June 2003 - Fractint - mailman.xmission.com

Multifractal_4
by Albrecht.Niekamp＠t-online.de 18 Jun '03

18 Jun '03

Hi, this hopefully is the version I will use for some time, as everything does what I expect. The images were not possible with previous versions and are really extraordinary. The_hat is the basic image. Fractal greetings, Al. -----------------------------start-par----------------------------------- Biomorphs { ; Time 0.39.11.31 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult242.frm formulaname=multifractal_4 ismand=y function=exp/exp/exp/sin passes=t center-mag=-0.497251/0.568314/19.72387 params=-0.5/0.375/12867.00011/40.3214026052/4048.02048/384.000008/384.00\ 024/128.0076800000001/512.0076800000001/768.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200III<3>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<25>iiijjjlll<3>sss<20>KKK } The_heart { ; Time 0.15.45.98 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult242.frm formulaname=multifractal_4 ismand=y function=exp/exp/exp/sin passes=t center-mag=-0.06546992645160482/-0.00653500612040142/332.451/1/90/3.8857\ 8058618804789e-016 params=-0.5/0.375/12812.00011/40.3214026052/2048.02048/384.000008/384.00\ 024/128.0076800000001/512.0076800000001/768.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200pqqrss<21>HIIFGGEFF<3>677455344122000<25>0bo0cq0es<3>0kz<25>09\ C08A068<2>022000111<24>niQpjRrlS<3>ysX<25>BB7996775<3>000<24>n00p00r00<3\ >y00<25>B00900700<3>000<2>455677899ABBBCC<22>opp } The_hat { ; Time 0.12.32.97 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult242.frm formulaname=multifractal_4 ismand=y function=exp/exp/exp/sin passes=t center-mag=-0.537836/0.38229/1.202675/1/-90/3.88578058618804789e-016 params=-0.5/0.375/12812.00011/40.3214026052/2048.02048/384.000008/384.00\ 024/128.0076800000001/512.0076800000001/768.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200pqqrss<21>HIIFGGEFF<3>677455344122000<25>0bo0cq0es<3>0kz<25>09\ C08A068<2>022000111<24>niQpjRrlS<3>ysX<25>BB7996775<3>000<24>n00p00r00<3\ >y00<25>B00900700<3>000<2>455677899ABBBCC<22>opp } Ruins {; that the weed has overgrown ; Albrecht Niekamp June, 03 reset=2002 type=formula formulafile=mult242.frm formulaname=multifractal_4 ismand=y function=exp/exp/exp/sin passes=t center-mag=-0.368627/-0.272217/24.0535/1/-90/3.88578058618804789e-016 params=-0.5/0.375/12812.00011/40.3214025131/2048.02048/384.000008/384.00\ 024/128.0076800000001/512.0076800000001/768.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200pqqrss<21>HIIFGGEFF<3>677455344122000<25>0bo0cq0es<3>0kz<25>09\ C08A068<2>022000111<24>niQpjRrlS<3>ysX<25>BB7996775<3>000<24>n00p00r00<3\ >y00<25>B00900700<3>000<2>455677899ABBBCC<22>opp } Windhose { Time 8.13.17 ; Albrecht Niekamp June, 03 reset=2002 type=formula formulafile=mult242.frm formulaname=multifractal_4 ismand=y function=exp/exp/exp/sin passes=t center-mag=-0.05573016812667020/+0.01426832175061791/45.21334/1/-90/-1.2\ 3373533611470521e-014 params=-0.5/0.375/12812.00011/40.3214026052/2048.02048/384.000008/384.00\ 024/128.0076800000001/512.0076800000001/768.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200pqqrss<21>HIIFGGEFF<3>677455344122000<25>0bo0cq0es<3>0kz<25>09\ C08A068<2>022000111<24>niQpjRrlS<3>ysX<25>BB7996775<3>000<24>n00p00r00<3\ >y00<25>B00900700<3>000<2>455677899ABBBCC<22>opp } --------------------------------start-frm----------------------------------- FRM:Multifractal_4 { ; Albrecht Niekamp 110603 ;only integers as first input, second input 5 digits to the right ;real(p2) 5digits: shape, outside, in1, in2, in3 ; 0_off 1_mand 2_jul 3_hyb.mand 4_hyb.jul +5_reset digit1: +5_warp ; input2 : five digits