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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: In the FOTD discussions, I keep talking about a mysterious 'parent fractal'. The parent is really not so mysterious however. It is simply the entire fractal created by the generating formula. Today's image is such a parent fractal. It resulted when I combined 0.65 part of Z^(-1.4142) with 0.65 part of Z^(1.4142) and added straight C. Like so many fractals created by the M-Mix4 formula, it appears to be two fractals in one. The main Mandeloid in the image is immediately obvious, but in the background lies part of a larger and unseen fractal. This unseen fractal appears as the bright stuff in the parent fractal. Its buds are apparent, but it is obviously a 'ghost' fractal. I suspect that the generating formula has more than one critical point, and this unseen fractal is what would appear if Z were initialized to another critical point. As it is, the image, with its deep blues and purples, is a rather somber one. Since I didn't even try to explore deeper into the fractal, I could hardly give it a name or rating, but it's still a pleasant thing to see, and with a calculation time of under 3 minutes, little time will have been wasted if the result is disappointing. The finished image will soon be posted to the FOTD web site at: Today was downright arctic here at Fractal Central. Enough sun broke through the clouds to make the day bright, but the brisk wind and temperature around 12F -11C made it risky to stay exposed for too long. The fractal cats never expose themselves to the weather however. They were quite satisfied to lie near the large radiator in the hallway, which was going full blast. As today's super-quick fractal shows, my day was very busy. And to make things worse, the heavy work will likely continue for another week at least. So far I have been able to keep the FOTD going. Hopefully, I'll be able to keep it going during the coming week. The next in the long series of never-before-seen fractals will almost certainly appear on schedule in 24 hours. Of course, 'almost' is no 100-percent guarantee, so check back tomorrow at this same time. Until then, take care, and if time, like space, is quantized, how long is the present moment? Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
FOTD_for_Feb_06_07 { ; time=0:02:57.02--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=ident inside=0
center-mag=-0.3004690/0/1.344086/1/-90/3.88576e-016
params=0.65/-1.4142/0.65/1.4142/0/0 periodicity=10
float=y maxiter=1500 logmap=yes
colors=0005R`5Q_5QZ5PY5PY4OX4OW4NV4MU4MT3LT3LS3KR3\
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zcmzcmzcmzcmzcmzcmzcmzcmz }
frm:MandelbrotMix4 {; 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,
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.
