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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: The HyperMandelbrot formula continues to amaze me. Todays image shows the same midget that appeared in the FOTD for December 9, the 'Hyperbrot Junior' fractal. Or perhaps I should say it shows the area where the 'junior' once existed. The midget itself has basically vanished, leaving behind only a tangle of twisting tendrils. I named these leftovers "The Craziest Midget" because they show the craziest thing to happen to a midget that I have ever come upon. To begin the craziness, check your assumption that there are 16 partially overlapping tendrils leading toward the remains of the midget. Count them and you will find only 14. (I have no idea what happened to the other two, but most likely the 14 tendrils are a reflection of a period-14 iteration cycle.) To continue the craziness, look at what once was a perfect minibrot midget. I admit that we are not seeing it sliced in a critical plane, but who ever saw a non-critical midget fill with tendrils and change into almost a delicate flower. Midgets simply erode away in an irregular and not particularly attractive manner when we slice them farther from the critical plane. But then, this is a 'hyper' Mandelbrot set. The image changes dramatically as the real(p2) parameter is slightly changed. And the remains of the midget also hold their position on the screen, making the scene a good candidate for a short animation. I used no fancy program features to create the image, only the standard equal-iteration bands with the inside set to black. The rating of an 8 reflects my surprise at seeing what happened to the midget as well as my opinion of the artistic merit of the image. When the 15-minute render time is taken into consideration, the overall worth registers a nominal 52. To see the curious midget, run the included parameter file or download the image from the FOTD web site at: The rain ended at noon here at Fractal Central on Saturday, but the clouds hung on for most of the afternoon, and the temperature reached only 52F 11C. When the wind arose, the fractal cats decided that they had had enough, and hurried back inside to get warm and enjoy their tuna. This morning is starting partly cloudy and chilly. The cats will likely find some fault with the day. For me the day looks slow, which is how I am learning to like it. Lots of spare time means lots of time for fractals, the next of which will appear right here in only 24 hours. Until then, take care, and watch the fractals grow. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
The_CraziestMidget { ; time=0:15:28.91--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=HyperMandelbrot
center-mag=-0.74865642436084960/+0.084463614790886\
82/4.364803e+007/1/177/1.89370992914605907e-008
params=0/0/0.105/0/1e-015/0 float=y maxiter=10000
inside=0 logmap=300 periodicity=0
colors=000JP8JR7KS7JT3KU7LVALWDMYGN_KN`NObQ8bJOcTc\
dacdjSmkUllWkoYjq_itxQ0wR0vS0uT0tU0sV0rW3qX6pY9oZM\
n_Om`RlaSkbTjbUiaVfaWd`Xc_YbZZaY_`Y`_YaZYbYYcXYdWY\
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tnfwmexldwkcwjbviauh`vg_wlZwgYwbXwZWvaVudUtgUsjXrm\
aqpgprmormnpmmnmljmkbhjZciIOZK9OLKRNVUPbVTdXQeZOg_\
MhaKicHkdFlfDmfCmgBeeAYc9Oc5Qa8S_BUZEWXHYVKZUKZUNh\
1jh3gh5eh6cb8aXA_UDaPKYDNZIQUNTQSWLUZFXZHSNINJKIEL\
D9N40K95PEAUIFZNJcSOiWTo`Yud`zb_x`_t_WoYUiWTaVK_WH\
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vJhwJmwKrwLvxMzzNzzOzzPzzQzzQzyRzzczzSzzTzzUzzVzzW\
zzWzzXzzYzzZzz_zz`zzazzazzbzzczzdnZeoYfoYgoXhpWhpW\
ipVjqUkqUlrTmrSnrRnsRosQpsPqtPrtOsuNtuMtuMuvLvvKwv\
KxwJywIzlxQmwRmvSmuTmtUnsUnrVnqWnpXooYonYomZom_pl`\
pkapjapibphcqgdqfdqeeqdfrcgrbhrbhrais`js_ksZlsYltX\
mtWntVotUotTpuSquSruRsuQs }
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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