June 2003 - Fractint - mailman.xmission.com

FOTD 09-06-03 (This is How Low [5])
by Jim Muth 09 Jun '03

09 Jun '03

FOTD -- June 09, 2003 (Rating 5) Fractal visionaries and enthusiasts: Today's image takes us to the bottom of the barrel, way down to the land of Z^(1.009)+C. At this abysmal depth, the sand-like fractal material has reached such a high maxiter that it is effectively beyond reach. But the areas of extreme discontinu- ities continue to multiply, and though still of a very high maxiter, are within reach for those with patience. The 'recip' function was an accident. The 'floor' function works best with this formula, but the image is good, and who's complaining. In today's fractal, the coloring makes the picture. A very broad palette is necessary to add definition to an otherwise featureless image, but when this is done, a series of feathery curving arms appears. I have named the image "This is How Low" because its exponent of Z is about as close to unity as it is possible to come and still get something other than an empty, featureless circle. I have rated the image at an average 5, more for mathematical interest than for artistic worth. If it were not for the render time of over 2 hours on my machine, the image might have rated a 6. But don't be put off by the slowness of the image. Give Paul and Scott a couple hours to render the image, then visit their web sites to download the completed image. 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 rain held off on Sunday here at Fractal Central. Despite a temperature that never reached 70F 21C, the fractal cats had a good day. When the cats are happy, I'm happy also, so I also had a good day. Today is actually starting with some sun, and no rain is forecast, making another good day near certain. Once the day's work is behind me, assuming the cats are happy, my day should once again be good. Tomorrow's FOTD might launch out in a new direction, or it might be a return to the MandelbrotMix4 formula and the midgets it draws. To see what happens, check back in 24 hours. Until then, take care, and hope for the best. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ This_is_How_Low { ; time=2:05:42.24--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=mandelbrotbc1 function=recip passes=1 center-mag=+0.07536313779841985/+0.000859404003554\ 35/8654862/1/51/-1.76329913170736319e-009 params=1.009/0/-182/1000 float=y maxiter=12000 inside=255 logmap=3216 periodicity=10 colors=000zlPzmQzmQzmQzmQzmRzmRymRymRymRymSxmSxmSx\ mSxmUwmTwmSwmSwmRvmRvmQvmQvmPumPumOumOumNtmNtmMtmM\ tmLslKskKsjJsiJrhIsgItfHueHvfGwfGxgFygFwhEwhEwiDwj\ CziDziDzhDzhDzgEzgEzfEzfEyeExeFwdFvdFucFtcGsbGrbGq\ aGpaGo`Hn`Hm_Hm_HmZIlZIlYIlYIlXIlXJlXJlWJlWJkVJkVK\ kUKkUKkTKkTLkSLkSLjRLjRLjQMjQMjPMjPMjONjONiNNiNNiM\ NiMOiLOiLOiKOiKPhJPhJPhJPhIPhIQhHQhHQhGQgGQgFRgFRg\ ERgERgDSgDSgCSfCSfBSfBTfATfATf9Tf9Uf8Ue8Ue7Ue7Ue6V\ e6Ve5Ve5Vg3Wf4Ve5Ve5Vd6Ud6Uc7Uc7Tb8Ta8Ta9S`AS`AS_B\ R_BRZCRYCQYDQXDQXEPWFPWFPVGOUGOUHOTHNTINSINSJMRJMQ\ KMQLLPLLPMLOMKONKNNKMOJMOJLPJLQIKQIKRIJRHISHISHHTG\ HTGGUGGVFFVFEWFEWEDXEDXECYDCYDBZD9YCBZDC_DD_DE`EF`\ EGaEHaEIbFJbFKcFLcGMdGNdGOeGQeHRfHSfHTgHUgIVhIWhIX\ iJYiJZjJ_jJ`kKakKblKclKclJblJalJalJ`lI_mI_mIZmIYmH\ YmHXmHXmHWmGVmGVmGUmGTmFTmFSnFRnFRnEQnEPnEPnEOnDNn\ DNnDMnDLnCLnCKnCJoCJoBIoB } 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_2
by Albrecht.Niekamp＠t-online.de 08 Jun '03

