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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Sometimes I venture into the cubic Mandeloid for a midget or two. On a few occasions I have delved into the quartic Mandeloid to see what if anything of interest lies there. But in today's fractal I have gone all the way to the quintic figure. Finding nothing of interest in a quick trip through the M-Mix4 formula, I unpacked one of my Julibrot rotation formulas and searched for a midget to rotate in the minus-quintic figure. When I found a midget, (quite an easy task in this fractal), it turned out to be so striking that no rotation was necessary. When I noticed that the midget seemed to be pointing to the four directions of the compass, I named the picture "North East South West", gave it a jazzy coloring, and declared it FOTD of October 28. In the quintic Mandeloid, the features split into powers of 5 as they approach the 4-lobed midgets. The outer pattern around the midget is obviously 5-sided. A count will reveal that the prominent green ring contains 25 elements. And a barely discernible ring of 125 elements lies closer to the midget. The parameter file dawdles along and finishes running in a little over 5 minutes. The GIF image file downloads in far less time. The GIF file may be found posted to the Usenet group: Although I did not rotate the midget today, it does some unusual things when rotated. I may devote a future FOTD to one of the odd slices through this midget. The fractal weather today was extremely perfect, with sunny skies and a temperature of 77F (25C) that drove the fractal cats to a state of ecstasy. They meditated in the sun the better part of the afternoon, while I was searching for fractals. And now the day is winding down, the fractal shoppe is dark, the cats are resting, and all else is quiet. It's the perfect time to call it a night and shut down. But I'll return tomorrow with more goodies. Until then, take care, and don't let a lost fractal spoil your day. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
NorthEastSouthWest { ; time=0:05:08.96 -- SF5 on a P200
reset=2001 type=formula formulafile=multirot.frm
formulaname=multirot-XY-ZW-min function=ident/flip
passes=1 center-mag=-1.07712932560607900/-0.00275300\
534013650/1.481368e+010/1/-87.5 params=0/0/5/0/0/0/0/0
float=y maxiter=1800 inside=0 logmap=128 periodicity=9
colors=000K0MK0O<3>S0VU1XW2YY3__3_a1Y<3>i0Xj0Xl0Xn0Xp\
AUqERrJOsMKtPFuO0tM0sM0rL0kL0dJ0ZI0TI0MG0GG0AF04D00D0\
0C00E00J30M60QA0UD0XI0_L0cP0gS0jX0o_0sc0vf4pcFj`PdY_`\
ViVSsPPzLO<3>zFTzDVzCV<2>z7bz6dz4ez3gz1jz0lz0oz0p<3>z\
0fz0cz0by0`y0`000700J00X00g00s00m00<3>X00S01O04J06F07\
A0A60C10D00G00I00J<2>00Q00S00T00X<2>00a00c00f00g00i00\
l00m00o00r00s00u00pF0lS0gf0cs0`i0f_ClPPrFax4oz9my<2>M\
ipQgmVfl<3>l``p_YuYXv_Tv_Qx_O<3>yaCzaAza7zc4zc1<2>zd0\
zd0xc0sc0ma3ia7d`A_`FV_IP_MLYPGYTAXX6X`0Vc0Vg0Vj0Qd0O\
_1LT4IP7FJAADD79G43J10M00S10X40`70fA0jC0oF0uI0yL0zM0z\
G0zC0zD0p93gCAYFJOIQFLY4Of0Qm0Tu0Xx4_zDazOdzXgzdgzmgz\
ogzogzpgzpgzrgzrgzsgzsgzugzugzvgzvgzxgz<3>zgzpgz_gzIg\
zJgzLgzLgzrgzrgzsgzsgzugzugzvgzvgzxgz<3>ygzzgzzgzzgzl\
gzlgzmgzmgzogzogz
}
frm:multirot-XY-ZW-min {; draws 6 planes and rotations
;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J
;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J
a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994,
z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3,
c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4:
z=(-z)^(p2)+c,
|z| <= 36 }
END 20.0 PAR-FORMULA FILE==================================
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times.
