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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: With today's image we continue the explorations of minibrots in the Mandeloids of very low order, going down from yesterday's 1.075 to 1.05. The parent fractal is a grossly oversized thing, shaped rather like a comet, with debris fields on both sides of its squared-off outer extremity. It was produced by calculating the formula Z^(1.05)+C at a level 13 turns up the logarithmic hyperspiral. Today's image is located at the edge of the southern debris field at the outer extremity of the parent. The exact spot is impossible to recognize on the surface, and I needed to use my not-so-secret method of identifying minibrots to ferret out the elusive little midget. In fact, I never did reach the minibrot itself. The resolution breaks down well before the minibrot becomes visible. But the pattern around it is quite interesting -- perhaps the best defined pattern I have yet found around a minibrot in a fractal of such a low order. Or maybe it's just that I put a bit of effort into the coloring. I named the image "Into the Depths", which is a fair description of the impression I get while studying it. I rated it at a 7.5, mostly because it is surprisingly rich for a scene in a fractal of such a low order, but also to give myself a pat on the back for the coloring. The calculation time of just under 2-1/2 minutes on a fireball 2000mhz machine should bring tears to no one's eyes. But computers are notoriously prone to stubbornness, so to guarantee dry eyes, I recommend visiting the FOTD web site at: The next FOTD will appear in 24 hours, most likely continuing the same theme with an exponent even closer to unity. Until then, take care, and take no fractal for granted. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Into_the_Depths { ; time=0:02:24.45-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC3 function=ident logmap=228
center-mag=-14.84534363332544/-23.4626947348403/4.\
554307e+010/1/-21.75/0 mathtolerance=0.05/1 float=y
params=1.05/0/13/1500 passes=1 maxiter=1500 inside=0
periodicity=10
colors=0000FTWQh00fKDZWLa00ZGIZOHYWFSE4JUCZRAbW9JT\
QJUFdzuJwcLUL`UJeQUQRNSUGjT9dT3WU9bVFqzLnzMoVMoVNz\
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cnUbmXblZbkaajcajeaihahj`gl`fo`fq_es_dv_cx_czX`wVZ\
tTXqRVnOTkMRhuAPXXrWVoWTm }
frm:MandelbrotBC3 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*fn1(p/(2*PI))
r=real(p2)+PI-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 PARAMETER FILE=========================================
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times.