08 Jun '03

Hi, not many words are needed about this one. Zoom out for more. There is a small modification in the formula, except that the text explanations are better and you can see, which function belongs to each factor. Yesterday`s images are not affected, so I suggest you just exchange the formula. Fractal greetings, Al. -------------------------------------start-par----------------------------- Zoomers_playground { ; Time 0.57.16.12 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult241.frm formulaname=multifractal_2 ismand=y function=exp/exp/exp/exp passes=t center-mag=-0.500313/6.66134e-016/1.173709 params=0.3102206488235115/0.9875484481337932/19182.101/41.321405/4048.02\ 048/384.000003/768.000218/256.0076800000001/512.01024/1536.01024 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200600<2>000<25>iiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0c\ q0es<3>0kz<25>09C08A068<2>022000211<24>oiQqjRslS<3>zsX<25>CB7A96875<3>00\ 0400<23>o00q00s00<3>z00<27>800 } Black&white { ; ; Albrecht Niekamp June, 03 ; ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult241.frm formulaname=multifractal_2 ismand=y function=exp/exp/exp/exp passes=t center-mag=+0.09277978820879434/-0.47206879974324510/196.0418/0.9356/17.\ 3385926046431678/0.333924698186814028 params=0.3102206488235115/0.9875484481337932/19182.101/41.321405/4048.02\ 048/384.000003/768.000218/256.0076800000001/512.01024/1536.01024 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200600<2>000<25>iiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0c\ q0es<3>0kz<25>09C08A068<2>022000211<24>oiQqjRslS<3>zsX<25>CB7A96875<3>00\ 0400<23>o00q00s00<3>z00<27>800 } -------------------------------start-frm----------------------------------- FRM:Multifractal_2 { ; Albrecht Niekamp 070603 ;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 ;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)*1000000) 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/10000) d=d-mm*10000 p6=trunc(d/100)/10 d=d-p6*1000 if (t) p6=-p6 endif p7=d/10 ; d=real(p3) mb=trunc(d) ba=(d-mb)*100000 ; d=imag(p3) sfac=trunc(d) b1=(d-sfac)*100000 ; 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) u=fn1(1/sfac) if (ismand) z=0 if (vb) c=u*0.4*log(sqr(pixel^mm)) ba=mb else c=pixel*u 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) 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 |z|<=ba }

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FOTD 08-06-03 (Undersea Fantasy [7])
by Jim Muth 08 Jun '03