frm2 use : 0_no 1_yes ;imag(p2) (-)digit1 : many_mods multipl. off 1_out 2_in1 3_in2 4_all ; digit2 : iter-reset 1_out 2_in1 3_in2 4_all ; input2 : many_mods_2digits frm1_2digits frm2_2digits bees_4digits ;real(p3) many_mods bailout, bailout ;imag(p3) shape : factor (fn1), outside : border-in ;real(p4) outside : factor (fn2), border-out ;imag(p4) maxiter1, factor1 (fn2) ;real(p5) maxiter2, factor2 (fn3) ;imag(p5) maxiter3, factor3 (fn4) ; da=real(p2) dd=trunc(da) da=round((da-dd)*100000)+11111 d=trunc(dd/10000) ex0=d>5 d=d-5*ex0 vb=(d==3)+(d==4) dd=dd-d*10000 d=trunc(dd/1000) ex1=d>0 dd=dd-d*1000 rs1=d>5 d=d-5*rs1 v1m=(d==3) v1j=(d==4) dd1=(d==2)+(d==4) d=trunc(dd/100) ex2=d>0 dd=dd-d*100 rs2=d>5 d=d-5*rs2 v2m=(d==3) v2j=(d==4) dd2=(d==2)+(d==4) d=trunc(dd/10) ex3=d>0 dd=dd-d*10 rs3=d>5 d=d-5*rs3 v3m=(d==3) v3j=(d==4) dd3=(d==2)+(d==4) ex4=dd>0 rs4=dd>5 dd=dd-rs4*5 v4m=(dd==3) v4j=(dd==4) dd4=(dd==2)+(dd==4) tt=ex0+ex1+ex2+ex3+ex4 ; d=trunc(da/10000) ab=(d==2) da=da-d*10000 d=trunc(da/1000) ab1=(d==2) da=da-d*1000 d=trunc(da/100) ab2=(d==2) da=da-d*100 d=trunc(da/10) ab3=(d==2) da=da-d*10 ab4=(da==2) ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) d=round((d-dd)*10000000000) da=trunc(dd/10) so1=((da==1)+(da==4)==0) so2=((da==2)+(da==4)==0) so3=((da==3)+(da==4)==0) dd=dd-10*da ir1=(dd==1)+(dd==4) ir2=(dd==2)+(dd==4) ir3=(dd==3)+(dd==4) ; mm=trunc(d/100000000) d=d-mm*100000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=real(p3) mb=trunc(d) ba=(d-mb)*100000 ; d=imag(p3) sfac=trunc(d) b1=(d-sfac)*100000 b0=b1/2 ; d=real(p4) ofac=trunc(d) b2=(d-ofac)*100000 ; d=imag(p4) mi1=trunc(d) fac1=(d-mi1)*100000 ; d=real(p5) mi2=trunc(d) fac2=(d-mi2)*100000 ; d=imag(p5) mi3=trunc(d) fac3=(d-mi3)*100000 ; bg=((ab+vb)==0) bg1=((ab1+v1j)==0) bg2=((ab2+v2j)==0) bg3=((ab3+v3j)==0) bg4=((ab4+v4j)==0) ; if (ismand) z=0 if (vb) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else if (bg) c=p9 else c=p1 endif z=pixel endif t=0 d3=(ismand==0) u=d3 : bo=z If (tt) t=t+1 if ((ex0)&&bo>b0) u=2*(fn1(t/sfac)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) ba=mb else c=pixel endif else z=pixel if (bg) c=p9*u else c=p1*u endif endif ex0=0 tt=tt-1 elseif ((ex1) && bo>b1 && bo<b2) u=2*(fn2(t/ofac)) rs=rs1 ab=ab1 if (dd1) if (rs) z=pixel endif vb=v1j d3=1 if (bg1) c=p9*u else c=p1*u endif else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1m if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir1) t=0 endif ex1=0 tt=tt-1 elseif ((ex2) && t>mi1) u=2*(fn2(t/fac1)) rs=rs2 ab=ab2 if (dd2) if (rs) z=pixel endif vb=v2j if (bg2) c=p9*u else c=p1*u endif d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v2m if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir2) t=0 endif ex2=0 tt=tt-1 elseif ((ex3) && t>mi2) u=2*(fn3(t/fac2)) ab=ab3 rs=rs3 if (dd3) if (rs) z=pixel endif vb=v3j if (bg3) c=p9*u else c=p1*u endif d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3m if (vb) if (so3) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir3) t=0 endif ex3=0 tt=tt-1 elseif ((ex4) && t>mi3) u=2*(fn4(t/fac3)) ab=ab4 rs=rs4 if (dd4) if (rs) z=pixel endif vb=v4j if (bg4) c=p9*u else c=p1*u endif d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v4m if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif ex4=0 tt=tt-1 endif endif if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) else z2=fn1(z)+c ;Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (ab) z=z*z+c+c*c-p7 ;Pusk s Istv n elseif (d3) z1=fn1(z)-c ;Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) else z2=z*z ;Pusk s Istv n z=z2*z2+(p6+u)*z2+c-p1 endif |z|<=ba } -------------------------------------end-----------------------------------

