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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: I have always been fascinated with the unknown, and to me nothing is more unknown than the fourth dimension. When I first learned of the fourth spatial dimension, I tried to picture four-dimensional objects as extremely convoluted shapes, with surfaces that were measured by their areas. Of course, the objects I pictured were not 4-D objects at all, but rather very complex 3-D objects. Actual four-dimensional objects have surfaces that are measured by their volumes. This surface volume is for me the most difficult thing to imagine. Logically, I know that a 4-D man seeing a 4-D hypersphere would observe an image of a 3-D sphere with every point of its opaque interior immediately visible. The four-dimensional effect would be achieved by the shading of the interior of the 3-D image of a sphere. If I could picture just this one 3-D surface, the rest of the 4-D oddities would seem simple. Two planes intersecting in a point would be no problem. Axis-planes would be no problem. Double rotation would be no problem. Visualizing the curvature and infinite extent of the pseudosphere would be no problem. But alas, I shall never picture a surface with volume, and all these four-dimensional wonders must remain forever a mystery. Today's fractal is no mystery however. It is another in my ongoing series of fractals with neon-tube-like elements. Its formula, Z^(-11)+11Z^(-1.1)+(1/C), is yet another example of my whimsy in action. I have named the picture "Pink Fractal Clouds", though the clouds are as much blue as pink. I would have given the image another rating of 7, but a second look convinced me that the colors are a bit garish, which dropped the rating to a 6. The running time of the parameter file is 3-1/2 minutes -- not too bad as fractals go. But if even this causes impatience, the completed GIF file of the image may be downloaded from Usenet at: If Paul's web site is not yet updated, try again in an hour or so. It soon will be up to date. The fractal weather today here at Fractal Central was just about perfect, with partly cloudy skies and a temperature of 74F (23C). The cats, who have forgotten yesterday's squabble, enjoyed their run in the sunshine. I would say more, but the fractal time is past 2am -- most certainly time to shut down the fractal shoppe and call it a night. But I'll return tomorrow about 3 hours earlier with more fractal news. Until then, take care, and see you soon. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Pink_Fractal_Cloud { ; time=0:03:27.02 -- SF5 on a P200
reset=2001 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+2.386247007680221/-2.486598562858512/2.7\
81989e+007/1/25 params=1/-11/11/-1.1/0/400 float=y
maxiter=1200 inside=0 logmap=28 periodicity=10
colors=000E1B<3>E07E07G19<8>R6LS6MU7NV8PW8Q<12>lFnmG\
pnGr<3>sIz<7>pFbpF_oEXoEUoER<3>mCImCGmCElBClBAlB8<14\
>kQWkRYkSZ<2>kVckVdkY`<3>kfNkiKkkGknDkp9kr6<3>fnDemE\
dmG<19>LriKrkJrl<3>Fsr<3>DtTCuNCuHCuBCu9Cv8<6>JwOKwQ\
LwSLwVMwXNyZ<3>RygSyiTykTyp<6>TyZTyWTzT<2>TzMTzJRzI<\
3>YzFZzE`zDbzDczCezBiz8<12>Iz_GzaEzc<2>8zi6zk2zl<4>8\
zq9zqBzr<3>FzvFzxGzv<16>XzXYzWZzU<2>`zQazPazP<12>ezM\
ezMezM<3>fzLEzF<2>EzC
}
frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}
END 20.0 PAR-FORMULA FILE==================================
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