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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Having watched a lot of prehistoric animals with their incomprehensible scientific names on TV last evening, I decided to give today's image an incomprehensible name. I named it "Fractopod Undulatus", which I suppose translates roughly as "Fractal-footed undulating creature". Actually, it's a scene in a remote part of the infinite spiral of the Z^1.71+C Mandeloid. This simple formula draws a distorted but unexpectedly recognizable fractal, which resembles the classic Mandelbrot set rotated 135 degrees CW. Today's scene lies in a secondary valley of a tiny bud in the East Valley area of the parent, which in this case would more properly be called the Southwest Valley area. The thing about the image that strikes me first is the subtlety of the discontinuities. Usually, the midgets in fractals of fractional powers are torn apart by the unavoidable discontinuities, but in today's image, these breaks are located in places where they are barely noticeable. The image is filled with tiny yellow dots, which sparkle like stars throughout. Each of these tiny dots enlarges to a complex of elements similar to the one that surrounds today's midget. Undoubtedly, more midgets lie in these smaller complexes, though these midgets are almost certainly beyond resolution. Because the image looks so much like so many that we have seen so many times before, I could rate it no higher than an average rating of 5. But it's still worth at least a glance, even if not quite worth the 1/2 hour required to render it from the parameter file. The hassle of running the parameter file can be avoided by letting Paul and Scott handle the hassle, and downloading the completed GIF image from their web sites at: The sun returned to Fractal Central Sunday, but the winds remained brisk and the temperature barely touched 50F 10C. Fractal cats, unlike their feral cousins, find such conditions too unpleasant to endure for longer than a few minutes. The dynamic duo grew sulky as the afternoon progressed, but forgot their troubles when the tuna appeared around sunset. And I'll forget *my* troubles when the day's work is finished. Unfortunately, the only way I know to finish work is to start it and keep going until nothing remains undone. So while I'm working, I'll say take care, and do flying birds ever get struck by lightning? Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
FractopodUndulatus { ; time=0:31:27.57--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC1 function=recip passes=1
center-mag=-0.441558671869633/-0.306673097759865/6\
756444/1/-7.5/-1.33158752357864785e-008 params=1.7\
1/0/-40/0 float=y maxiter=4800 inside=0 logmap=780
colors=00003C13C33C43E53E73F83F93GB3GC3IE3IF3JG3JI\
3KJ3KI3JG3JF3JG4II4IJ4IK4IK4GM5GN5GO5GO5FQ5FR7FS7F\
S7EU7EV7EX8EX8CY8CZ8C`8C`9Ba9Bb9Bd9Bd89d9Bd9Bd9Bd9\
Cd9Cd9Cd9EdBEdBEdBFdBFdBFdBGdBGdBGdCIdCIdCIdCJdCJd\
CJdCKdEKdEKdEMdEMdEMdENdENeCMdENbEOaFQaFQ`GRZGSYGU\
YIUXIVVJXUJYUJYSKZRK`QMaQMaOMbNNdMNeMOeKOfJOhIQiIQ\
iGRjFRlERmESmCSnBUp9UqBVs9Uq9Sq9Rq9Qq9Oq9Np8Mp8Kp8\
Jp8Ip8Gn8Fn7En7Cn7Bn79m78m77m55m54m53l51l50l50l50l\
80iB3fE4eG7bI8aKBZNCYQFVSISUJRXMOZNNaQKbRJaUKaVKaY\
KaZKa`K`bK`dK`eK`hK`iKZlKZmKZnKZqKZsKbtKhtEmt8st3w\
t0zw0yt0ws0uq0qn0nm0ml0ji0ih0hf0ed0db0ba0`Z0ZY0YX0\
VU0US0SR0RQ0QR0OR1NR1MR3KR3JR4IS5JR4JR4JQ3KO3KM1KK\
1KK1MI0MI0MG0MF0NE0NC0NC0O90O90O70O50Q30Q30Q30Q10R\
30R40R50S70R80Q90OB0OE0NG0MJ0MM0KO0JR0JS0IU1GX3FY4\
FZ4E`5Cb7Cd8Be99f99iB8jC7lE7mE7nG7pJ7qM7sO7tR7uU7w\
X7xZ7ya7zd7zf7zi8zl9znBzq
}
frm:MandelbrotBC1 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*fn1(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| < a }
END 20.0 PAR-FORMULA FILE==================================
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times.