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FOTD 17-06-03 (Deep in Inner Space [9])
by Jim Muth 17 Jun '03

17 Jun '03

FOTD -- June 17, 2003 (Rating 9) Fractal visionaries and enthusiasts: Does today's visionary fractal image actually rate a 9? Well, maybe not, maybe a rating of 8 would be more accurate, but I've been hard on myself lately and it's about time I give myself a break, so I decided that today's image rates a 9, which equals 'one of the all-time best'. The parent fractal was produced by subtracting Z from Z^(-1.08) and adding (1/C). The resulting image resembles a distorted and somewhat lopsided Mandeloid standing on its nose. Today's scene is located in the East Valley area of this parent, which in this case is a north valley. I named the image "Deep in Inner Space" because I'm in a rather subjective mood this morning. The picture has unusually smooth coloring, at least on my fractal monitor, with the bands being almost invisible. The overall effect is one of a serene, hazy, fantastic fractal landscape, with gossamer arms composed of clouds of invisible smaller midgets extending outward from the central midget in a star-like shape. The price to pay for all this serenity is the 1/2 hour required to render the scene from the attached parameter file. And even that price may 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> Lots of clouds spoiled the day here at Fractal Central on Monday, but the temperature of 73F 18C was close to perfect, and the fractal cats made the most of it. Today is starting cloudy again, with rain forecast for later in the day. The duo will have a marginal day at best. I'm having a fair to good day -- so far that is. I hope the pleasantness can continue. With any luck at all, it will. In any case, until next time, which will arrive in 24 hours, take care, and last year the farmers prayed for rain. This year their prayers are being answered. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Deep_In_InnerSpace { ; time=0:29:24.20--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.02357251356169931/+0.372397927789504\ 30/1.14291e+008/1/10/1.30309761642993793e-006 params=1/-1.08/-1/1/0/300 float=y maxiter=2500 inside=0 logmap=644 periodicity=10 colors=000EAUFBVFBVFBWFBWFBXGBXGBYGBYGBZGBZHB_HD_H\ D`HD`HDaIDaIDbIDbIDcIDcJDdJDdJDeJEeJEfJEfLEgLEgLEh\ LEhLEiMEiMEjMEjMEkMFkNFlNFlNFmNFmNFnOFnOFoOFoOFpOF\ pJGqMFqNFqOFqPFqQFpREpSEpTEpUEoVEoWDoYDoYDn_Dn_Dna\ BnaBmbBmcBmdBmeAmfAmgAmhAmiAlj9lk9ll9lm9kn9ko7kp7k\ q7jr7js7js6ju6iu6iv6iv6ix4kw6jw6iw6iw6hw6hv7hv7hv7\ gv7gv7fv7fv9ev9ev9dv9cv9cuAbuAbuAauAauAauAatB_tB_t\ B_tB_tBZsDYsDYsDXsDXsDWsDWsEVsEVsEUsEUsETtBUsDTsET\ sETrFTqFTqGTpHTpHToITnITnJTmLTmLTmMTlMTlNTkOSjOSjP\ SiPShQShRShRShSSgSSfTSfUSeUSdVSzVSzWSzpPzpQzpRzpSz\ pSbQTaPUaNUaLV_IW_FX_GW_HWaHWaIWaIWaJVaJVaLVbLVbMV\ bMVcNUcOUdOUdPUdPUeQTeQTeRTfRTfSTfSTgTSgUShUShVShV\ ShWRhWRhXRiXRiYRiYRjZQj_Qk_Qk_Qk_QlaPlaPlaPmaPmbPm\ bPmcOmdOndOneOneOofNofNogNpgNphNreMqgNphNoiOnjOmlP\ mmPlnPkoQjqQirRhsRjuPktQmtRntRpuSrvUsvTuwTvxSxySzz\ RzzRzzQzzQzzPzzPzzOzzOzzN } 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 16-06-03 (Vision of a Square [7])
by Jim Muth 16 Jun '03

16 Jun '03

FOTD -- June 16, 2003 (Rating 7) Fractal visionaries and enthusiasts: Things are far more settled today here at Fractal Central, though city workers and home-owners are still cleaning up where the flash flood struck on Friday at the bottom of the fractal hill. The only problem here inside F.C. is a huge backlog of work, which must be cleared away before things will be totally back to fractal normal. Today's fractal is named "Vision of a Square". I gave it this name because the square in question, which is delineated by the blue area, is not immediately apparent, and gradually appears in the awareness, almost like a mystical vision. But even if the square eludes detection, the graceful filaments are worth a name in themselves. The parent fractal adds together 3.9 negative parts of Z^2 and Z^3 before adding 1/C. The fractal produced by this formula is a grossly oversized, double-lobed thing that requires several outzooms before it fits on the screen. Today's scene is located in a small bay on an inland shoreline near the X-axis of this parent. Much of the image consists of bof61 inside fill. This fill is the reason that the central midget is so poorly defined. But despite the poorly-defined central midget, the image rates a 7. The 6-minute render time 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> Though it remained cloudy, only a few drops of rain fell here at Fractal Central on Sunday. The neighborhood Father's Day cook- outs went as planned, and the fractal cats enjoyed a pleasant afternoon outdoors in the temperature of 81F 27C. They needed no treats of tuna to put them in good moods. Today is promising to once again be pleasant. But I'll not be able to say for sure that it will be pleasant until the day and the work are behind me. Until then, anything can happen and usually does. Until tomorrow, when the next FOTD will appear, take care, and be wary of stray fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Vision_of_a_Square { ; time=0:06:29.32--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+7.70124460252959/+3.08060831519806/6.0\ 07398e+009/1/172.5/3.78867931411924763e-005 params=-3.9/2/-3.9/3/0/0 float=y maxiter=800 inside=bof61 periodicity=10 colors=000WOFSOEOODJOCFOCBOB7OA3OACLLLJWTGeaEpiCzZ\ RqPehSbeV`cYYa`W_cUYbTUaSRaRN`RK`QG_PD_PAZMCYKEXHF\ WFHWDIVAKU8MT5NS3PS1QV2OX3MZ3K`4Jb4Hd5Ff5Dh6Cj6Al7\ 8n76p85r83t91v90rC5oE9lGDiIHfLMcNQ`PUYRYVUbSWfPYjM\ _nJarIbqHbpGcoFcnEdmDdlDekCejBfiAfh9gg8gf7he7he9eb\ Ab`A_YAXWAVUASRAPPAMMAKKAHIAEFABDA9BBCECEHDGJEIQFM\ TGOVHQYIS`JUdKWiLYkM_nNarOcvLfzJkzXpzoqzvsznvmdx`W\ xPYvNZrM_nL`jK`fJ`bI`ZH`VG`RFaNEbJDZFC_CBhEAmFArGA\ wHAzI9zJ9zK9zL9UN8UO8UP8fQ8fR7fS7fT7fU7S8KP9MN9NLA\ PJAQHBSFBTCCUACW8DX6DZ4E_2E`4Ga5Hb6Ic7Jd8Kd9MeANfB\ OgCPhDQhESiFTjGUkHVlIWlSNs`FyYHjVIXSKIQL4PM5PN5OO5\ OP6OQ6NR6NS6MS7MT7MU7LV7LW8KX8KY8KY8LZALZCL_DL_FL`\ GL`IMaKMaLMbNMbOMcQMcRTfUZhWdjYjl_imYhmXgmVfnUenSd\ nRcoPboOaoM`pL_pJZpIYpHXnKWlMVjOUhRUgTTeVScYRa_Q_a\ QZcT``VbYYdV_fSbhPdjMglJinGlpDnrAqt7sv4uw2qlFmaSiR\ deHpfGqfGrfGrgGshOHcOG_OF } 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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4-Dimensional Rubik's Cube
by Paul N. Lee 14 Jun '03

