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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: July, 2001 has been declared midgetless month, quadratic-midgetless that is. So I need a way to follow the theme while still pampering my obsession with these tiny holes that fill the border of the Mandelbrot set as well as many other fractals. Today I have chosen to work around the no-midget theme by viewing the hole from a different direction. Those who would like to see the hole in its full quadratic-midget aspect can do so by entering either the p3 or p4 coordinates into the Mandel formula as center coordinates and letting it iterate. The coordinates show that today's scene lies deep in the Seahorse Valley area of the Mandelbrot set, or more accurately, the extension of Seahorse Valley into the four-dimensional Julibrot. I'll not try to describe the orientation of today's image in that 4-D object, since 4-D things are impossible for we 3-D limited beings to visualize. As is usually the case in the odd slices, the area around the hole, which in this case has been pulled into a thin slit, is stretched and distorted. The 2,4,8... series can be followed to the 'four' level, but the 'eight' level is nearly lost in the stretching and distortion closer to the hole. I named the image "Sea-What" because, though it is a view of a seahorse, it is like nothing to be found in the familiar "Seahorse Valley". And since it's not really an outstanding image, I could rate it at only an 8. The image may be viewed by running the attached 7-minute parameter file or by picking up the GIF image from Paul's web site at: The fractal weather today was sunny and hot until 5pm, when a very strong thunder-storm moved in, dropping the temperature from 93F (34C) to 70F (21C). The fractal cats enjoyed the sudden coolness, but disliked the noise that accompanied its arrival. It's now almost 11am -- time to do something useful. So until next time, take care, and just because the fourth dimension can't be pictured doesn't mean it's not there. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Sea_What { ; time=0:07:41.65--SF5 on a P200
reset=2001 type=formula formulafile=allinone.frm
formulaname=multirot-XZ-YW-new passes=1
center-mag=+0.00000327661430389/-0.000000049069920\
32/1.729035e+007/0.003293/-179.142/88.744
params=183/92/2/0/-0.749695276287/0.032780202799\
/-0.749695276287/0.032780202799 float=y
maxiter=12000 inside=0 periodicity=10
colors=000ICEJEFKFGLGHMHINIJOJKPKLQLMRMNSNOTOPUPQV\
QRWRSXSTXTUYUVZVW_WX`XYaYZbZ_c_`d``eaafbbgcchddiee\
jffkggkhhliimjjnkkollpmmqnnroospptqqurrvsswttxuuyv\
vzwwzxwxvuvutttrssqqqpopnmomlnljljhkifjheifcheafd_\
ebZdaXc_VaZT`YS_WQZVOYUMWSLVRJUQHTOFRNEQMCPKAOJ9NI\
BOKDOLFOMHPNJPOKPPMQROQSQQTSQUURVVRWXRYZSZ`S_bS`dS\
aeTbgTdiTekUfmUgoUhpUikVlgVnbVqZVsXWrWXrUXrTYqSYqQ\
ZqPZqO_pM`pL`pKapIaoHboGboEcoDdnCdnAen9en8fm6fm5gm\
4gm5fl6fl7el7ek8ek9dkAdjAcjBcjCciCbiDbiEbiFahFahG`\
hH`gH`gI_gJ_fKZfKZfLZeMYeMYeNYeOXdPXdPWdQWcRWcRVcS\
VbTUbUUbUUaVTaWTaWTaUS`TR`SQ`RP_QP_PO_NN_MMZLLZKLZ\
JKZIJYGIYFHYEHYDGXCFXBEXAEXBDWCDVDDVECUFCTGCTHCSIB\
RIBRJBQKAQLAPMAONAOO9NP9MQ9MQ8LR8LS8KT8JU7JV7IW7HX\
7HX6GY6GZ6F_5E`5Ea5Db5Cc4Cd4Bd4Be3Af39g39h38i27j27\
k26k26j37j47j47j57j67j67i78i88i88i98iA8iA8hB8hC9hC\
9hD9hE9hE9gF9gG9gGAgHAgIA
}
frm:multirot-XZ-YW-new {; Jim Muth
; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect
e=exp(flip(real(p1*.01745329251994))),
f=exp(flip(imag(p1*.01745329251994))),
z=f*real(pixel)+p3, c=e*imag(pixel)+p4:
z=z^(p2)+c,
|z| <= 36 }
END 20.0 PAR-FORMULA FILE==================================
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times.