08 Jun '03

FOTD -- June 08, 2003 (Rating 7) Fractal visionaries and enthusiasts: With today's image, we sink all the way down to an exponent of Z^(1.015) and the hard-to-find chaos that lies in the resulting fractals. We examine this lowly fractal at a point 275 levels down the logarithmic spiral, though from the degree of disorder in the image, I assume the spiral has long since ceased to resemble the spiral shape we are familiar with. Not only is the image filled with discontinuities, but the discontinuities are discontinuous. The whole thing vaguely reminds me of an undersea scene, and I named it "Undersea Fantasy" accordingly. It's a spectacularly colored image, with colors perhaps a bit too gaudy, so I held the rating to a 7. As I warned earlier, the chaos in these very low fractals is of a very high maxiter and quite hard to bring out. The render time of 1 hour and 5 minutes for today's image demonstrates this fact. This slowness will grow only worse as we continue our descent toward our ultimate but perhaps unreachable goal of Z^(1.009). Luckily for fractalists with other things to do, the finished image of today's fractal will soon be available on 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> With the temperature hovering around 66F 19C, heavy rain fell all day here at Fractal Central on Saturday. It came to an end shortly before sunset, but by that time the cats' day had been totally spoiled. Their moods were sour, and the tuna treat only partially restored their spirits. Today is starting cloudy, but at least it is dry. If all goes well, and the forecasted showers hold off, the dynamic duo will have a better day. The fractal basement took on water in the rain, so my task for today will be to dry things out down there. Until next FOTD, take care, and how low can you go? Stay tuned to see. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Undersea_Fantasy { ; time=1:05:47.33--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-4.41217/0.0769257/4.96124/1/12.5/1.784\ 961067841095e-013 params=1.015/0/-275/10000 float=y maxiter=12000 inside=255 logmap=202 periodicity=10 colors=050LJYNJXNSXPHVPHV_HTQGTSGSSGQTGQTEPVEPVENS\ ENXDLXDKeDKYDI_BI_BH`BH`BFb9Eb9Ed9CY9Ce7AV79g79`77\ h67h65j65j64k52k52m51m51o50o50p50h50r50r50s50s50k5\ 0s50s50s50s50s50s50s50s60m60s70s70s90s90hB0sB0uD0u\ D0uE0uE0uG0uG0uH0uH0jJ0uJ0uK1uK1jM1uM1uO1wO2wP2wP2\ wR2wR2wS4wS4wU4wU4wV4wV5jX5wX5wY5wY5x_7x_7xa7xa7xc\ 7xc9xd9xd9xf9xf9xgAxgAxiAxiAxjAzl9xjAxjAwjAwjAuiAu\ iAuiAsiAsgArgArgArgApgApfAofAofAofCmdCmdCkdCkdCkcC\ jcCjcChcChcChaCgaCgaCeaCe_Ce_Cd_Cd_Eb_EbYE`YE`YE`Y\ E_XE_XEYXEYXFYVGXVHXVIVVJVVKVULTUMTUNSUOSSPSSQQSRQ\ SSPSTPRUPRVNRWNRXLPYLPZLP_KP`KOaIObIOcHOdHOeHMfFMg\ FMhEMiEKjEKkCKlCKmAKmAJmAJm9Jm9Jm7Hm7Hm7Hm5Hm5Gm4G\ m4Gm4Gm2Gm2Em1Em1Em1Em0Dm0Dm0Dm0Dm0Bm0Dm0Dm0Em0Em0\ Gm0Gm0Hm0Hm0Jm0Jm0Km0Km0Mm0Mm0Om0Om0Pm0Pm0Rm0Rm0Sm\ 0Sm0Um0Um0Vm0Vm0Xm0Xm0Xm0Ym0Ym0_m0_m0am0am0cm0cm0d\ o0do0fp0fr0gr0gs0is0iu0ju } 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 07-06-03 (First Flight [6])
by Jim Muth 07 Jun '03