14 Jun '03

For those individuals interested in challenges, mathematics, or just a bit of fun, may wish to visit the following web page: http://www.superliminal.com/cube/cube.htm Windows and Linux executables (with source code) available, along with an article on how to calculate the permutations of 4D Magic Cubes. Sincerely, P.N.L. ------------------------------------------------- http://home.att.net/~Paul.N.Lee/PNL_Fractals.html http://www.Nahee.com/Fractals/

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FOTD 14-06-03 (A Midget Collision [4])
by Jim Muth 14 Jun '03

14 Jun '03

FOTD -- June 14, 2003 (Rating 4) Fractal visionaries and enthusiasts: Due to a flood and power failure, I had little time to find an honorable fractal for today. What I did find was a collision and partial merger of two midgets in the fractal created by adding portions of Z^4, Z^5. The real(p3) parameter is very critical to the shape of the combined midgets, and changing its value by as little as 0.000001 makes a noticeable change in the image. I named the image "A Midget Collision" because that's what it is. I rated it at a 4 because that's all it's worth. The render time of just over 1 minute takes some of the disappoint- ment from the FOTD. As always, the image can also be seen by visiting one of the FOTD web sites and downloading it from there. 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> Friday, with its temperature of 86F 30C, was a fine day until 7pm when a thunder-storm of biblical proportions arose, flooding the fractal basement to a depth of 6 inches and cutting the power. (I have always wondered how a sump pump is supposed to keep the water down when the storm causes a power failure, as usually happens.) But it was far worse a couple blocks down the road, where a sudden 10-foot flood washed the neighborhood cars into a single heap of wreckage, with a Lincoln Towncar sitting proudly on top. There were numerous high-water rescues in the area. Luckily, the fractal cats were well ensconced in the darkest closet during the spectacular noise. More severe storms are forecast for later today, so we'll see how it goes. For me, I'm going to finish as many chores as possible before the next deluge and power failure. It's sunny at the present, and the cats are in the yard. All is temporarily well. Until next FOTD, take care, and be at ease. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Midget_Collision { ; time=0:01:48.75--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-10.8815/-1.72085e-015/3.908693 params=1/4/0.1/5/-0.991909/0 float=y maxiter=1200 inside=0 logmap=yes symmetry=xaxis periodicity=10 colors=000QFDNFDLECJEBGEAEDACD99C87C77C06C45C74CB3\ CE3CH6EI8FIBGIDHIFIIIJJKKJMLJPMJRNJUOKWPKYQK`RKbSK\ o`YpX`qTcrPfsLisHkpFhnEelDbiC_gBXeAUc9S`7PZ6MX5JU4\ GS3DQ2AO18R6BTBDVFGXKI_PKaTNcYPeaShfUjkWloZnt`pxbm\ wakv`hu_ftZdsZarY_qXXqWVpVToVQnUOmTLlSJkRHkRKlPMmO\ OnMQnLSoJVpIXpGZqF`rEbrCesBgt9it8ku6mv5ov4pu7puApu\ CqtFqtIqtKrsNrsPrsSsrVsrXsr_tqbtqdtqgtqiqphnpglpgi\ offofdoeaoeZndXndUncRncPmbMmbJmaHmaFk_EjYDiWCgUBfS\ AeQ8cO7bM6aK5_I4ZG3YE8_HCaJGbLLdNPePTgRYhUajWekYjm\ _nnarpcvoesmdpmcmmbkmbtoJqqKoqKloKjmKgmLemLbmL`mLY\ mMWmMTmMRmMQmLPmKOmJOmINmHMmGLmFLmEKmGJmIImKHmLGmN\ FmPEmRDmSCmUBmWAoY9qZ8s`7ub6wd5xeJzdXzcjzcnz8rzMvz\ _czeLzk2zqAznHzlPziWzgczdjzbkzalz`lz_mzZnzYnzXozWB\ zkWzbozVpzWpzXqzYqzYrzZrz_sz`sz`tzatzbwzftzbJzK`zS\ qzZkzXfzV`zUWzSQzRLzPBzHEzLGzOJzSLzVOzZQzaTzeVzhUz\ cUz_TzVTzRSzMSzIXzGUzFSzE } 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 13-06-03 (Mistral [7])
by Jim Muth 13 Jun '03

