neither man nor cats. The man passed the time accomplishing some useful work. The cats passed the time sulking like the mature cats they are. Whatever became of the happy, playful kittens they were 10 years ago? Today is starting cloudy, but a clearing is on the horizon, and I expect the day will turn out far better. And I have only a modicum of work to finish, which should make the day a good one by the time it ends. Until the next FOTD appears in 24 hours, take care, and I wonder how much data a Siegel disk can hold. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= SiegelDisk_Fractal { ; time=0:15:25.16--SF5 on a P200 reset=2002 type=julia passes=1 center-mag=0/0/0.97\ 12963 params=-0.390547/-0.586796 float=y inside=255 maxiter=500000 logmap=yes symmetry=origin periodicity=12 colors=0000000000000000000000000000000000000000000\ 000000000000000000000000000300600AI0EC0I60K00O00S0\ 0W00_00c00g03k0Co0Ks0Uz6ezEozNzzWzzezzozzvzvzzkzz_\ zzNzzEzz3zv0zs0zo0zo0zb0zR0zE0z30k00_00K0080000000\ 000000Kz0No0NR0N30R00R00R00_00e00o00v00z0Cz0Rz0ez0\ vz0zz0zz0zz0zz0sz0ok0kb0eR6bIC_8IU0NR0UN0_I0eE0kC0\ s80z30k00b00R00I0080000C00K00I0CE0_C0z00z00z00z00z\ 00z00z00z08z0Kz0Wz0hv0vv0zz0zz0zz0zz0zz0zz0zz0zv0z\ o0vh0vb0sW0sR0oK0oE0k80k30o00s00s00v00v00z00z00z00\ z00v00o00h30b80WC0UI0NN0IU0C_06b03h00o00v00z00z30z\ 63z8RzCszEzzIzzKzzKzzKzzKkvKWoKKkEEhC8e83b30_00W00\ U00R00N00K00I00E00C0080080000000000000003608C30UI0\ kW0zU0zR0zR0zN0zN0zK3zK8zIEzEKzERzC_zCez8kz8sz6zz6\ zz0zz0zv0zk0zb0zU0zK0zC0z36z0_z0zzzzzzzzzzzzzzzzzz\ zzzoz0_zIRz_UzRUzIWz8Wz0_z0_z0kz0vz0zz0zz3zz6zsCzz\ Ezz8zz3zz0zz0zz0vz0kz0ez0 } END PARAMETER FILE=========================================

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FOTD 03-01-03 (Negative [5])
by Jim Muth 03 Jan '03

03 Jan '03

FOTD -- January 03, 2003 (Rating 5) Fractal visionaries and enthusiasts: Today's image is another 'evaporated' one that consists entirely of inside fill. It strongly resembles yesterday's image, which consisted of FMOD inside fill, but today's image is made of bof60 fill. While studying the image, searching for a suitable name, I could not shake the impression that I was looking at a negative. I finally settled on the name "Negative". This name has nothing to do with my opinion of the image's worth, which is average -- it refers solely to the appearance. The image was created by adding 1 part of Z^(-6.66) to 7 parts of Z^(-1.75) before adding (1/C). The variety in the fractals created by combining negative powers of Z appears nearly inexhaustible. I have been exploring these fractals for a year or so, and have not yet scratched the surface. The 12-minute render time can be avoided by downloading from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The clouds hung around all day Thursday here at Fractal Central. With a temperature of 39F 4C, it was far too unpleasant outdoors for the dynamic duo, who spent the day sleeping by the heat and occasionally asking for food. Today is starting just as unpleasantly, and it is raining as well. I fear the cats will remain unhappy. I now find myself with quite a bit of work to do and a limited time in which to do it. So until next FOTD, take care and think positive when the world is negative. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Negative { ; time=0:12:47.20--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.20995120647748890/+0.778751248577170\ 40/18264.3/1/-42.5/-3.61434354667622415e-011 params=7/-1.75/1/-6.66/0/1e+100 float=y maxiter=1500 inside=bof60 logmap=yes periodicity=10 colors=000uwztwzswMrwNqwPpvQouUntXms`lrckqfjpaioY`\ gUU`QMTMFLI8EE7FD7FC7FB7GA7GA7G97H87H77H76JB6LE6NH\ 6PK6RO5TR5VU5XX5Z`5`c4bg4dkXfo`irekufmukovqqzNjfRd\ `V_VYVQ_XR`ZRa`RbbRddRefRfhRgiRikSjmSkoSlqSnsSouSp\ wSqwS050lsUipUgnVdlVbiW_gWYeXVbYT`YQZZOWZLU_JS_MUc\ PVgSWkUXnXYr_Zva_ycavectgeqigokimlkjnmhpofrqctsauu\ _pvYkvXfwVbwUYwSTwROwQKwOFwNAwL5wK1wJ5wN9tRDqUHnYL\ k`PhdTegXbk`_ndXrgVuhXthYsh_rh`qhbpicoienifmihliik\ gemebnc_oaWp_TqZQrXNsVJtTGuRDvQAwREtRHrRKpROmRRkSU\ iSYfS`dScbSf`SeYSeWSeUSdSSdQSdOSdMScKScIScGSbESbCS\ bASb8TaCT`GT_JT_NTZQUYUUXXUX`UWcUVgVUjVUnVTqVSuVSx\ YUv`WubYte_sgardbqacpZdoWenTfmQglOhkLijIjiFkhClg9m\ f6ne4oe5kg5hi5ek5bm5Zo5Wq5Ts5QtBPoHPkNPgTPcZP_dPWj\ PSpPOuPKtQLsRMrSNqSNpTOoUPnVQmVQlWRkXSjYTiYTQHuMMt\ JQtFUsCZs8br5fr7gm8gi9geAgaBgXCgTEhPFhLGhGHhCIh8Jh\ 4Ke6Kc8Ka9LZBLXCLVELTFMQH } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Fractal Calendar 2005
by Fractal Forum 02 Jan '03