07 Jun '03

FOTD -- June 07, 2003 (Rating 6) Fractal visionaries and enthusiasts: Today's image takes us into even lower territory -- down below yesterday's Z^(1.04) into the land of Z^(1.025)+C. Down in these depths, the chaos becomes harder to find, but as today's image shows, it is still there. The lengthy real(p2) parameter shows that the value was found by the Fractint randomizer. I could have rounded it to a 7 with little change in the parent fractal. Yesterday's image reminded me of a fleet of fantastic space craft taking off from a Martian invasion base. Today's image reminds me of jagged shards of something being swept up and away into infinite space by a sudden wind. Since the wind is the first in thousands of years to blow in this particular place, I named the image "First Flight". Today's image attempts the same effect as yesterday's superior image, but compared to that image, today's rates only a 6. But today's image is not without its interest. Despite the almost total descent into chaos, there are still traces of order in the image. The curving trails of bright debris in the background appear on the verge of organizing and creating a new class of order. I must examine this tendency of chaos to organize in fractals with exponents even closer to unity. The 16-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> A mostly cloudy but mild day here at Fractal Central on Friday left the duo of fractal cats satisfied. After spending the afternoon enjoying the temperature of 75F 24C, they ended the day enjoying a treat of turkey. Their moods will be far less pleasant today however. It is already raining, heavy rain is forecast and a flood watch is in effect. I'm going to spend the day searching for fractals, working on the CD, or just plain watching the rain. Until next time, take care, and let's see a few Mandelbrot midgets. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ First_Flight { ; time=0:16:40.24--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=recip passes=1 center-mag=-2.62369017010877200/-0.375504820890258\ 10/91.72629/1/175/-1.06827741097603734e-012 params=1.025/0/6.942381054109317/1000 float=y maxiter=4200 inside=255 logmap=190 periodicity=10 colors=000iYDeaDa_F_XHbVHHXIjVIHVKHVKFULFULFUNDSPD\ SPDSQCQQCQSCQSASUAPUAKH9Q`APVANQANSALSCKQCKPCINCIN\ YHLDFKDFIXDIDCHDCFWADFADV9CF8AF8AH79H78H57H47H45I2\ 4I12I12I01I00K00K00K00K00I00K00L00N00P00Q00S00S00U\ 00V00X00Y00_00_00a00c00d00f00h00j00j01l01n01p01r01\ s02s02v02w02z02z04z04z04z04z04z05z05z05z05z05z07z1\ 8z28z59z79z8AzAAzCCzDCzHDzIFzKFzNHzPHzQIzUIzVKzXKz\ _LzaNzcNzfPzhPzjQwnQwpSwrSvvUvwVvzVszXszXszYqzYpz_\ oz_nzKmzAkz8izAgzCezEczGazI_wKYvMWsOUrQSpSQpUOnWMl\ YKj_IjaGhcEfdCdeAdf8cg6ah5_i6_j7Yk7Xl8Vm9Vm9UmASmC\ QmCQmDPmFNmFLmHLmIKmIImKHmLHmLFmNDmPCmPCmQAmS9mS8m\ U8mV7mV5mX4mY4nY2o_1pa0qa0rc0sd0vc0zd0zd0zd0zf0zf0\ zf0zf0zh0zh0zh0zh0zj0zj0zj0zj0zl0zl0zl0zl0zj0zj0zj\ 0zj0zh0zh0zh0zh0zh0zf0zf0zf0zf0zf0zd0zd0zd0zd0zc0z\ c0zc0zc0zc0za0za0za0za0za0z_0z_0z_0z_0zY0zY0zY0zY0\ zY0zX0zX0zX0zX0zX0zU0zS0z } 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 29-05-03 (All Inside Stuff [6])
by Jim Muth 07 Jun '03