13 Jun '03

FOTD -- June 13, 2003 (Rating 7) Fractal visionaries and enthusiasts: Today is Friday the 13th here at Fractal Central as well as nearly everywhere else on earth. Because the number thirteen has always been considered unlucky, and in the middle ages criminals were usually executed on Friday, it is supposed to be an unlucky day. Well, it's not supposed to be unlucky, it's simply that many people consider it to be unlucky. This, of course, is superstition. Rational-thinking people realize that belief in superstitious things is a sign of irrational thinking. (Even though I now know that precognition exists, I am still a rational-thinking person.) Nothing in a calendar day of the week and a date that were determined by men can cause bad luck. Bad luck is nothing more than randomly distributed and often self- produced misfortune. But we now know that the world extends into regions where reason alone can no longer give all the answers. So who can say for sure that irrational thinking is always wrong and today is not somehow jinxed? Today's fractal is named "Mistral". A Mistral is not a mis- spelling of the word 'mis-trial', it is a cold north wind that blows for long periods of time in southern France. After a while, it becomes quite annoying to those not accustomed to it. I chose this name for whimsical reasons. There is nothing windy about today's image, which subtracts Z^(1.1) from Z^(-1.1) before adding (1/C). The parent consists of several scattered and distorted Mandel- oids. Today's scene lies in the East Valley area of the most prominent Mandeloid. It is a rather lively scene, which rates a 7. Its brilliant colors are fairly bubbling with activity. If I had been in a better mood, I might have rated it an 8, but sweeping water into the sump for 45 minutes is an annoying task, so the image rates only a 7. The parameter file renders in 6 minutes; the image file down- loads in less than one minute. Running the parameter file is more fun; downloading the completed image is more convenient. The individual fractalist must make the decision. The image can be found, ready for download at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> A very muggy day Thursday led to torrential and very noisy thunder-storms in the late afternoon and evening, which left an inch of water in the fractal basement. Before the rain arrived, the temperature reached 86F 30C. Luckily, the dynamic fractal cats had already satisfied their wanderlust by the time the rain began, and weathered the noisy storms hiding in the closet. When they finally came out, their fears were eased by a consol- ing treat of tuna. Today promises to be a repeat, so I expect a repeat performance from the duo. (Hopefully, not from the basement.) Until next FOTD, take care, and tomorrow I'll tell of any bad luck that might happen today. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Mistral { ; time=0:06:39.59--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.01259329587616971/+0.353654150329713\ 80/2.773255e+012/1/130/-0.000177204568416973463 params=1/-1.1/-1/1.1/0/0 float=y maxiter=1200 inside=0 logmap=130 periodicity=10 colors=000PGHTAGV4EX0CZ0Cb08d26e64g82iC0kG0mJ0oL0s\ P0uT0vX0x_0ze0zh0zm0zo0vj0m`0eV0XP0NJ0GG06A0040000\ 0000000ENGbzLZzPVuTRoXNi`JddGZgEVm6ds0mv0vz0zzczzc\ zzZzu0zk0zd8zVGzNNzEVz6bz0iz0qz0vz0sz0qz0mz0kz0iz0\ ex0du0bs0Zq0Xm0Tk2Ri4Pe6Ld8Jb8H`C2JE0460802A0AC0HG\ 0PH0VJ0VJ0TJ0TJRJLNLNHLPENR8PT4RV0RX4Tb6Tg8TmAVsCV\ xEVzHRvLPqNNkRLgVJbXGX`ETbCNeAHi8Ek48o22s00u00x00z\ 00m40bC0RL0ET02b00i00d00Z00V04P08L0AG6EACH6HJ0NN0R\ R0XT0bX0g`0mb0qZ0qX0qV0qT2qRAqPHqNPqLXqTbm`gkgmims\ guxezzdzzbzz`zzbuzdkvdbseRmgHgg8bi0Zi8NVGCHP04X00V\ 84VPGVgTVxdVzoRzsPzuLzxJzzGxzEvzCsz8oz6mz2iz0ez0dz\ 0`z0Zz0bz4dzAgzGizLkvRoqVqk`ueev`kxVqzPvzkzzusxzkq\ zdiz`bzdXzgPzkHzoAzs2zv0zz0zz0zz0zz0zz0zz0zz0zz0zz\ 0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0z\ z0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0\ zz0zz0zz0zz0zz0zzXzzRzzLz } 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 12-06-03 (Your Cheating Fractal [5])
by Jim Muth 12 Jun '03

