June 2003 - Fractint - mailman.xmission.com

FOTD 04-06-03 (All Cracked-up [7])
by JimMuth＠aol.com 04 Jun '03

04 Jun '03

FOTD -- June 04, 2003 (Rating 7) Fractal visionaries and enthusiasts: I have named today's unusually somber excursion into the land of fractal discontinuity "All Cracked-up", though it really gives no impression of being unusually discontinuous. The outstanding feature is the preponderance of deep blues, with only a few spots of brilliant relief from the overall depressed mood. (Maybe it's mimicking the fractal cats.) In keeping with the unintentional theme of the month, today's image is once again part of one of the infinity of fractals created by the simple formula Z^(1.5)+C. This time it is the fractal found 12 turns up the complex logarithmic spiral, which itself is a total abstraction. In low-order fractals such as today's, as the exponent of Z drops ever farther below the value of 2, the midgets become ever more difficult to find. When the exponent is 1.5, the midgets are rather difficult to track down, though it is still reason- ably simple to do. In fact, the task of finding midgets is doable down to an exponent of 1.2. Below that value, finding them is a matter of luck. The lowest-order midget I have yet found is one with an exponent of something like 1.04. In this range, midgets are nothing more than irregular, circular holes, with no bays and no organized patterns surrounding them, though the parent fractals are filled with large fields of interesting and discontinuous chaos. Today's image has been rated by me at a 7. Actually, the rating of 7 is true only in a dimly-lit room. In bright light it rates only a 5 or 6. The render-time from the attached parameter file is a reasonable 6 minutes. By downloading the completed GIF image from one of the FOTD web sites, the time can be made even more reasonable. The FOTD web sites can be found at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The rains set in on schedule Tuesday afternoon here at Fractal Central. The temperature reached 63F 17C. The cats' moods deteriorated as expected, and the customary treat of tuna only partially restored their good spirits. The rain, which is still falling this morning, will likely continue intermittently into tonight. I feel sorry for the sulky duo. I've got my own problems to sulk about. Customers who want more material on a single page than can possibly fit there are a real nuisance. But I'll work it out. Until next cracked FOTD, take care, and where do fractals end? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ All_Cracked-up { ; time=0:06:44.25--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=+0.69857471108285760/-0.230797030040254\ 00/1.203615e+009/1/42.5/-6.40805482036294061e-006 params=1.5/0/12/0 float=y maxiter=1600 inside=0 logmap=120 periodicity=10 colors=00049F48Q47L47G03C34G65J96NC6QE7TH8PK8_N9cC\ AfJAaOJaLKbIKcFKdCKe8Kf4Hg0Ig3Lh6Nj9OmCQpESsHUvKWy\ NYzQ`zSczZCidEZpGPkOMzWJmcGzrDbXTSJhH6wG4pF3jF2dE1\ ZE0TF3RF6QG8PGBOHENHGMIKLIPJJUIJZHKcGKhFLmELmDLmCE\ mH7hM0cQ5ZW9U`EPfIQkMWqR`vVfzZkz`jzajzbjzcizdizeiy\ fixghvhhuihtjhsifoiekicgibci``i_XiYTiXPiWMmYNpZNt_\ Ow`OuYRtWUsTXqR_pPboMemKhlHkkFnjDqeFjaHdYIYTKSPMLL\ NFHYPDhY9sfgGZeI`dJabKbaMc`NdZOeYPfWRgVShUTiSUjRWk\ PXlOYmNZnMXkLVhKTeJRbJQ_KUYLXXM`WNcVOgUPjSQnRRqQSu\ PSxOAanDYkGViJSgMPePLbSI`VFZYCXZGZ_J``MaaPcbTdcWfd\ ZgeaifejghlhkminoiqpkoqmlsnitpfvrdwsayuZzvXzwUwwRs\ wPowMkwKhwHdxF`xCXxAUx7Qx5Mx2Ix0Fw2Gx4Gy6Gz7Gz9GzB\ GzCHzEHzGHzHHzJHzLHzMHzMIzMIzMJzMJzMKzMKzMLzMLzMLz\ MMzMMzMNzMNzMOzMOzMOzLNzLMzKMzKLzJKzJKzIJzIIzHIzHH\ zHHzGFzFEzEDzDCzCBzBAzA9zBDzCHzDLzEPzESzFWzWaz_azb\ azRpzFzzExzDszCnzBizBdzA_ } 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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Multifractal_1
by Albrecht.Niekamp＠t-online.de 04 Jun '03

