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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: For today's image we return to the same parent fractal that held yesterday's image. This fractal resulted when I mistakenly subtracted Z^(1.68) from Z^(1.4142) instead of subtracting the Z^(1.618), Golden Ratio which I had originally intended. This parent fractal is a very large near-Mandelbrot set, with a messed up Elephant Valley and a runt-like main positive stem. In yesterday's image we examined the inner detail of Elephant Valley; in today's image we examine the detail of the abortive main stem. What we find there is an area reminiscent of the railyard effect found in the negative X-axis area of fractals such as the one created by the formula Z^(2.003)+C. And as along that fractal's negative X-axis, today's parent fractal is chock full of midgets along its positive X-axis. Today's image shows one of these. I named the image "Why Me?". I gave it this name when I considered the vanishingly small chance that this particular fractal would ever see the light of day. I rated it at a 6 because to me it seems just a tiny bit above FOTD average. If I had put more effort into the coloring, I might have raised the image to a rating of a 7, but I fear the rating of a modest 6 will remain forever fixed. One thing that will not remain forever fixed however is the calculation time. As computers get ever faster, the calculation time will shrink from its present 1-1/3 minutes on a P2000, and no one can say how brief that time may eventually come to be. But the fastest and easiest way to see the image today is to forget calculating it and view it on the FOTD web site at: Tuesday turned out average in all respects here at Fractal Central. The weather was neither unusually good nor bad, the work was neither unusually heavy nor light, the fractal cats were their typical selves, and the day's fractal is neither good nor bad. It is a routine slightly above average. I'll try again tomorrow to find a truly great image. Of course there is no guarantee of success. I don't find most of the FOTD fractals. They find me. Until 24 hours have passed, take care, and don't take a fractal sitting down. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Why_Me? { ; time=0:01:22.39-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandAutoCritInZ function=ident inside=0
center-mag=+5.893397025006797/+0.00381731276127494\
/3.196234e+008/1/-162.5/0 logmap=172 periodicity=10
params=-1/1.68/1/1.4142/0/0/0/0 maxiter=2500
float=y
colors=000IAfH0eG0dF0cE0bD0aC0`B0_A0Z90Y80X70W60V5\
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0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zzdzzaz\
z_zzRzzIzz9zz0zz9zzHzzPzzXzzdzzlzzizzfzzdzzazzZzzX\
zzUzzSzzZzzdzzfzzhzzjzzkzzmzzozzpzzgzz_zzRzzJzzAzz\
2zz6zzAzzDzzHzzLzzOzzMzzK }
frm:MandAutoCritInZ {; 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 PARAMETER FILE=========================================
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times.
