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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image shows a most curious fractal hole. But it most certainly is not a Mandelbrot midget. And it certainly is not a Julia set, though it does have some Julia characteristics. Nor is it an Elliptic set, a Rectangular set, a Parabolic set, or an Oblate set. It is actually a set in a slice oriented about half way between the Parabolic and Elliptic directions. As the value of the center point of today's image indicates, the scene is located in the vicinity of the large midget located at -1.75 of the Mandelbrot set. Since we are exploring 4-D space when we examine the Julibrot, it is impossible to describe the exact direction from the -1.75 midget in which today's scene lies. The thin straight yellow line at the edge of the solid inner area is actually one of the Mandelbrot valleys of the large -1.75 midget sliced from the side. It seems counter-intuitive that, from the side, a Mandelbrot valley should appear as a straight line, but the Mandelbrot aspect of the Julibrot is actually shaped like a nest of 4-D hypercylinders, which, like 3-D cylinders, appear straight when sliced parallel to their length. I named today's image "A Whatsit Midget" because I have no idea what else I might name it. The rating of a 6 seems about right for an image that is more a mathematical curiosity than an artistic triumph. The render time of a little over 1/2 minute should make the task of rendering almost enjoyable. And the job of rendering may be eliminated entirely by viewing the finished image on the FOTD web site at: Heavy clouds, fog on the hills, occasional rain, and a temperature of only 63F 17C made conditions far less than ideal here at New Fractal Central on Thursday. But the fractal cats, who can look outside but are not permitted to go there, do not concern themselves with mundane things like weather. They spent the day searching for trouble. Luckily, they failed to find much of it. My day was near normal, and it looks as though the next week or so will remain uneventful. One of these days I'm going to give up graphic design work and start earning my living by selling fractals. Oh well, we can dream, can't we? The next FOTD will appear in 24 hours. Until then, take care, and the secrets of the universe may be hidden in these fractals -- if only we had the key to unlock the secret door. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
A_Whatsit_Midget { ; time=0:00:38.56--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=multirot-xz-yw-new passes=t
center-mag=-0.16772097072767390/-1.749397401235292\
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CzyCzyCzyDzyDzyEzzEzEBzDB }
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 PARAMETER FILE=========================================
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