04 Jun '03

Hi, summer in the city and lots of ways to have fun, but nevertheless I found a basic image which is unique sofar. I succeeded to use the many_mods frm as inside for the hybrid julia, which has no inside. The result is a complete mix, even the basic structure. I think, this is fascinating. Fractal greetings, Al. -----------------------------start-par----------------------------------- Mixdown { ; Time 0.39.12.83 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal_1 ismand=n function=exp/sin/exp/cosxx passes=t center-mag=-0.0315457/2.22045e-016/0.9303941 params=-0.2724234748374889/0.09260841170049135/384.00001/3072.4505/128.0\ 256000000001/768.0256000000001/256.0256000000001/768.0307200000001/12298\ .7/2.16 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200777<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<26>999 } --------------------------------start-frm----------------------------------- FRM:Multifractal_1 { ; Albrecht Niekamp 270503 ;only integers as first input, second input 5 digits to the right ;real(p2) factor1, border1 ;imag(p2) (-)bailout,input bas.frm1_2digits input bas.frm2_2digits ;real(p3) maxiter2, border2-in ;imag(p3) factor2, border2-out ;real(p4) maxiter3, border3-in ;imag(p4) factor3, border3-out ;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 digit1: 1_out1 2_out2 3_both +5_shape ; digit2: 1_in1 2_in2 3_both ;imag(p5) digit1 : many_mods multipl.shutoff 1_in/out1 2_in/out2 3_both ; digit2 :1_iter1reset 2_iter2reset 3_both +5_shape effect ; input2: Number of sides 2 digits (many_mods L.Allison) ; d=real(p2) fac1=trunc(d) b1=(d-fac1)*100000 ; d=imag(p2) da=d<0 if (da) d=-d endif ba=trunc(d) d=round((d-ba)*10000) p6=trunc(d/100)/10 d=d-1000*p6 if (da) p6=-p6 endif p7=d/10 ; d=real(p3) mi2=trunc(d) b2=(d-mi2)*100000 ; d=imag(p3) fac2=trunc(d) ob2=(d-fac2)*100000 ; d=real(p4) mi3=trunc(d) b3=(d-mi3)*100000 ; d=imag(p4) fac3=trunc(d) ob3=(d-fac3)*100000 ; da=real(p5) t=da<0 if (t) da=-da endif start=2-t dd=trunc(da) da=round((da-dd)*100) if (dd<5) start=0 vb=(dd==3)+(dd==4) else d=trunc(dd/10000) vb=(d==3)+(d==4) dd=dd-d*10000 d=trunc(dd/1000) dd=dd-d*1000 or1=d>5 d=d-5*or1 vv1=(d==3) vv2=(d==4) dd1=(d==2)+(d==4) d=trunc(dd/100) dd=dd-d*100 or2=d>5 d=d-5*or2 vv3=(d==3) vv4=(d==4) dd2=(d==2)+(d==4) d=trunc(dd/10) dd=dd-d*10 inr1=d>5 d=d-5*inr1 v1=(d==3) v2=(d==4) d1=(d==2)+(d==4) inr2=dd>5 dd=dd-inr2*5 v3=(dd==3) v4=(dd==4) d2=(dd==2)+(dd==4) endif ; d=trunc(da/10) da=da-10*d ab=d>=5 d=d-5*ab bb1=(d==1) bb2=(d==2) ab1=(da==1) ab2=(da==2) ; d=imag(p5) dd=trunc(d) mm=round((d-dd)*100) 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 (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 : if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) else z2=fn4(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) z2=z*z z=z2*z2+(p6+u)*z2+c else z2=z*z ;Pusk s Istv n z=z2*z2+(p6+u)*z2+c-p1 endif bo=|z| If (wo) t=t+1 if (bo>b1) u=2*(fn1(t/fac1)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else z=pixel c=p1*u endif wo=0 if (ir1) t=0 endif endif elseif (start) t=t+1 if (start==2) if (bo>b2&&bo<ob2) 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&&bo<ob3) 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: [Fractint] test
by Jim Muth 04 Jun '03

04 Jun '03

At 04:52 PM 6/3/03 -0700, J. Wilson wrote: >Jim, > >This is one of your most outstanding tests. > >Congratulations. I enjoy simplicity! Jim M.

