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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image is a scene somewhere in HyperSeahorse Valley. The area of near total chaos at the center of attraction is the remains of a perfectly normal M-set minibrot. (To see the true minibrot, reset all parameters to zero.) As I continue to experiment with the HyperMandelbrot2 formula, I am becoming more convinced that the images it draws are true slices of the 4-D HyperMandelbrot set, and not mere artifacts. In the true classic M-set version of today's image, there are 8 well-defined yellow-orangish elements surrounding the minibrot, while in today's version, there are 14. What has happened is that the original 8 elements have each split into two, but two of the split pairs overlap in such a manner that they both appear as a single broader element, giving the impression of only 14 elements in all. Inside the space that once was the original minibrot, much the same thing has happened, but the area is so chaotic that little sense can be made of it. I will continue to work with this formula for a while, trying to figure it out. The image is named "Minibrot Madness", which is a fair name for it. The rating of a 7 means that I think it is above average, though not exceptional. The calculation time of 2-1/2 minutes may be eliminated by viewing the finished image on the FOTD web site at: Tuesday began with freezing rain and icy pavements here at Fractal Central. But by midday the temperature rose above freezing, and the rest of the day brought just plain rain. The fractal cats enjoyed the view for a while, then went to sleep. My day was busy enough for satisfaction, but not too busy for a fractal. The next FOTD will appear in 24 hours. Until then, take care, and it was hard enough to think in four dimensions. Now we have eight dimensions to worry about. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Minibrot_Madness { ; time=0:02:34.26-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=HyperMandelbrot2 passes=1 periodicity=0
center-mag=-0.748072864967/+0.071474507622/773813/\
1/-5/0 params=0/0/0/0/0.08/0/1e-012/0 maxiter=1200
float=y inside=255 logmap=316
colors=000P28P38P48P58P68P88P98PA8QB8RC8TD8WG9ZJA`\
LBaOBbSCcVDc_EccEdgFdlGdnGanLZlPXkTUiXSg`PfeNdiKbm\
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PAZRAZUAZXAY_AYbAYdAYgAYj9Ym7Yp5Yr4Zs7Zs9_tC_tE_uG\
`uJ`vLavOawQawSbxVbxXbxZawaavcaue`tg`si`rk_qn_pp_o\
rZntZmvZlxRhqJdjBadBdXBgPBjHCeMDaQEXVFTZGPbHKgIGkJ\
BpK7tK3xM7uOBrQFoSJmTKmUKmUKmUKmUKmUKmUKmUKmUKmUKm\
UKmUKmUKmUKmUKmUHmUAmU4lW8jYCi_FgaJfcNdeQcgUaiY`k`\
_hb`edcbgm`jrYnvVqzTuzQzzNzzLzzOnmRicUdZWZYZUXaPWc\
KVdMWeNWfOWgQWhRWhSWiNQiJKiFFhGGgGHfGIeGIdGJdHKcHL\
bHLaHM`HN`HNYIRWJUUKYRL`PMdNNgKOkIPnGQrEQuFVpG_lHd\
hIicJn_KsWUxScvRmuQzsPzrOmpNcoMYmL_lKajJciIdgHffGh\
dFjcElaDm`DnZCoXBpVAqT9rR8sP7tN6uL5uK4rM3pN3nO3lQ3\
jR3gS3eU3cV3aW3_Y3XZ3V_3Ta3Rb3Pc3O_5OX7OU8ORAOOBOK\
DOHEWJ7YF7_B8a78c39e09JFS }
frm:HyperMandelbrot2 {; periodicity must be turned off
a=(p1),b=(p2):
q=sqr(a)-sqr(b)+pixel,
b=(p3+2)*a*b+p4,
a=q,
|a|+|b| <= 100 }
END PARAMETER FILE=========================================
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times.