07 Jun '03

FOTD -- May 29, 2003 (Rating 6) Fractal visionaries and enthusiasts: I see on the Fractint list that the 'bug' in the program that has caused the MandelbrotMix4 formula to run incorrectly has been identified and can be fixed without too much effort. This obviously will have an impact on the upcoming FOTD-CD. Until now, I have been feeling a bit guilty about the unreason- able delay in releasing the FOTD-CD. Now however, it appears the delay will be a good thing, for it will enable me to release a disk that does not depend on a bug in the program to render the images correctly. Of course, this means a further delay in the release of the disk while any needed changes that might arise are being done, but after a delay of nearly a year, that will be of little consequence. Meanwhile, whenever I find the time, I am still working on the task of identifying and renaming the images on the disk, so that they can be matched with their corresponding discussions without confusion. And on a non-fractal topic, I'm now receiving spam snail mail. Yesterday, I received in the snail mail an air-mail letter from Zimbabwe, which is a country in the southern part of Africa. The enclosed letter was a print-out of the same fraudulent offer that I have received so many times in the e-mail. The letter tells me that a probably fictional Mr. Twala has in his posses- sion 9.2-million US dollars that he wants to transfer out of his country. To do this transfer he needs my bank account number. Once he has the account number, guess what will happen to any money in the account. I find it hard to believe that anyone would fall for such an obvious scam, but whoever is sending these letters must be finding some pigeons naive enough to fall for his scheme, because the postage on the envelope amounts to 700 Zimbabwe dollars or whatever their monetary unit is, and he must send out thousands of such letters. At least the stamps on the envelope, which picture a newly constructed dam, are attractive. Today's fractal is also attractive, though not quite as attrac- tive as the dam in Zimbabwe. It is another 'evaporated' image, this one located near the right edge of the fan of the parent fractal. I named the image "All Inside Stuff" as a description, and rated it a 6 because it is interesting but not that great. The render time of 19 minutes is somewhat slow for a 6-rated image, but immediate relief is available at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> It rained all morning here at Fractal Central on Wednesday, then the sun appeared and the afternoon was sunny. The temperature reached only 65F 18C, when 79F 26C is normal, but the dynamic pair had a great several hours in the yard, enduring the wet grass with little complaint. Today once again holds a chance of rain. It remains to be seen how the duo will adjust. I'll do my adjusting when the work is done and the next fractal is found. That time will likely be around 3pm. Until next time and next FOTD, take care, and don't give up hope for the FOTD-CD. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ All_Inside_Stuff { ; time=0:19:39.03 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+1.69799788216427200/-0.966528307188927\ 90/366675.9/1/-132.5/-9.33145443554606047e-009 params=-10/-1.1/-1/-11/0/1e+100/0/0 float=y maxiter=1200 inside=bof61 periodicity=10 colors=000eiOfhQggThfWjeZkdalccmbfoaip`lq_orZqqVoq\ SmpPkpMioJgoGenDcnAan7_l6Zk6Zj6Yh6Yg6Yf6Xd6Xc6Wb6W\ `6W_6VZ5VX5UW5UV5UT5TS5TR5SQ5SO5SN5RM5RK5QJ4QI4QG4\ PF4PE4OC4OB4OA4N84N74M64M00054M56M58M5AM6CM6EM6HM6\ JM7LM7NM7PM7RM7TM9VOAWPCXQDYRF_SG`TIaUJbVLdWMeXOfY\ PgZRh_Sj`UkaVlb000Yod_pe`qfbrgctheuifvjhwkkynixlhw\ jfvieugctebsd`sb_r`Yq_XpYVoWUnVSnTRmRPlQOkOMjM000J\ hJIhHGgGFfEDeCCdBAc97e68d79c89b9AbABaBB`CC`DD_EDZE\ EZFEV`FXHGTZGWJHVKIVLIUMJTMKTNKSOLRXLRQMQRNPSNOTOO\ UPNUPMVQMWRLXRKYSKZSJ_TI`UIaUHhVGbWGmWFdXErYEfYDrZ\ ChZCw`EiaGibIjcKjdMjeOkfQlgSlhUliWmjYmkZnl`nmbondo\ ofophpqjprlqsnqtprurrytuvsrtsoqslosjlrgjrdgraer_bq\ X`qUYqRWqPTpMRpJOpGMpERmCVjBZgAce9gb8k_7rZ6pY6oY6n\ X6mX6lW6kW6jV6hV6gV6fU6eU6dT6cT6bS6aS6_S6ZR6YR6XQ6\ WQ6VP6UP6SP6RO6QO6PN6ON6NM6MM6KL6LM6LM6MM6MN6NN6NN\ 6ON6OO6PO6PO6PO6QP6QP6cjL } 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==================================

3 2

Multifractal_2
by Albrecht.Niekamp＠t-online.de 06 Jun '03

06 Jun '03

Hi, hereïs what kept me silent the last days. This formula has a new structure, as I found out, how to check and uncheck all options and still they are executed in the correct order and the switching sequence is terminated after the last checked item. Also distorted structures are down to a minimum. I think this is the best one so far. Fractal greetings, Al. --------------------------------------------------------------------------- Janusbird4 { ; Time 0.33.16.49 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult241.frm formulaname=multifractal_2 ismand=y function=exp/exp/exp/exp passes=t center-mag=-0.500313/6.66134e-016/1.173709 params=0.3102206488235115/0.9875484481337932/10182.101/40.321405/4048.02\ 048/384.00004/768.00032/256.0076800000001/512.01024/1536.01024 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200600<2>000<25>iiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0c\ q0es<3>0kz<25>09C08A068<2>022000211<24>oiQqjRslS<3>zsX<25>CB7A96875<3>00\ 0400<23>o00q00s00<3>z00<27>800 } Rubberboat { ; ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult241.frm formulaname=multifractal_2 ismand=y function=cos/exp/exp/exp passes=t center-mag=-0.48/6.66134e-016/1.103753 params=0.3102206488235115/0.9875484481337932/10189.101/40.321402/4048.02\ 048/384.00004/768.00032/256.0076800000001/768.01024/1536.01024 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200600<2>000<25>iiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0c\ q0es<3>0kz<25>09C08A068<2>022000211<24>oiQqjRslS<3>zsX<25>CB7A96875<3>00\ 0400<23>o00q00s00<3>z00<27>800 } -------------------------------start-frm------------------------------------ FRM:Multifractal_2 { ; Albrecht Niekamp 040603 ;only integers as first input, second input 5 digits to the right ;real(p2) 5digits: shape, outside, in1, in2, in3 ; 1_mand 2_jul 3_hyb.mand 4_hyb.jul +5_reset digit1 +5_warpeffect ; 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 ;real(p3) many_mods bailout, bailout ;imag(p3) shape : factor, border ;real(p4) outside : factor, border ;imag(p4) maxiter1, factor1 ;real(p5) maxiter2, factor2 ;imag(p5) maxiter3, factor3 ; 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)*1000000) 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/10000) d=d-mm*10000 p6=trunc(d/100)/10 d=d-p6*1000 if (t) p6=-p6 endif p7=d/10 ; d=real(p3) mb=trunc(d) ba=(d-mb)*100000 ; d=imag(p3) sfac=trunc(d) b1=(d-sfac)*100000 ; 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>b1) 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 c=p1*u endif ex0=0 tt=tt-1 elseif ((ex1) && bo>b2) u=2*(fn1(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) 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 |z|<=ba } ---------------------------------------------------------------------end---- -----------