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test
by Jim Muth 03 Jun '03

03 Jun '03

test...

2 1

FOTD 03-06-03 (Unity and a Half [6])
by Jim Muth 03 Jun '03

03 Jun '03

FOTD -- June 03, 2003 (Rating 6) Fractal visionaries and enthusiasts: We seem to be developing a theme for the month of June. I had no intention of having two 'theme' months in a row, but sometimes fractals have a will of their own, and a theme of midgets in the many Z^(1.5)+C fractals seems to be developing. Today's image is the third consecutive scene in the set of fractals created by the formula Z^(1.5)+C. As the lengthy real(p2) parameter shows, the parent fractal was found by the evolver feature. I could have rounded off this parameter to -46.7 with little change in the resulting image. Fractals with exponents in the X.5 range are the most prone to the type of discontinuities that fill today's image. Fractal discontinuities decrease in significance as the exponent nears integer values, and vanish entirely when the exponent is an integer. I normally use the <floor> function with the MandelbrotBC1 formula, but for a change, I used the <recip> function in today's image. In today's image, which lies in the most-discontinuous range of exponents, the attractive symmetrical patterns that surround midgets in the classic Mandelbrot set are totally absent. Today's half-midget is surrounded by a kind of star-burst with an obvious break in the upper part. This break totally destroys any pretense of symmetry, though it does make an interesting feature. To add more interest, I rendered the image with the outside set to < fmod > and the proximity set to 0.5. The other outside options also make interesting variations of the basic scene, and are worth checking. I named the image "Unity and a Half" as a description of the exponent. I could rate the final result at only a 6. The rating is held down by the coloring, which could have used a bit more work. At least, the render time of 6 minutes is reasonable. The download of the finished image file is even more reasonable. That 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> Another perfect day here at Fractal Central on Monday produced perfect cats. The not-quite-dynamic duo spent the better part of the day in their porch chairs, watching the world, enjoying the temperature of 73F 23C, and remembering the days when they were actually dynamic. Today, unfortunately, is starting cloudy, with rain promised by afternoon. For me, it will be just another workday. Until next time and next fractal, take care, and sometimes fractals are not all they're cracked out to be. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Unity_and_a_Half { ; time=0:06:08.50--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=recip passes=1 center-mag=-0.73254313764763500/+0.180334958341697\ 00/4.605696e+007 params=1.5/0/-46.74114200262459/0 float=y maxiter=4200 inside=0 proximity=0.5 outside=fmod symmetry=none periodicity=10 colors=000CvNBnPBfRBZTASVAKXACZA5`WSZpnYokZnhZmeZl\ bZk_ZjX_iU_hR_gO_fL_eI_TFYHCXMIYQNYVSYZXYbaYgfYkkY\ opYkk`gfccae_XhXSjTNmPIpLDrH8uE4wF6rF7mG9hGAcO8TV6\ Ia47WGFQSMKcUEo`9zgBxcCv`DtYErVGpSHnPIlMJjJKiGPlJU\ nMZpPcrShtVmvYks_ipagmcfjedggbdi`ak_ZmYWoWTqUQsTNu\ RPrPQoOSmMTjLUhJWeIXcGY`E_YD`WBaTAcR8dO7eMBcOEaPI`\ RLZSOYTNTRMPPWnaSoYOpVJqRFrNBsK7tG3tD5qE6nF8lG9iHB\ gICdJEaKF_KHXLIVMKSNLPONNPOKQPIQY9Kf1Fg7DgCCgIBhNA\ hT9hY8ic7ih6im5ciAYfFScJN`OHYTBVX5Sa0Pe3Of6Og9OhBO\ iEOjHOkJOkMOlPOmROnUOoXOpZOp_Kl_Hh_Dd`A``6X`3T`0Qb\ 2Td3Ve4Xg6_h7aj8ckAfmBhoCjpEmrFosGquItvJvxKxyLzwOy\ vQxuSwtVvsXurZtqaspcroeqnhpmjollnkomjqlislngkrWkUg\ W6sGBcSGOcL8nODmQHlTMkVRjYWi__iadhdhgfmfiqekudiwib\ vkbti_odWj_TfVQaQMXLJTGFOBCJ69F1BE2CE3ED3FD4HC4IC5\ JB5LB6MA7OA7P98R98S89T89SBBSDCSGESIFSKHRNIRPKRRLRU\ MRWOQZPQ`RQbSQeUQgVQiWJpR } 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 03-06-03 (Unity and a Half [6])
by Jim Muth 03 Jun '03