02 Jan '03

This is an open call for you to submit your fractal artwork for consideration for inclusion in the Fractal Universe ® Calendar 2005. All the information you will need is detailed on the following website: http://www.fractalforum.com Please make your submissions and any additional enquires you may have via the contact form on the above website. This message has been posted to some of the fractal art newsgroups, mailing lists, and forums. If you think it may be of interest to others please feel free to forward it, as it is written here, to other 'net sites where fractal artists meet to share and discuss fractals. Thanks and good luck! Linda Allison and Tina Oloyede xxxxxxxxxxxxxxxxxxxxxxxxxxx Fractal Forum http://www.fractalforum.com xxxxxxxxxxxxxxxxxxxxxxxxxxx

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FOTD 02-01-03 (Jellyfish [8])
by Jim Muth 02 Jan '03

02 Jan '03

FOTD -- January 02, 2003 (Rating 8) Fractal visionaries and enthusiasts: For the second day of the second year of the third millennium we have a fractal image that rates a much-above-average 8. It is one of my 'evaporated' scenes, where I take an image that contains a negative power of Z, find something interesting, and then raise the bailout radius to one-googol, which causes the screen to go blank. Next, I apply one of the non-flat inside fills to the image, which now consists totally of 'inside' points. Sometimes, nothing much happens, but usually, the inside fill reveals the 'ghost' of the scene that originally was there. Thus, today's image is a ghost, a thing which in the world of fractals certainly does exist. I was a bit puzzled when the time came to give a name to the image. It reminded me of something...but what? Then, after pondering for several minutes, I thought of a jellyfish. This was it. The image, with its appearance of transparency, reminds me of a jellyfish drifting gently in a warm ocean current. Of course, no real jellyfish is so symmetrical. It is the effect of transparent elements before an infinite blue background that earns the name. The warhorse MandelbrotMix4 formula calculated a critical plane of the expression 45Z^(-0.8)-36Z^(-0.9)+(1/C) to create the parent fractal of today's image. When calculated with the default bailout radius, this parent is little more than a circle filled with great blobs of fractal glop. But a small bud of Mandel-material lies on the X-axis, and today's image is located at the tip of a filament stretching from a sub-bud of this bud into an open area, where it finally dies out. The 37-minute render time of the attached parameter file is slow. Those with other things to do as the normal work routine resumes will want to download the completed GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> With the temperature hanging in the middle 40'sF (around 6C), it rained steadily all day Wednesday here at Fractal Central, some- times quite heavily with occasional claps of thunder. Some minor flooding was reported around the area, but F.C. remained dry. The dynamic cats were very depressed however as they sat at their window, watching the rain and wishing they could go out. An evening treat of tuna helped ease their depression, but they still ended the day in a sullen mood. Though today is starting cloudy, at least the rain has ended, which is a good sign. Now, if the mud in the yard would dry, the dynamic ones might have a pleasant day. It will take more than a dry yard to make my day pleasant however. This will not happen until the design work is finished, and it will not be finished until I begin. So until tomorrow, take care, and be kind to your fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Jellyfish { ; time=0:30:23.25--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=t center-mag=-0.4004091333751482/+0.0215282924423132\ /3.080974e+007/1/80/-1.5530640837951859e-007 params=45/-0.8/-36/-0.9/0/1e+100 float=y logmap=yes maxiter=1200 inside=fmod proximity=1 periodicity=10 colors=000UPqUQpURnUSlUTjUUhUVfUXeUYdWZcY_b_a`ab_c\ cZedYfeWgeVfeUfeTeeSefQdfPdeOceNcfLbfKbfJafIafHZeK\ XdMVcNTbPQaQO`RM_TK_UHZVFYXDXYBWY8V_6U`4Ta2Tb1S`1S\ _1SZ1SX1SW1SW1SV1RV1RV1RU1RU1RV1RV1RW1QX1QX1QY1QZ1\ QZ1Q_1Q`2R_2RZ3SY3SX4TX4TW4UV5UU5VU6VT6WS7WR7XQ7XQ\ 8YP8YO9ZN9ZNA_MA_LA`KBaJBbJCcICdHDdGDfGDfFEgEEgDFh\ CFiCGjBGjAGk9Hl9Hm8In7Io6Io6Hn8HmAGmBGlDFlEFlGEkHE\ jJDjKDiMCiNCiPBhQBgSAgUAgV9eX9eY8e_8d`7cb7cc6be6bf\ 5ah5ai6`g6_e6Zd6Yb7Xa7W_7VZ7UX7TV8SU8RS8QR8PP8OO9N\ M9MK9LJ9KHAJGAIEAHDAGBAF9BE8BD6BC5BB3BB2BB2BC2BC2B\ D2BD2HQ5Mb8RoAQnCQmEQlFPkHPjIPiKPhMOgNOfPOeQOdSNcT\ NbVNaXN`YM__MZ`PYbUYcZagcejhimmmqrrtwwwzzzwxtrtnmp\ hhmbcfVZ`NaUSbEWcA_gBShBLfCEbC7ZC0YE1XG2WH3VJ4UK5T\ M6SN7RP8RQ9PP9NO9KNAIMAGLAEKAFJFGJKGJOHJTIJYIJaJJf\ KJkKJoLHpLGpLFpLEpLDpLCqLBqLAqL9qL8qL7rL6rL5rL4rL3\ rP7pTAoXDn`GmdJlhMklPjpSi } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Best concise definition of fractal ?
by Anna Baron 02 Jan '03

02 Jan '03

Hi folks! Grateful for all your answers which I've enjoyed - all of them interesting attempts to reduce such a complex subject to a simple definition. Special thanks to Jos H.'s for having been particularly entertaining, giving me enough food for reflection :) Cheers all! Anna __________________________________________________ Do You Yahoo!? Everything you'll ever need on one web page from News and Sport to Email and Music Charts http://uk.my.yahoo.com

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FOTD 01-01-03 (Broken Symmetry [7])
by Jim Muth 01 Jan '03

