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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: I'm in a bit of a rush this morning, stuck with an unexpected large job and a customer who needs it sooner than immediately. So today's discussion is brief and late. Today, we continue studying the 'HyperMandelbrot' formula, which draws slices of the Mandelbrot figure created by 4-part hypercomplex numbers. In Mandel-type fractals, the distortions of the midgets often mirrors that of the parent fractal. While exploring the HyperMandelbrot fractal yesterday, I wondered if the corresponding distortions were true of this fractal also. I found that it is partly true. The midget in today's image does not show the appearance of its parent, the parent is a perfect Mandelbrot set, but it does show what will happen to the parent fractal when the parameter values are farther removed from zero. The midget's plight also makes a rather striking image, aided in a large degree by manipulation of the colors on my part. The detail on the inside of the midget is not inside stuff made visible by an active inside fill. It is true high-iteration outside stuff, and can be zoomed in on like any other 'outside' feature. I named the little midget "Junior", and the image, "Hyperbrot Junior". The rating of 7 means I consider the image to be above average. The render time of 8 minutes gives the picture an overall worth of 86 -- not bad for a picture of a typical midget lying in Seahorse Valley. All this may be seen by running the included parameter file, or by downloading the finished GIF image from: The Wednesday weather was absolutely perfect here at Fractal Central, with warm sun, moderating winds, and a temperature of 61F 16C. Needless to say, the cats were ecstatic. In fact, it took a surprise serving of tuna to lure them back inside when the sun went down. But this morning is starting cloudy, with a forecast of rain. Things do not look good for the dynamic duo. For me it's more of the usual. The next fractal will appear in 24 hours. Until that hallowed moment arrives, take care, and be at ease. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Hyperbrot_Junior { ; time=0:08:08.18--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=HyperMandelbrot passes=1 inside=0
center-mag=-0.7486564238863157/+0.084463614911547\
23/3.10774e+007/1/177/0 params=0/0/0.0125/0/1e-015\
/0 float=y maxiter=10000 logmap=300 periodicity=0
colors=000iPFlXMpdSslZqmdonghhjbblWXoPRrJLtCFw69yA\
EwEIuINtKMrMLqOKoQJnSIlUHkWGi_FgaEecDcdCceBceAcdDc\
cGccJcaNc_QdYSgWVkUYnS`rQcuOfsNiqTkoYmmZmk_mi_mgYm\
eWmcUmaSm_QmYOmWMlULkSKjQOhPSgSVfVZdZbcafadi`gm_jq\
YmsXpuVpsVppUnlTlhSieRgaQeYPbUP`QOZNNWJMUFLSBKP7KN\
AMMDOLGQKJSKMUKPWKSYKV_KWaKYcK_dKaeKcdKecKfaKi_KlZ\
KoXKqWKmUKjSKgQKcOK`MKYLJXOIWRIVUHUXHT_HSbGReGQhGP\
kFOnFNqFMtELwELwEMvIMtLMqONnSNlVNiYNf`OcdO`gOZjOWm\
PTqPQtPNwPLzQKwSJrVImWHhYGccKZkNUoQPsUKxXFzXAsX8lU\
CeRFZOISLLMIOGFRADUCESDFRFFSGGSHGTJHULHUPIVSIWVJWZ\
JWaKWcKWcIX`HXZGXWEWUDVRCVPAUO9TM8TM7TK6RI5PG4NE3M\
C2LA1K80J60I40G20E00C00A00800600400000000000000000\
0000000000000QuSPsRNqQMnPLlOJjNIhMHeLFcKEcJDcICcHN\
cJYcKfnLzzMyyKvwIrtGnqFkoDhlBej9gg8id9kaAmZCoWEqTG\
sQIuNKwKMxHOyEQyBSy9UyAWyBYyC_yDbzEezFhzGkzHnzIqzJ\
tzKwzKzyJzxJzwIzwIzvIzuHz }
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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