03 Jun '03

FOTD -- June 03, 2003 (Rating 6) Fractal visionaries and enthusiasts: We seem to be developing a theme for the month of June. I had no intention of having two 'theme' months in a row, but sometimes fractals have a will of their own, and a theme of midgets in the many Z^(1.5)+C fractals seems to be developing. Today's image is the third consecutive scene in the set of fractals created by the formula Z^(1.5)+C. As the lengthy real(p2) parameter shows, the parent fractal was found by the evolver feature. I could have rounded off this parameter to -46.7 with little change in the resulting image. Fractals with exponents in the X.5 range are the most prone to the type of discontinuities that fill today's image. Fractal discontinuities decrease in significance as the exponent nears integer values, and vanish entirely when the exponent is an integer. I normally use the <floor> function with the MandelbrotBC1 formula, but for a change, I used the <recip> function in today's image. In today's image, which lies in the most-discontinuous range of exponents, the attractive symmetrical patterns that surround midgets in the classic Mandelbrot set are totally absent. Today's half-midget is surrounded by a kind of star-burst with an obvious break in the upper part. This break totally destroys any pretense of symmetry, though it does make an interesting feature. To add more interest, I rendered the image with the outside set to < fmod > and the proximity set to 0.5. The other outside options also make interesting variations of the basic scene, and are worth checking. I named the image "Unity and a Half" as a description of the exponent. I could rate the final result at only a 6. The rating is held down by the coloring, which could have used a bit more work. At least, the render time of 6 minutes is reasonable. The download of the finished image file is even more reasonable. That 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> Another perfect day here at Fractal Central on Monday produced perfect cats. The not-quite-dynamic duo spent the better part of the day in their porch chairs, watching the world, enjoying the temperature of 73F 23C, and remembering the days when they were actually dynamic. Today, unfortunately, is starting cloudy, with rain promised by afternoon. For me, it will be just another workday. Until next time and next fractal, take care, and sometimes fractals are not all they're cracked out to be. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Unity_and_a_Half { ; time=0:06:08.50--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=recip passes=1 center-mag=-0.73254313764763500/+0.180334958341697\ 00/4.605696e+007 params=1.5/0/-46.74114200262459/0 float=y maxiter=4200 inside=0 proximity=0.5 outside=fmod symmetry=none periodicity=10 colors=000CvNBnPBfRBZTASVAKXACZA5`WSZpnYokZnhZmeZl\ bZk_ZjX_iU_hR_gO_fL_eI_TFYHCXMIYQNYVSYZXYbaYgfYkkY\ opYkk`gfccae_XhXSjTNmPIpLDrH8uE4wF6rF7mG9hGAcO8TV6\ Ia47WGFQSMKcUEo`9zgBxcCv`DtYErVGpSHnPIlMJjJKiGPlJU\ nMZpPcrShtVmvYks_ipagmcfjedggbdi`ak_ZmYWoWTqUQsTNu\ RPrPQoOSmMTjLUhJWeIXcGY`E_YD`WBaTAcR8dO7eMBcOEaPI`\ RLZSOYTNTRMPPWnaSoYOpVJqRFrNBsK7tG3tD5qE6nF8lG9iHB\ gICdJEaKF_KHXLIVMKSNLPONNPOKQPIQY9Kf1Fg7DgCCgIBhNA\ hT9hY8ic7ih6im5ciAYfFScJN`OHYTBVX5Sa0Pe3Of6Og9OhBO\ iEOjHOkJOkMOlPOmROnUOoXOpZOp_Kl_Hh_Dd`A``6X`3T`0Qb\ 2Td3Ve4Xg6_h7aj8ckAfmBhoCjpEmrFosGquItvJvxKxyLzwOy\ vQxuSwtVvsXurZtqaspcroeqnhpmjollnkomjqlislngkrWkUg\ W6sGBcSGOcL8nODmQHlTMkVRjYWi__iadhdhgfmfiqekudiwib\ vkbti_odWj_TfVQaQMXLJTGFOBCJ69F1BE2CE3ED3FD4HC4IC5\ JB5LB6MA7OA7P98R98S89T89SBBSDCSGESIFSKHRNIRPKRRLRU\ MRWOQZPQ`RQbSQeUQgVQiWJpR } 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 02-06-03 (Burbles [7])
by Tim Wegner 03 Jun '03

