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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's old forgotten formula is an early attempt to examine the odd planes of the Julibrot. In a way it succeeds, but its extra baggage makes its use more difficult than need be. For today's fractal, the formula has created a very unusual variation of the Julia set of East Valley of the Mandelbrot set. The artistic worth of the image is un-notable, but the mathematical interest raises the total worth to a rating of 6. The p1 parameter places the scene in East Valley of the Mandelbrot set, while the p2 parameter slices the 4-D Julibrot in a direction very close to the Julia orientation. The p3 parameter adds the extra decoration that makes the image mathematically notable. The overall effect is one of an endless spiral, only one level of which appears on the screen. I named the image "Mandel Variation-6". A name like 'Julia Variation' might have been more appropriate, but names are names, and the name I have given the image will be its name for all eternity. Except for those with internet-proficient-but-Fractint-challenged computers, rendering today's image will be no problem, for it finishes in only 26 seconds, and that is on my tired old P200 workhorse machine. Those with amnesiac machines that have forgotten how to run DOS programs can see the image by downloading it from the FOTD web site at: Sunday turned out milder than expected here at Fractal Central, with a lot of sun, a fresh breeze, a few scudding clouds, and a high temperature of 66F 19C. The cats were satisfied, though not overjoyed. Today is starting sunny but chilly. The cats are still sleeping and have yet to comment. The next FOTD will appear in 24 hours. Until then, take care, and see the new world revealed by fractals. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Mandel_Variation-6 { ; time=0:00:26.26--SF5 on a P200
reset=2004 type=formula formulafile=jim.frm
formulaname=ManJul2CPwr inside=255
center-mag=-0.000916065/0.00366617/0.507824/1.0765
params=0.255/-0.0006/1e-010/0.001/-50/10 float=y
maxiter=10000 outside=real periodicity=10
colors=000SXkZYheZek_bcT`WMZOFYG8W82VB4UE5TH6SK7RM\
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eiYeiYeiYeiYehYehYehYdhYdhYdgYdgYdgYdgYdgYdfYcfYcf\
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bYabYabYabYaaY`aY`aY`aY``Y``Y``Y``Y_`Y__Y__Y__Y__Y\
_ZY_ZY_ZYZZYZZYZYYZYYZ000 }
frm:ManJul2CPwr {; Jim Muth
; Creates and rotates ^2 Hyperbrot Figure
; P1 sets point of rotation, P2 sets angle of rotation
; P3 sets power of C
z=c=pixel:
z=sqr(z)+p1+(p2*(c^p3)),
|z| <= 100 }
END PARAMETER FILE=========================================
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times.