1 0

FOTD 06-06-03 (Martian Take-Off [8])
by Jim Muth 06 Jun '03

06 Jun '03

FOTD -- June 06, 2003 (Rating 8) Fractal visionaries and enthusiasts: For today's image we return to the chaos along the shoreline of the Z^(1.04)+C Mandeloid. I really should not say *THE* shoreline, I should say *A* shoreline, because the Z^(1.04)+C Mandeloid has an infinity of shorelines, and the shoreline in question is but one of that infinity. The shoreline is actually part of the parent as it appears in the slice 40 turns up the logarithmic spiral. As the exponent of Z is lowered ever closer to unity, the chaos in the more remote logarithmic slices of fractals first grows more chaotic, with large areas of what I call sand. The sand is present down to an exponent of around 1.01, where, due to its increasingly high maxiter, it becomes so hard to reveal that it is impractical to explore. Below this point, the Mandeloid fractals resemble mere jagged pieces of rock. The amount of sand peaks at an exponent of around 1.1, where it sometimes contains quite interesting sub-patterns. As the exponent is raised, the sand never really disappears, but becomes confined ever closer to the shoreline. By stretching my imagination, I saw in today's image a scene on a fantastic Planet Mars. Using a bit more imagination, aided by the film "War of the Worlds", I saw a fleet of space ships taking off on their way to invade earth, and named the image "Martian Take-Off". I assume that, thanks to its bacteria, the earth will survive the invasion of the fractal space craft. There is something about the image that I like. Maybe it's the jagged rust-colored rocks and space ships, maybe it's the blue of the Martian sky. Whatever it is, I rated the image at a much- above-average 8. With the help of a little imagination, the invasion fleet can be seen by running the parameter file and eagerly waiting for 15 minutes. The fleet can also be seen by downloading the pre- rendered 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> Fine sunny weather and a temperature of 77F 25C here at Fractal Central on Thursday made for contented cats. The aging duo made the most of the situation by spending the day in the yard, watching for the new grey-and-white cat who moved in up the hill a couple weeks ago. Luckily for someone, the cat never showed up, and the once-dynamic duo had a restful day. Today is starting sunny again, which should assure the duo another good day. My day will be busy as I finish the work I failed to finish yesterday. And when the work is finished, I'll launch the search for the next FOTD fractal. Until next time, take care, and is there earth life on Mars? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Martian_Take-Off { ; time=0:15:11.76--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-7.03071/1.76031/1.456008/1/30/1.657771\ 14258247593e-013 params=1.04/0/40/1000 float=y maxiter=1800 inside=255 logmap=26 periodicity=10 colors=070zzTzzQzzQzyQqwOosOlqOioMgmMdkMaiKYgKXeKT\ cIQaIOYIKWHIUHFSHDNF9OF7MF5KDPMDRHDSOB0AB07BUP9079\ 079XU7ZR7Z77K77P79U79Z79c79Z79U79Z79K79F79A79c7907\ 9U7927B07B57B77B97BB7BD7BF7BH7BI7BK7BM7BO7BQ7DT7DV\ 7DX7DY7D_7Da7Dd7De7Dg7Di7Dl7Dn7Di7He7Ia7MY7OV7TTAV\ VDXXH__KadOeeSggWgl`doc_tgXvkTxoOzsKzwHzzDzz9zzBzz\ BzzDzzDzzFzzFxyHxyHvyItwItwKquKouKouMnsMlsOisOiqQg\ qQeqTeoTdoVaoVamX_mXYkXYkYXkYVi_Vi_TiaQgaOgdOgdMee\ KeeKegIcgHcgHaiFaiDalD`lB`n9`n9Yo7Yo5Yq3Wq3Wt2Wt0U\ t0Uv0Sv0Sx0Sx0Qz0Qz0Qz0Oz0Oz0Oz0Mz0Mz0Mz0Kz0Jz0Jz0\ Hz0Hz0Fz0Fz0Dz0Dz0Bz0Bz0Az08z08z07z07z07z07z07z07z\ 07z07z07z07z07z07z07z07z07z07z07z07z07z07z07z07z07\ x07x07x07x07x07x07x07x07x07x07x07x07x07x07x07v07v0\ 7v07v07v07v07v08v0Av0Bv0Dv0Dv0Fv0Fv0Hv0Ht0Jt0Jt0Kt\ 0Kt0Mt0Mt0Ot0Ot0Qt0Qt0St0St0Ut0Ut0Wq0Wq0Yq0Yq0`q0`\ q0aq0aq0cq0cq0eq0eq0gq07m } 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==================================