03 Jun '03

Jim M wrote: > The FOTD for June 2 once again takes advantage of the multi- > valued nature of the complex log function. Jim, it was silly of me to request that someone make a fractal that illustrates the discontinuities of some of the transcendental functions like Log(). The examples are already legion in your work and an the work of many of the other fractal artists. Burbles has clear and obvious discontinuities. A fractal like the classic Mandelbrot has none, and cannot, because the underlying formula has no discontinuities. Tim

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FOTD 02-06-03 (Burbles [7])
by Jim Muth 02 Jun '03

02 Jun '03

FOTD -- June 02, 2003 (Rating 7) Fractal visionaries and enthusiasts: The FOTD for June 2 once again takes advantage of the multi- valued nature of the complex log function. The iterated expres- sion is a very simple Z^(1.5)+C. The trick in the MandelbrotBC1 formula is that an unlimited number of different images can be produced by the expression Z^(1.5), depending on which of the infinity of returned log values are chosen. The real(p2) parameter of the formula makes the choice. Today's image is part of the particular Z^(1.5) fractal that results when the real(p2) parameter of the MandelbrotBC1 formula is set to -31. The amorphous thing at the center is a midget of order 1.5. I have no idea what the jagged-edged colored disks surrounding the midget are. I have never seen anything quite like them. I have named the picture "Burbles". Those disks reminds me of something bubbling. The rating of a 7 seems correct for the image, which has more math interest than artistic worth. To see these truly unique fractal burbles, run the attached parameter file and wait 5 minutes, or download 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> Sunday started blustery and chilly here at Fractal Central, but by afternoon, the sun appeared, the wind slacked off, and the temperature rose to 66F 19C. The cats had a good day. This morning is starting much better. The cats will likely have another good day. For me, it's several hours work before my day will be good. Until next time, take care, and keep blowing those burbles. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Burbles { ; time=0:05:06.76--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=+0.72523926124837650/+0.172183551614105\ 20/488923/1/-62.5/9.1405363139562823e-010 params=1.5/0/-31/0 float=y maxiter=12000 inside=0 logmap=105 symmetry=none periodicity=10 colors=000GstKptNmuQkuThvXev_cwb`weYxiWxlTyoQyrOyo\ NvmNskMpiMmgMjeLgcLdaLa_KZYKWWJTUJQSJNQIKOIHMIEOJG\ QJISJJUJLVJMXJOZJQ`KRbKTcKUeKWgKYiKZkK`lKajRdhYgfd\ jdkmbrp`xsYvrWtrUsqRqqPppNnpKmoIkoGjnDhnBgm9em6dl4\ bl2al3bk3cj3di3ei4fh4gg4hf4hf5ie5jd5kc5lc6mb6na6o`\ 6o`5la5ia5fa5ca5`a5Yb5Vb5Sb5Pb5Mb9PcDSdGVeKYfN`gRc\ hVfiYijalkdolhrmlunoxoszpvzpozahyNaw9aw9aw9aw9aw9b\ vAbuBbuBctCctDcsDcsEdrFdrFdqGdqHepHepIepIeoJeoJfnK\ fnLfmLfmMglNgkNgkOgjPhjPhiQhiQhhRihSigSigTifUjfUje\ VjeWjdWkdXkcYkcYkbZla_la_l``m`am_am_bmZcnZcnYdnYen\ XeoXfoWfoWgoVhpVhpUipUjpTjqSkqSlqRlqRmrQnrQnrPorPp\ sOpsOqsNrsNrtMstMttLttLuuKvuKvuJwuJwsJwqKwoLwmMwkN\ wiOwgPweQweRweSwfTwfTwgSwgSwgSwgSuhRwiRwiRwjQwjQwk\ QwkQwkPwlPwlPwmOwmOwnOwnNwnNwoNwoNwpMwpMwqMwqLwrLw\ rLwrLwsKwsKwtKwtJwuJwuJwvJxvJywJzwJzxJzxJzyJzyJzzJ\ zzJzzJzzJzzJzzJzzJzzJzzJz } 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 01-06-03 (Curlers [5])
by Jim Muth 01 Jun '03