01 Jan '03

FOTD -- January 01, 2003 (Rating 7) Fractal visionaries and enthusiasts: It's a new year here at Fractal Central, and we start it off with a sudden switch to an optimistic outlook and a trip to the Z^(sqrt(2))*(0.6(C))+C fractal to find an image that rates a 7. The parent fractal was drawn by the JimsCompMand formula, which is simply a generalization of the cmplxmarksmand formula of Fractint. The strange little midget in the image lies in the East Valley area of the largest midget on the main stem of the Z^(1.4142)+C Mandeloid. Yes, I can already hear the voices telling me that the Z*(1.4142)+C Mandeloid has no main stem, that the stem vanishes as the exponent of Z is dropped to a value less than 2. This is true, but the parent Mandeloid of today's image is not exactly the Z*(1.4142)+C figure. In the JimsCompMand formula, Z^(1.4142) was multiplied by 0.6(C) before (C) was added. This multiplication causes the fractal to split apart along the negative X-axis, and this splitting causes the non-existent negative stem to emerge from never-land into the world of fractal reality, where it can be examined as though it had never vanished. The prominent midget is still there on the revealed stem, grossly distorted of course, with its East Valley still easily recognizable. The stem itself still zig-zags down into the center of the valley, and it still has midgets strung along it, though at such a low power of Z, the midgets are rather difficult to pick out along the zig-zagging and branching stem filament. Today's scene lies quite deep, so deep in fact that it actually shows signs of breaking up, and needed the mathtolerance reset to /1 to reach the magnitude. I have included the mathtolerance setting in the parameter file so that the image will draw at the correct magnitude at all resolutions. I named the image "Broken Symmetry" because of the spectacular discontinuity that, along with the coloring, spoils (or makes) it. This is the one of the greatest degrees of disorder that I have yet come upon, though undoubtedly an infinity of midgets with even more disorder do exist and are waiting to be found. The 13-minute render time is a bit trying, and may be avoided by visiting Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> and downloading the completely rendered image from there. The weather was much improved Tuesday here at F.C., with mostly sunny skies, light breezes, and a temperature of 55F 13C. The small amount of dampness remaining in the yard did not deter the dynamic ones from enjoying a 2-hour romp, which helped their moods immensely. In fact, they ended the day in such a pleasant mood that they were satisfied with their normal diet. But today is rainy, and I doubt that their pleasant moods can weather the storm. Check tomorrow to see how they make out. As for me, I'll probably do little more than watch football on the TV. Until next FOTD, take care, and here we go again with another whole year to get through. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Broken_Symmetry { ; time=0:13:24.99--SF5 on a P200 reset=2002 type=formula formulafile=jim.frm formulaname=JimsCompMand passes=1 mathtolerance=/1 center-mag=-1.36389419716712900/+0.671782211838532\ 70/1.326342e+013/1/102.501354055520352/3.885780586\ 18804789e-016 params=1.4142/0/0.6/0/0/0 float=y maxiter=5400 inside=0 logmap=285 periodicity=10 colors=000DaZEc`FebGgdHifIkhJmjKolLqnMrpNvrOztTmmY\ fga_afTVkMPoGJpIIpKIpMHpOHpQHpSGpUGpWFpYFpZFl`HibJ\ edKbfMZhOWiPTkRPmTMoUIqWFsYCtZGhSKYLOMESB7W01Z57aA\ DdFJgJPjOVmT`pYfsakp_imZgjXfhWdeUbbTa_R_YQYVOXSNVQ\ MUOMWMMXLMZJM_IMaGMbEMcDMeBMfAMh8Mi7MjDHbJCWP7OV3H\ R8JNDKKILGNMCSN9XO5aP2eQ4gT6iW7jY9l`AmbCoeEqhFrjHt\ mIuoOI`QJaSKaULbVMbXNbZOc`PcaQdcRdeSdgTehUejVflWfm\ XfQX1PW2PW3OV4OV4NU5NU6MT7MT7SQBXOEaMHfKKkINpGQuET\ tCWsBYr9_q8ap7do5fn4hn3jh8mbCoXGrRKtMOvOQsPSqQUnRW\ lSXjTZgU`eWbbXd`YeZZgW_iU`kRamPbnNVeHNYBFQ57I08J69\ KCAKHBLNCLTDMYEMcFNiFNnKOkOPhSQfWQc_RadSZhSWlTUpUR\ tUPrTNqSMpRLnQJmPIlPHjOFiNEhMDfLBeLAdK9bJ7aI6`H5_H\ 4YG6XF8VEAUDBWCDYBF_AGa9Ic8Ke7Mg6Ni5Pk4Rm4So7PqIXt\ TYwc_zcazcczaez_gzYizYkzYmzYozYpzXqzXrzXszXtzXuzXv\ zXwzXxzUyzVzzVzzVzzVzzVzzVzzjzzizzhzzgzzgzzfzzezzd\ zzdzzczzbzzbzzazz`zz7zz7z } frm:JimsCompMand {; Jim Muth z=c=pixel: z=z^p1*(c^p2)+c, |z| <= p3+100 } END 20.0 PAR-FORMULA FILE==================================

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