12 Jun '03

FOTD -- June 12, 2003 (Rating 5) Fractal visionaries and enthusiasts: Today's hastily-found scene is a play on the number 6. It is typical of the scenes found in fractals created by combining two negative powers of Z and adding the reciprocal of C. With so little effort behind it, the image cannot be considered rating any better than an average 5, but it still might be worth the 7 minutes required to render it. I named the picture "Your Cheating Fractal" for whimsical reasons after I heard a song with almost the same name on the fractal radio. As far as I know, fractals are not conscious, and therefore can not cheat. But I have heard it said that everything has a degree of consciousness, and since fractals are members of the set of everything, they also might be conscious, and therefore actually have an ability to cheat. The parent fractal resembles a Mandelbrot set with its East Valley missing, and surrounded by an extended field of chaos. Today's scene is located near the inland limit of the chaos field surrounding the main bud of the parent. The 7-minute render time can be avoided 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> Wednesday was a near perfect day here at Fractal Central -- at least for cats. For humans it was a bit muggy, with high humidity and a temperature of 86F 30C. The cats spent several presumably happy hours in the yard, while the humans did their human work. A heavy thunder-storm came up just after nightfall, but by that time, the cats' good day had been established. Today promises to be a repeat. I assume the cats will repeat their good mood. My mood will improve when the work is finished and the next FOTD is found, though it is not too bad as things stand now. Until next time, take care, and be faithful to your fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ YourCheatingFractl { ; time=0:07:23.53--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+6.00228958244036100/+3.223452857127679\ 00/2.140219e+009/1/-80/0.00351184647968315333 params=0.6/-0.6/0.06/-6/0/525 float=y maxiter=1200 inside=0 logmap=156 periodicity=10 colors=000rVhrSjrQkrOlqSnpVopZpoarnesnhtmlvlowlrxg\ iocag_TZVLRRCIN4APH9QU9Sf9Ts9SpARnARkBQiBPfCPdCOaD\ O_DNYDMVEMTELQFKOFKLGJJGJHGDVR7ha1vkGicUXXVW_VWaWW\ dWWfXWiXWkYWnYWpZWsZWu_Wx_Wz`Tv`RsaPpaNmbLjbJgbHcc\ F`cDYdBVd9Sd7PbENaLL`RKZYIYdGXjFVgITdLSaOQ_RPXUNUX\ MS_KPbIMeHJhFHkEEnCBqB9tGEoKJkOOfSTbWYY_bUYdWWeYVg\ _ThaSicQkdPlfNmhMojKplJqmInjIkhHifHfdGdbGa`F_ZFXWE\ UUESSDPQDNOCKMCIKtxTuuVurWuoXulYuiZuf_uc`u`auYbuWc\ nTahR_aPZWNXPLVJJUCHS6FR5FU5FX4F_4Fb3Fe3Fh2Fk2Fn2F\ q6Dk9BfCA`F8WI6QL5LK7OJ8RI9THAWGCZFD`EEcDFfCHhBIkA\ Jn9Kp8Jl8Ii7Jh7Jg7Jf7Je6Jd6Jc6Jb6Ja5K`5K_5KZ5KY4KX\ 4KW4KV4KUFdQQyNUrSYkX`dadYfgSjfTgeUdeUbdV_cWYcWVbX\ TbXQaYO`ZL`ZJ__G__EX`GUaIRbKOcMMcOJdQGeSDfUAgW8gY7\ iV7jT7kR7lO6mM6nK6pH6qF5rD5sA5t85u65v4Av5Fv5Kv5Pv5\ Uv5Zv5cv5hv5mv5lsAkpFjnKikPhiUgfZfdch_hjVmlQrnMwcN\ mTOdIOWJRXsfarcbradrZerXg } 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 11-06-03 (The Past [6,7,8])
by Jim Muth 11 Jun '03

11 Jun '03

FOTD -- June 11, 2003 (Rating 6,7,8) Fractal visionaries and enthusiasts: Today's FOTD is late because, for some reason, the phone has been dead all morning. I think a truck ran into a telephone pole somewhere nearby. But whatever the problem was, it has now been eliminated and things are back to normal. (It was actually rather pleasant to have part of a morning without phone interruptions. I got a lot of work done.) Today's image rates a 6 in bright light and an 8 in subdued light. It is a very somber image created by the simplest of formulas -- Z^33+Z^2+C. The image is so somber in fact that it can be fully appreciated only in semi-darkness. When studying the image in subdued light, I get a feeling of something from the distant past -- something mysterious from long ago and far away, almost forgotten, remembered only by the feeling it once produced. What this nearly forgotten thing is I have no idea, so I named the image "The Past". The render time of 4 minutes is quite reasonable for an image that rates somewhere between a 6 and an 8 depending on the light. The small amount of effort required to download the finished GIF image from one of the FOTD web sites can eliminate even this short wait. 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> Tuesday was another perfect day here at Fractal Central, with lots of sun and a temperature of 81F 27C. The fractal cats spent nearly 6 hours in the yard, enjoying the great weather. But they were not as lively as they once would have been in such conditions. I saw almost no zooming around the yard, scampering up the holly trees, or chasing birds. I did see lots of sitting and thinking. This is how it goes with cats approaching the geriatric stage of life. I am now thinking of the remaining work that must be done. But, unlike cats, I must do more than just think. So until 24 hours from now, take care, and where is the ultimate fractal? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Past { ; time=0:04:26.39--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+0.24755150217609540/-0.055896930341567\ 15/7.643967e+008/1/55/5.69510350649504726e-007 params=1/33/1/2/0/0 float=y maxiter=500 inside=0 outside=tdis symmetry=none periodicity=10 colors=000X9uRBzMGzGHz9Mz3Oz5Kz7Hw9Gh90AB9EE70N5TQ\ 9_TEfWMo`Sua_zYgzVozRrzOjzKozHrzEwz9zz5zz0zz0zz0zz\ 0zz0zz0zz3zz5zz9zzEzzHzxKzuOzpRzmVzfXzjTzmPzpMztHz\ wEzz9zz5zz0zz0zz0zz0zz0zz0zz0zz7zzKzzXzzfzzpzzmzzj\ zzhzzdzzazz_zzXzzTzzRzzOzzKzzHzzEzz9zz7zzBzzGzzKzz\ OzzRzzVzzYzzazzdzzhzzlzzozzrzzuzzxzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzztzzozzjzzdzz_\ zz9zzBzzEzzGzzHzzKzzMzzzzzwzzdzzzzzzzzxzzpzzjzzazz\ Tzz9zzBzzBzzEzzEzzGzzGzzHzzHzzKzzKzzMzzMdV00zYfzXd\ zVdxTduTdpRdmPdjPddOdaMdY0jz0hz0hz0hw0hu0ht0fp0fo0\ fm5fjwuKuuEtt5tt0or3lp7xGHhoBdmG_lHXjMThPPfTzK0tR0\ cYGY00T90PRGfX9cYEa_GY_KXaMTcORcROdTlEzcOtVXfmfxjd\ uhdtfdpcdoadl_djXdfVddTdaPd_OdXz0TtBVcRV0t00r00p00\ o05m57l9BjGGhMKfRzz0uYzr_zp_zm_zlazhawfatcapacmYcj\ XcfTdcRd_OdXGzjHzdKzaMpYrj3lh9dfGYfMRdRh0xf0ud3tc7\ ra9p_Eo_GmYKlXMjVOfTRdTTc } 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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Multifractal_3
by Albrecht.Niekamp＠t-online.de 10 Jun '03

