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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's fractal is kind of a mystery. I'm not sure if it is a real fractal or an artifact. The formula is simply a variation of the hypercomplex formula in fractint.frm, with a few more variable parameters added. The strangeness lies in the imag(p3) parameter, which is 10^(-012). It seems unlikely that such a small value could make such a big difference in the appearance of the parent fractal. I suspect that we may be dealing with some kind of mathematical imprecision here, but if so, I have no idea what it might be. Regardless, the fractals the formula creates appear as real as any other fractals. They may be zoomed into up to the limit of double-precision math, though the fact that the periodicity must be set to zero hints that the fractal-reality of this fractal might be questionable. It's a rather somber image, with a pronounced 3-D effect, which looks its best when the screen brightness is turned well down. I named the image "Double Trouble". It comes in two halves and there is always that troubling doubt about its validity. The rating of a 6 seems appropriate. The render time of just under one hour is necessary due to the large maxiter of 15000 and the necessity to turn off periodicity checking. But this time will be cut to 10 minutes or so on the fastest machines. If even this is too slow however, it would be best to wait until Paul posts the finished GIF image to the FOTD web site sometime later today. The web site may be accessed at: A steady chilly rain fell all day here at New Fractal Central on Tuesday. The fractal cats spent a good part of the day watching the cars splashing by. In my department, the big rush job that is supposed to be soon coming in has so far failed to appear. It is still promised this weekend however, so we'll have to see how it goes. The next fractal will go as scheduled in 24 hours, I presume. Until then, take care, and the crazy schedule will soon be over. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Double_Trouble { ; time=0:59:28.63--SF5 on a P200
reset=2004 type=formula formulafile=jim.frm
formulaname=HyperSquare passes=1 periodicity=0
center-mag=-0.17649147506615800/0/2086.338/1/90/\
-1.23373533611470521e-014 params=0/0.5/10/0/0/\
1e-012 float=y maxiter=15000 inside=0 logmap=443
colors=000UFKUDJUBIUBIUAHUAHU9HU9HU8GU8GU8GU7GU7GU\
6FU6FU5FU5FU5FU4EU4EU3EU3EU1FU2EU3EU4EU5EV6EV7EV8D\
V9DVADWBDWCDWDDWEDWFCXGCXHCXICXJCXKCXKBYKBYKBYKBYK\
BYKBYKBYKAYKAYKAYKAYKAYKAYL9YM9YM9YN9YO9YP9YQ7YR8`\
R8`S9`R9`RA_QA_QB_PB_PC_PCZPDZPDZPDZPEZPEYPFYPFYPG\
YPGYPHXPHXPIXPIXPJXPJWPJWPKWPKWPLWPLVPMVPMVPNVPNVP\
OUPOUPOUPPUPPUPQTPQTPRTPRTPSTPSSPTSPTSPUSPUSPURPVR\
PVRPWRPWRPWQPVQPVQPVQPVQPVSQVRPVQPVPOVPOVOTUNSTNSS\
MRQLRPKRNKQMJQKIQJIPIHPGGOFFODFOCENADN9CO7DN8EN8FN\
8FN9GN9HM9HMAIMAJMAJMBKLBLLBLLCMLCNLCOKCOKDPKDQKDQ\
KERJESJESJFTJFUJFUIGVIGWIGWIHXIHYHHZHHZHI_HI`HI`GJ\
aGJbGJbGKcGKdFKdFLeFLfFLfFMgEMhEMiEMiENjENkDNkDOlD\
OmDOmDPnCPoCPoCQpCQqCRqCSpDTpDUpEVpEWpEXpFYpFZpG_p\
G`pGapHbpHcpIdpIepIfpJgpJhpKipKjpKkpLlpLmpMnpMopMp\
oNqoNroNsoOtoOuoPvoPwoPxoQyoQzoRzoRzoRzoSzoSzoTzoT\
zoTzoUzoUzoVzoVzoVzoWzoWz }
frm:HyperSquare {; Jim Muth
a=(p1),b=(0,0):
q=sqr(a)-sqr(b)+pixel
b=p2*a*b+p3
a=q,
|a|+|b| <= 100 }
END PARAMETER FILE=========================================
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times.