01 Jun '03

FOTD -- June 01, 2003 (Rating 5) Fractal visionaries and enthusiasts: We've been talking about multi-valued functions a lot lately, so here's a formula and an image that takes advantage of multiple values. It's not a new formula; I have posted many FOTD images created by it in the past. But it gives an example that good things can sometimes come from fractured fractals. The formula being iterated is Z^(1.06)+C, a formula that normally would produce nothing but a tiny featureless dot in the center of the screen. (Change the real (p2) parameter to pi to see this dot.) But thanks to those multiple values and today's formula, which takes advantage of them, the tiny dot has been transformed into an immense cigar with many fields of chaos around its edges. Today's scene is a blow-up of the edge of one of those fields of chaos. I have named the image "Curlers" because of the many loops that fill it. Not really impressed with the image, I have rated it at only a 5. The render time of 1/2 hour is almost entirely expended on the top inch or so of the image, so don't be concerned when nothing much happens for a while. Those who prefer not to wait the 1/2 hour can download the finished image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Rain fell off and on all day Saturday here at Fractal Central, while the temperature reached 73F 23C. A thunder-shower at 6pm climaxed the day's events as well as the cats' dis-satisfaction. Needless to say, a good treat of tuna was needed. Today is starting cloudy, windy and chilly, with occasional bursts of light rain -- not a good sign for fractal cats. For me, it's a sign I might not be able to trim the grass, but may have to go along on a shopping trip. Until next time, take care, and don't get broken up over fractured fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Curlers { ; time=0:38:53.19--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-6.07363/12.6745/0.4719481/1/72.5/-1.23\ 3735336114705e-014 params=1.06/0/121.2/3000 float=y maxiter=4200 inside=0 symmetry=none periodicity=10 colors=0007EXCCZHB`M9bR7dW6f`4hd3je7feAceE`eHYfLVf\ OSfSPfVLfZIgaFgeCgh9gl6go3dl5bi6`f8Zc9W`BUYCSVEQSF\ NPHLMIJJKHGLFDMHHPJKSLNVMQXOT_QWbRZdTagVdjWglXgmYf\ mxSuxRvsSsoSpjTmfTjaUhYUeTVbPV_KWXGWVFYQF_ME`IEbDD\ c9De5Df1Fc5Ga9H_DIXHJVLKTPLRTMOXNM`OKdPHhQFlRDpSBs\ PAnM9iJ8dH7_E6VB5Q94L63G32B116D3NP5c`7tZ8qY9oXAmWB\ kVCiUDgTEeSFcRGaQH_PIYOJWNJUPMTQPSSRSTURUWRWZQX`QZ\ cP_eP`hObjOcmNdoNbmMalL`jKZiJYhIXfHWeGUcFTbESaDR_C\ PZBOXANW9MV9OXBPZDQ`ERaGScIUeJVgLWhNXjOYlQZmR_kP`i\ OagNbeMccLdaKd_JeZLeYNfXPfWRgVThUVhTXiSZiR`jQbkPdk\ OflNhlMj`VqQcxSerUflWgfYi`ZjW`kQbmKdnEeo9`n8Wn7Sn6\ Nn5In4En39n24n10n09j4Ig8QdCOeAMf9Kg7Ig6Gh5Ei3Cj2Bj\ 1bl6hn9moCrqFwrItnJrkKphKmdLkaLiZMfVNdSNbPO_LOYIPW\ FQTBQR8RP5RKGPFRNBaL6lJ2wI4wJ6wJ7wK9wKBwKCwLEwLFwL\ EvNEuOEtPDsRDrSDqTCpVCoWCnXBmZBl_Bk`AjbAicAhdAheDk\ cGmbJoaMq_PsZSuYVwX4IT2GU } 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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