10 Jun '03

Hi, Multifractal now has five frms to choose from. Beautiful new structures! Pagoda is a special zoom, as it contains all five, but no chaotic spots, and thatïs where I wanted to get at. Iïm still working on a better way to embed the new frm, "Bees" by Ray Girvan, so maybe tomorrow there is a new formula. I hope, this is alright with you, as I´m constantly trying to improve my baby.. Fractal greetings, Al. ---------------------------------START-PAR--------------------------------- Pagoda { ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult241.frm formulaname=multifractal_3 ismand=y function=exp/sin/sin/exp passes=t center-mag=0.374349/-0.833852/19.72387/1/154.999999999999972/7.671641100\ 15983169e-014 params=0.5/-0.375/12829.1001/40.3214026/4048.02048/384.000001/384.00024/\ 256.0076800000001/512.01024/768.01024 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200III<3>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<20>KKK } Mfr3_basic { ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult241.frm formulaname=multifractal_3 ismand=y function=exp/sin/sin/exp passes=t center-mag=-0.537836/4.44089e-016/0.9861933 params=0.5/-0.375/12829.1001/40.3214026/4048.02048/384.000001/384.00024/\ 256.0076800000001/512.01024/768.01024 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200III<3>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<20>KKK } ------------------------------------start-frm------------------------------- FRM:Multifractal_3 { ; Albrecht Niekamp 090603 ;only integers as first input, second input 5 digits to the right ;real(p2) 5digits: shape, outside, in1, in2, in3 ; 0_off 1_mand 2_jul 3_hyb.mand 4_hyb.jul +5_reset digit1: +5_warp ; input2 : five digits frm2 use : 0_no 1_yes ;imag(p2) (-)digit1 : many_mods multipl. off 1_out 2_in1 3_in2 4_all ; digit2 : iter-reset 1_out 2_in1 3_in2 4_all ; input2 : many_mods_2digits frm1_2digits frm2_2digits bees_4digits ;real(p3) many_mods bailout, bailout ;imag(p3) shape : factor (fn1), outside : border-in ;real(p4) outside : factor (fn2), border-out ;imag(p4) maxiter1, factor1 (fn2) ;real(p5) maxiter2, factor2 (fn3) ;imag(p5) maxiter3, factor3 (fn4) ; da=real(p2) dd=trunc(da) da=round((da-dd)*100000)+11111 d=trunc(dd/10000) ex0=d>5 d=d-5*ex0 vb=(d==3)+(d==4) dd=dd-d*10000 d=trunc(dd/1000) ex1=d>0 dd=dd-d*1000 rs1=d>5 d=d-5*rs1 v1m=(d==3) v1j=(d==4) dd1=(d==2)+(d==4) d=trunc(dd/100) ex2=d>0 dd=dd-d*100 rs2=d>5 d=d-5*rs2 v2m=(d==3) v2j=(d==4) dd2=(d==2)+(d==4) d=trunc(dd/10) ex3=d>0 dd=dd-d*10 rs3=d>5 d=d-5*rs3 v3m=(d==3) v3j=(d==4) dd3=(d==2)+(d==4) ex4=dd>0 rs4=dd>5 dd=dd-rs4*5 v4m=(dd==3) v4j=(dd==4) dd4=(dd==2)+(dd==4) tt=ex0+ex1+ex2+ex3+ex4 ; d=trunc(da/10000) ab=(d==2) da=da-d*10000 d=trunc(da/1000) ab1=(d==2) da=da-d*1000 d=trunc(da/100) ab2=(d==2) da=da-d*100 d=trunc(da/10) ab3=(d==2) da=da-d*10 ab4=(da==2) ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) d=round((d-dd)*100000000) da=trunc(dd/10) so1=((da==1)+(da==4)==0) so2=((da==2)+(da==4)==0) so3=((da==3)+(da==4)==0) dd=dd-10*da ir1=(dd==1)+(dd==4) ir2=(dd==2)+(dd==4) ir3=(dd==3)+(dd==4) ; mm=trunc(d/1000000) d=d-mm*1000000 p6=trunc(d/10000)/10 d=d-p6*100000 if (t) p6=-p6 endif p7=trunc(d/100)/10 d=d-p7*1000 p8=d/100 ; d=real(p3) mb=trunc(d) ba=(d-mb)*100000 ; d=imag(p3) sfac=trunc(d) b1=(d-sfac)*100000 b0=b1/2 ; d=real(p4) ofac=trunc(d) b2=(d-ofac)*100000 ; d=imag(p4) mi1=trunc(d) fac1=(d-mi1)*100000 ; d=real(p5) mi2=trunc(d) fac2=(d-mi2)*100000 ; d=imag(p5) mi3=trunc(d) fac3=(d-mi3)*100000 ; if (ismand) z=0 if (vb) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else c=p1 z=pixel endif t=0 d3=(ismand==0) u=d3 : bo=z If (tt) t=t+1 if ((ex0)&&bo>b0) u=fn1(t/sfac) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) ba=mb else c=pixel endif else z=pixel c=p1*u endif ex0=0 tt=tt-1 elseif ((ex1) && bo>b1 && bo<b2) u=2*(fn2(t/ofac)) rs=rs1 ab=ab1 if (dd1) if (rs) z=pixel endif c=p1*u vb=v1j d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1m if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir1) t=0 endif ex1=0 tt=tt-1 elseif ((ex2) && t>mi1) u=2*(fn2(t/fac1)) rs=rs2 ab=ab2 if (dd2) if (rs) z=pixel endif c=p1*u vb=v2j d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v2m if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir2) t=0 endif ex2=0 tt=tt-1 elseif ((ex3) && t>mi2) u=2*(fn3(t/fac2)) ab=ab3 rs=rs3 if (dd3) if (rs) z=pixel endif c=p1*u vb=v3j d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3m if (vb) if (so3) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir3) t=0 endif ex3=0 tt=tt-1 elseif ((ex4) && t>mi3) u=2*(fn4(t/fac3)) ab=ab4 rs=rs4 if (dd4) if (rs) z=pixel endif c=p1*u vb=v4j d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v4m if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif ex4=0 tt=tt-1 endif endif if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) else z2=fn1(z)+c ;Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (ab) z=z*z+c+c*c-p7 ;Pusk s Istv n elseif (d3) z1=sin(z)-c ;Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) else z2=z*z ;Pusk s Istv n z=z2*z2+(p6+u)*z2+c-p1 endif |z|<=ba } -------------------------------------------------------------end-frm-------- --------------------------------

