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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: The four-dimensional HyperMandelbrot set is virtually ignored. And why not? Very little totally new stuff is to be found in it. But is it actually as devoid of new stuff as would first appear? Today's image answers that question with a resounding NO! Today's under-used formula draws the 4-D HyperMandelbrot set, and does some strange things with it. I do not fully understand all the things this formula does, but one thing is certain. It plays some very interesting tricks with the familiar elements of the classic Mandelbrot set. The familiar M-set has been quite well explored, at least down to the level where the slow arbitrary-precision math kicks in, and most of the features to be found in its upper depths have been well investigated. It would be curious indeed if something truly new were to be uncovered in this range. Well, today's image uncovers something totally new. As far as I know, nothing like it has ever been found in the familiar two-dimensional M-set. Today we are investigating the four-dimensional Hyper-M-set however, so it is no wonder new things are popping up. I named today's image "Something New" because that's what it is. I rated it at an exceptional 8 because it truly is something new. The calculation time of 55 seconds is on the P4-2000. On the P200 it would take about 3 minutes to finish. But why not forget inconveniences like calculating parameter files? View the finished image on the FOTD web site at: With full sun and a temperature of 75F 24C, Tuesday was not quite perfect here at Fractal Central; the sky was slightly hazy. But despite the lack of a pure blue sky, the day came so close to having perfect weather that only a professional weather observer would notice the deficiency. The fractal cats most certainly never noticed the gray haze. They were far too busy watching four squirrels that were running around in the yard all afternoon. My day was average. Only the above-average fractal saved it from being a dull day. The next FOTD will appear in 24 hours. Until then, take care, and reasoning about fractals could be unreasonable. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Something_New { ; time=0:00:55.15-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=HyperMandelbrot passes=1 periodicity=0
center-mag=-0.11351018609400590/+0.857731703162649\
10/13846.92/1/-12.5/1.19338289250592311e-011 float=y
params=0.33/0.33/1/0/0/5e-015 maxiter=980 logmap=40
inside=0
colors=000GFp7Jp9LqANrBOrCQsDRsETtFUtGWuHYvIZvJ`wK\
awLcxMdxNfyPhzOjzOkzNlzNmzNnzMmzMkzMizLgyLexLcwK`v\
KYuKVsJSsJQrJOrIMqIKqGGrIJqKLqLNpNPpORpQUoRWoTYoV_\
nWanYdmZfm`hmajlclleqodnlcljbjgahe`eb`c`_aYZ_WYXUX\
VRXTPWRMVOKUMHTKFRGBTIDUJEVKFWLGYMHZNJ_OK`PLbQMcRN\
dSOeTQgURhVSiWTjXUkYVjZWiZXi_Yh_Zg`_g``faaeabebcdb\
dcceccfbdgadh`fgadhabia`jY_iUZiRZhNYhKYgGXgCWf9Wf5\
Ve2Ve2Xc2Yb2Za2_`2a_2bZ2cY2dX2fW2gV2hU2iT2kS2lR2mQ\
2nP7mRClTHkVMjXQiYVh__gadfcgcchedhgdiheijeilejmfjo\
fjqfkrgktgkugksekrckqako_knYkmWklUkjTkiRkhPkgNkeLk\
dJkcHkbFk`Ek_CkZAkY8kW6kV4kU2nS0kT1hU1eU1bV1_W1XW2\
UX2RY2PY2MZ2J_2G_3D`3Aa37a34b32b3IT9XKEZMG_NH`OJbP\
KcQLdRNfSOgUQhVRjWSkXUlYVnZWo_YpaZrb`scatebwgdyiez\
kgzjfzifzhezgeyfexedwcdvbcuact`cr_brZbrYbrWarVarU`\
rT`rS`rQ_rP_rO_qP`pP`oP`nP`mQakQaiQagQaeRbcRbaRb_R\
bQTcZRbgPapOajX`dd_ZmZTuY }
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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