1 0

Multifractal_1 par
by Lee H. Skinner 06 Jun '03

06 Jun '03

Here is a most unusual image - a zoom into Al's Mixdown. Bon_Voyage { ; Cruise Ship ; t= 3:06:40.91 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=multifractal_1 ismand=n function=exp/sin/exp/cosxx passes=1 center-mag=-0.08292638608437355/+0.15195752455824630/\ 3171.241/1/17.5000000000002487/6.87387646802761765e-0\ 13 params=-0.2724234748374889/0.09260841170049135/384.00\ 001/3072.4505/128.0256000000001/768.0256000000001/256\ .0256000000001/768.0307200000001/12298.7/2.16 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 symmetry=none periodicity=0 rseed=-2436 cyclerange=2/253 colors=000000U6X<2>F9LAAG7FO4KW0Qc<3>5Xc6Zc7`c7aa7c_7\ eY<3>FcgHciJbl<3>S_v<3>civflvinvlqvotvsww<2>zzz<3>rwz\ ovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI<4>XCAaB9fB7<3>zA0<13>S\ A1QA1NA1<3>D92<3>NN7PQ8SU9<3>`fDhrI<3>UnXRm_NlcJkgFfp\ Aaz<3>PJoSFlWAi_5fc0ce7_jFRoNIzb0<2>zz1zzC<2>zzz<3>jq\ dfo_blU<3>Mb8<3>LQ8KM8KJ8<2>I88H44G00<3>TA5WD6ZF7aI8e\ LAhMBiODjQF<3>qeBriAtm9vq8xu7zz5zz4zz3<8>zY4zV5zS5<3>\ zE6wE6tD6<10>w8Px8Rx7S<3>z5_<3>f5Ma5IW4E<2>_4H<3>P3DN\ 2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0gy0h<3>u1mt1n\ s1or2q<2>v2u<4>Z6`600enG } 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 }

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32k
by bill ragette 06 Jun '03

06 Jun '03

help! can any one help me to get fractinct to use the new disk video mode supposedly 32k x 32k? the biggest option appears to be 2048 x 2048 i've tried fooling with makefcfg, but can't get that option to appear i have a brand new laptop with tons of memory thanks easy _________________________________________________________________ Protect your PC - get McAfee.com VirusScan Online http://clinic.mcafee.com/clinic/ibuy/campaign.asp?cid=3963

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FOTD 05-06-03 (Low-Low Textures [5])
by Jim Muth 05 Jun '03

