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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's fractal scene lies in the not-quite-imaginary land that is created when 1.3 parts of Z^(0.92) are subtracted from 1.3 parts of Z^(-1.08) and (1/C) is added instead of straight C. This parent fractal appears to the sense of sight as a twisted, stretched, pinched-off Mandeloid with a large bud on the northwest shore of the main bay. This large bud might or might not be the period-2 bud. I did not check. The shoreline of this large bud is crowded by unusually plentiful and unusually small sub-buds, each bud with a band of chaos stretching out and terminating in a flat disk. Today's scene is located near the terminal point of one of these bands of chaos on the west shore of the large bud. When rendered using the normal equal-iteration method, today's image is pretty boring, but the 'tdis' option (I should use this option more often) really brings it to life, giving the whole thing a kind of art-nouveau appearance, reminiscent of the turn of the 20th century. And curiously enough, the scene maintains its attractiveness when zoomed both into and out of. This trend could continue forever, which is why I named the image "Forever Fractal". When rating time arrived, I decided on a 7. It's an above-average scene, at least by my standards. And the render time of just over 5 minutes on my tired old machine is bearably short, at least for a Sunday, when many have nothing to do but watch the TV. Those who would rather not miss 5 minutes of that game may download the completed GIF image from: The promised philosophy is already written, and will appear in tomorrow's Philofractal version of the FOTD. Friday and Saturday were chilly here at Fractal Central, with temperatures both days just above freezing. But there was just enough sun to make outdoor life bearable for the fractal duo, who spent just enough time outdoors to prevent cat boredom. However, today started with heavy snow, which is just now changing to rain. I fear the worst moods might be in store for Thomas and Tippy. For me, the worst has been avoided. By working all day Saturday, I avoided the work back-up that was threatening. But there is still a bit of work to be cleared away before Monday, so until next time, take care, and be skeptical of things that are not true, while being wise enough to know the difference and tolerant enough to know that you could be mistaken. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Forever_Fractals { ; time=0:05:11.35--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-0.17434825437380250/-0.158570929431714\
50/1.873532e+009/1/-52.5/0.000439570302683295333
params=-1.3/0.92/1.3/-1.08/0/0 float=y maxiter=1200
inside=0 outside=tdis periodicity=10
colors=000zzUzOOzLQzJQzHTzETyCUyAUy9Uw5Ww4Wu2Yu0Ys\
0Zs0Zs0Zq0`q0`o0bo0bm0dm0dm0dl0`l0Zj0Yj0Wj0Uh0Th0O\
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HzqJzzLzzj0zlQ4jT9jTCjTGjUJjUMjUTjWWjWZjWbjWfhYhfY\
hfZhdZhdZhb`h``h`bhZbjZbj }
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 20.0 PAR-FORMULA FILE==================================
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