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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's circular image is a scene in Hyperseahorse Valley of the Hypermandelbrot set. I know that it looks nothing like a scene in the familiar Seahorse Valley, but Hyperseahorse Valley is a horse of an entirely different color. The HyperMandelbrot formula that created the image is the most enigmatic one in my active list. It appears to draw some of the Mandelbrot slices that the type=hypercomplex formula misses, though actually, I am not sure exactly what it does draw. We know that these hyper-elements exist in the 8-dimensional Hyperjulibrot figure because we see them in the images created by the type=hypercomplexj formula, which draws a far greater variety of slices than the type=hypercomplex formula, but some of the images appear so unlikely that I cannot shake the impression that they are artifacts of mathematical imprecision rather than true fractals. But whatever the images are, the HyperMandelbrot formula is infinitely versatile, and I have barely scratched the surface of what it can do. The rating of an 8 is based mostly on the mathematical interest of the image. The artistic worth is merely average. The name "Hyperseahorse Valley" describes the location of the scene in its parent fractal. The calculation time is a disappointingly slow 1/2 hour even on the super-speedster 2000mhz machine. The calculation is so slow because the periodicity must be turned off when working with the HyperMandelbrot formula. But all is not lost, for the completed image is posted on the FOTD web site at: A fairly average but brilliantly sunny day here at Fractal Central on Wednesday went un-noticed by the fractal cats, who spent the day chasing each other up and down the hallway. By the time the evening tuna treat was served, they were totally exhausted. My day was fairly busy, but under control. The next FOTD, which will be another scene in Hyperseahorse Valley, will be posted in 24 hours. Until then, take care, and what the heck are those 'rods' the UFO fans are talking about. I doubt that they are discussing the anatomy of the eye. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
HypersehorseValley { ; time=0:29:22.50-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=HyperMandelbrot inside=0 maxiter=32767
params=0/0/0.2/0/1e-007/0 logmap=212 periodicity=0
center-mag=-0.743377645/+0.1010200296/4126.308
float=y
colors=000`PWaRYbS_cUadUbfUdgUfhUgiVijWkhXjcYiZZhU\
_gP`fOaePacQbaRbbSccTcdUdeUdfVegWehXfiYfjZgk_gl`hm\
ahnbiobipYghUfaQeVLcNHbGDa99`2DY7GVCJTHMQMPORSLWVI\
`YGe`DjcBof8ti6xhCvhHuhNthSshYrgbqghpgmogsngxmhsei\
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G93E72C52A32C45D58E6BG7EH8HI9JJAMLBPzCuzDmzDczBLvA\
9rC9mE8cG8UI8RK7RM7QO6QQ6PS6PU5OW5OY4N_4Na4Mc3Me3L\
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kNgkOhlPhlQilRjlRjmSkmTkmUlmVlnWmnXnnYnnYooZoo_po`\
qoaqpbrpcrpdspdsqetqfuqguqhvrivrjwrjwrixqiypizohzn\
hznhzmgzlgzkgzjfzjfzifzhezgezfezfdzedzddzcdzcczdbz\
eazf`zf_zgZzhYzhXziWzjVzj }
frm:HyperMandelbrot {; periodicity must be turned off
a=(p1),b=(0,0):
q=sqr(a)-sqr(b)+pixel,
b=(p2+2)*a*b+p3,
a=q,
|a|+|b| <= 100 }
END PARAMETER FILE=========================================
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