05 Jun '03

FOTD -- June 05, 2003 (Rating 5) Fractal visionaries and enthusiasts: In yesterday's FOTD I wrote that I had once found a midget in the Z^(1.04)+C fractal. The graph of Z^1.04 is nearly a straight line, and since linear functions do not make fractals, it should not be expected to create a fractal. But in today's image, we wander far from the principal image, and at the remote level 100 turns up the logarithmic spiral, Z^(1.04)+C produces an interesting parent fractal -- a sprawling oversized bay with much chaos on the southern shoreline and a smaller amount of chaos on the northern shoreline. Today's image is a scene in the chaos along the northern shore- line of the parent. I have named the image "Low-Low Textures", since the exponent of Z is so small and the image consists of nothing more than a simple texture, with the elements endlessly repeated at smaller scales. Yes, I once did find a real midget that did not vanish when the maxiter was increased in one of the Z^(1.04)+C Mandel fractals. I have no idea where I found it. There could be an infinity of midgets in today's image, in fact there certainly are, but in the range of 1.04 they are so tiny and buried so deeply, with no hint of symmetry around them, that they are virtually impossible to find. I rated today's image at a perfectly average 5. If I had actually found one of those impossible-to-find midgets, I might have rated the image a 6. The render time on my worn-out fractal machine is 1/100 second less than 6 minutes. It will be faster on more vigorous units. The fastest way of all to see the texture in today's image is to download the completed 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 rain continued through the day here at Fractal Central on Wednesday. The temperature hovered at 57F 14C. The two fractal cats had no time at all in the great outdoors, and as a result, were unhappy cats. A treat of tuna in the evening made them less unhappy, but fish is no substitute for a trip to a great place. The feline duo ended the day in a mood of resignation. I finished yesterday's work on time, and hope to do the same today. The next fractal will arrive in 24 hours. Until then, take care, and hidden jewels are sometimes found in the lowly places. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Low-Low_Textures { ; time=0:05:59.99--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-6.563247556907927/+1.425281219594758/2\ 66.6667/1/-5/9.7999386383662568e-013 params=1.04/0\ /100/1000 float=y maxiter=600 inside=255 logmap=116 symmetry=none periodicity=10 colors=000LJWMKXMLYMNYNOZNP_NQ`OSaOTbOUbPVcPXdPYeQ\ ZfQ`gQagRbhRciRejSfkSglShlTjmTknTloUmpUoqUpqVqrVrs\ VttWuuWvvWwvVvuVuuVutVttVstVssVrsUqsUqrUprUprUoqUn\ qUnqTmpTlpTlpTkoTjoTjoTinTinShnSgmSgmSfmSelSelSdkR\ ckRckRbjRbjRajR`iR`iR_iQZhQZhQYhQXgQXgQWgQWfPVfPUf\ PUePTePSePSdPRdOSePRdPRdQRdQQdRQdRQdSPcSPcSPcTOcTO\ cUOcUNbVNbVNbVNbWMbWMbXMbXLaYLaYLaYKaZKaZKa_J`_J``\ J``J``I`aI`aI`bH_bH_cH_cG_cG_dG_dFZeFZeFZfEZfEZfEZ\ gEZgDYhDYhDYiCYiCYiCYjBXjBXkBXkAXlAXlAXj9TlAXmA`oB\ cpBgqCksCntDovCpuDquDruDsuDttDutDvtDwtExsEysEzsEzs\ EzrEzrEzrFzrFzrFzqFzqFzqFzqFzpGzpGzpGzpGzoGzoGzoGz\ oHznHznHznHznHznHzmHzmIzmIzmIzlIzlIzlIzlIzkJzkJzkJ\ zkJzjJzjJzjJzjKzjKziKziKziKziKzhKzhLzhLzhLzgLzgLzg\ LzgLziKzgLzfLzeLzdLzcLzbLzaMz`Mz_MzZMzYMzXMzWNzVNz\ UNzTNzRNzQNzPNzOOzNOzMOzLOzKOzJOzIPzHPzGPzFPzEPzI7\ zJ9zJAzJBzKDzKEzKFzLGzLIz } 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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