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FOTD 10-06-03 (Viofti [7])
by Jim Muth 10 Jun '03

10 Jun '03

FOTD -- June 10, 2003 (Rating 7) Fractal visionaries and enthusiasts: Today's fractal image is named "Viofti". I have no idea what the word means. It could have a meaning in another language, though I doubt it. The word came into my head as I studied the image, searching for a name, and somehow it seems to fit the otherwise indescribable scene. The image is an 'evaporated' one, consisting totally of trapped 'inside' points made visible by the 'fmod' option. The parent fractal, which is really there when the bailout radius is more reasonable, was created by iterating the quite simple formula -0.5Z^(-6)-3(1/Z)+(1/C). There is no need to describe this parent, for in today's image it no longer exists as a real fractal. The scene of today's image is actually quite close to a ghost midget, which I might feature in a future FOTD. As it is, the surreal objects floating before a space of infinite depth have such vivid definition that I rated the image a 7 even though it holds no midget. An additional good point of today's image is its speed. The render time of 5 minutes is a welcome relief from images such as yesterday's, which took 2 hours to finish. And believe it or not, today's image produces more fractal bang in 5 minutes than yesterday's did in 2 hours. If the 5-minute wait is still not brief enough, the download of the completed image is even faster. The download can be found at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> A mostly sunny day here at Fractal Central on Monday, with an afternoon temperature of 79F 26C, made the fractal cats happy, and me as well. Due to the pleasant weather, they spent the entire afternoon in the yard. When the day was finished, they settled into sleep without the need for a treat of tuna or turkey. Today promises to be another near-perfect day. Could the dynamic duo possibly be angelic two days in a row? I've got a bit of work to wrap up before I can concentrate on fractals, so until next FOTD, take care, and see you in 24 hours. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Viofti { ; time=0:05:10.11--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+3.56320848149254700/-2.845364409269308\ 00/1763.087/1/-2.50000000000225331/1.1933828925059\ 2311e-011 params=-1/-6/-6/-1/-0.5/1e+100 float=y maxiter=900 inside=fmod proximity=1 symmetry=none periodicity=10 cyclerange=13/255 colors=000WbaW`bVZdUXeTVgTThh8wFyaEsdDnfChiPWhS8nP\ 8qN8sQIjTRbW_UZhMaqEWbMXcOYcPZcQ_dR`dSadTbdUceVdeW\ eeXfeYgfZhf_if`jfakgblgcmgdmgelhfkhgjhgjhhihihhihh\ jghjfhkfhlehldhmchmchnbhoahoahp`hp_hq_hrZhrYhsYhsX\ gpWfnWekVdiUcfUcdTbaSa_S`XR_VR_TQZQPYOPXLOWJNVGNVE\ MUBLT9LS6KR4KR2MP3NN3PL4QK4RI5TG5UE6WD6XB7Y97_78`6\ 8b49c29d19c3Db4Ha5La6O`7S_8W_9ZZAbYBfYCiXDmWEqWFtY\ Iu_KuaNucPueRugUviWvjYvl`vnbvpewrgwtiwvlwxnwypwuos\ qnommlilhekebjaZiZVhVRgRNfOKeKGdHCcD8bA4a61`36Z8BX\ DGVHKTMTRRXP_aNceLfiJjmHorFsuDvwBwvDuuEssFrqGooHmm\ IkkJijKgiLegMceNadO_bOY`NWZMUXLSWKQUJOSIMQHKOGINFK\ O2LO3LO4MO5MO6NP7NP8OP9OPAPPBPPCPQDQQEQQFRQGRQHSRI\ SRJTRKTRLURMURNUXUOb_IcYKcXLcWMcVNcUOcTPcSQcRRcQSc\ PTcOUcMWcLXcKYcJZcI_cH`cGacFbcEccDdcCecBfaDd`FcZHb\ YIaXK`VMZUNYTPXRRWQSVPUUNWSMYRLZQJ`PIbOHcNFeLEgKDh\ JBjIAlH9mG9gI9aJ9XK9RM9MN } 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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