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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: As I pondered today's image, I was reminded of nothing in particular. The decorations around the midget do resemble several computer animations I have seen. And they sometimes impressed me as the tentacles of some fantastic monster lurking on the sea floor. But all these impressions are so vague that I named the image with the very simple and non-descriptive name, "Object Around Midget". The MandelbrotBC formula is responsible for the image, which is part of the infinite Z^(sqrt2)+C fractal. This fractal is my most frequently explored with an exponent of Z between 1 and 2 because in this fractal the midgets are easier to find than in most fractals lying in this exponent range. Confining explorations to the fractal created by only one exponent between 1 and 2 is not limiting, since when drawn by the MandelbrotBC formula, the fractal is infinite in surface extent as well as depth and variety. On my 200mhz Pentium the image takes almost 3/4 of an hour to render. It will therefore be an hour or so before it is available on the Web at: The fractal weather today (actually yesterday, April 26) was just about average for this location at this time of year, with warm sun and a temperature of 65F (18C). These conditions had the fractal cats in the yard most of the afternoon, acting like kittens. Such behavior is most undignified for cats of their venerable age of 9 years. As for me, it's past 8:15am, and I've got a busy day before me. So until next time, take care, and enjoy the flowers of Spring of the leaves of Autumn. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
ObjectAroundMidget { ; time=0:43:53.22--SF5 on a P200
reset=2001 type=formula formulafile=branchct.frm
formulaname=MandelbrotBC passes=1 center-mag=-0.15\
578257934389980/+1.535940899307265/4.223478e+008/1\
/12.5 params=1.414213562373/0/0/0 float=y
maxiter=6000 inside=0 logmap=-1150 periodicity=10
colors=000SaZOfUHiRDnM8qJ2vE0yB0x80rZ0mU0hP0cM1`H4\
YE8ZADd6Hi2Mp0Pt0Op0Ml0Ki0Jf0Ha0GZ0EW0DS0BP0MfOXvn\
RkiK`dEP`AEX44S00O00K00J00H00G00E04D08B1DA2G82K74P\
66U46X47`G8aR8ccAdnBfzBhzD`zDSqEKhEEZG7PG0GG07K0EO\
4KRARUEXXKc`PicWpf`vdkzcvzazz`zzXzzWzzSzzRzzOzzMxz\
KuxHqvGnsDkqBhnAflRWhhKdnAhu0ky0nx0ix0fx4ax7ZxBUxG\
RxKMxOJxSExXBx`8vXDvUGvRKuPOuMSuJWsG`sEcsBhq8kq6pq\
4sp1xp0zp0zp0zzK`zOZzRZzUXzXXz`WzcWxfUviUslUppSnsS\
kvRhyRfzPczPazPazUZzSXzRWzPSzORzMPzMOzKKzJJyHHyGGy\
GRlJ``MiOPsBSz0Wz0Zp6hWMpBcx0uz0qz0py0nx2mu4msAmnG\
mkMmhRmdXmacmXhmUnmRumOymKcmnJmzMmzOmzPmzSmzUmzWmz\
Zmz`mzamzdnzfqzhuzixz0zD0zE4zGBzHJzHRzJZzKfzMnzMqz\
PuzSxzUzzXzzZzzazzcXz0az0dz0hz0kz0nz0qz0uz0xz0sz0n\
z0iz0dz0az0Xz0Sz0Oz0Jz0Gz0Bz07z02z00z01zG1zX2zn2zz\
1zv0zl0zc0zW0zM0zD0z40z00z06z2Bz6Hz8OzBUzEazHhzKnz\
OuzRzzUzzX7z0Bz4hziczfZza
}
frm:MandelbrotBC { ; Inspired by Andrew Coppin
e=p1
p=real(p2)+PI
q=2*PI*trunc(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| < 100
}
END 20.0 PAR-FORMULA FILE==================================
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times.
