FOTD -- August 08, 2002 (Rating 5) Fractal visionaries and enthusiasts: Today's image is a scene in that great abstraction known as the Julibrot. The iterated formula is Z^2+C, which draws our old friend the first fractal of all, the Mandelbrot set. But the same formula also draws a horde of Julia sets, which might have come first, and though they are not as well known, a horde of perturbed Mandelbrot sets can also be drawn by the simple formula. But wait, that is not all. The Z^2+C formula also draws families of sets which have no official names, though I call them Oblate, Parabolic, Elliptic, and Rectangular sets. These six families of fractals represent the six mutually perpendicular orientations through the four-dimensional object known as the Julibrot. Yes, I realize that a four-dimensional object is an absurdity. Such an object could exist only in a space of four dimensions, and a quick glance at the world shows that there is no room for a fourth dimension. Our three familiar dimensions take up all the space that exists. If anyone doubts this, I challenge the doubter to go out to an open area and point his arm to a direction that is not one of our familiar 3-D directions. Yet, the Julibrot figure does not know that it cannot exist, because it is there and it will not go away. I know it is there because I can calculate and then see slices through it, and I can rotate those slices in most any direction I desire. Today's image for example is one of a midget on a filament in the east suburbs of the large midget at -1.75 on the negative stem of the M-set. But it does not look like a Mandelbrot midget. Nor does it look like a Julia set for that matter. In fact, it is none of the four other types of sets either. It is a nothing set -- a slice through the Julibrot at the point of the Mandelbrot midget, in a totally oblique direction. But sometimes, even nothing can be something, and today's nothing set makes a picture which contains much of the character of the Mandelbrot midget of which it is an odd slice. Because it is an odd slice of a Mandelbrot midget, I named the image "Odd Mandelbrot" The rating of a 5 seems about right, and the render time of under one minute is certainly right. As always, the completed GIF image ia available on the WWW at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Wednesday was almost perfect. The blue skies, gentle winds, and temperature of 80F 27C kept the fractal duo outdoors for a good part of the day. And when it was finally time to return indoors, they did so reluctantly. I now find myself with a moderate amount of work that needs to be done. Since it's always better to have work behind one rather than before, I'll have to get the work behind me. Until next FOTD on Aug 10, take care, and prosper. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Odd-Mandelbrot { ; time=0:00:50.09--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new center-mag=-0.00000\ 000000474777/+0.00000000001270966/3.405492e+010/0.\ 1549/64.5600772360675847/76.4411018546430654 params=45/-45/2/0/-1.746325272478873/0.00829666984\ 6033399/-1.746325272478873/0.008296669846033399 float=y maxiter=1500 inside=0 logmap=132 colors=000c83d82e82fB5gD7gG9hICiKEiNGjPIkRLkUNlWPl\ ZRm`UnaWncYod_mebkgdihfehfbg`_eTWcMI`IGZEEWACU6AS3\ HO4NK5UG6_C7f88l59i68g68e67c77a76_76Y85W85U84S84P9\ 4N93L93JA2HA2FA1DB1BB09B07B0BI2FO3JU4N_6Re7Vk8Vo8S\ jCSjCPeGNaKKXOHTSFOWCK_9Fc7Bg46k22o76kC9gHDdLG`QKX\ VNU_RQcUMhYJm`FqcCeWCUOCIGC69CM5E`1Fh3Dp4Bw5Ar4Bn4\ Ci4Ce4Da4DX4ET4EO4FK4FG4GB4G74H34H78JBBKEFMIINMLOP\ PQTSRXWT_ZUcaVgeXjhYnl_ro`urarp_ooZlnYjmXglWdkVajU\ _hTXgSUfRReQPdPMcOJbNHaML_LOYLRXLUVLXUL_SLbRLePKhO\ KkMKnLKqJKtIKwGKzFKyGMxHNwIOvJPuKQtKRsLTrMUqNVpOWo\ PXnPYnOZoNZoM_pL_pK`qJ`qHarGbrFbsEcsDctCdtBduAeu9e\ v8fv7fw7gx6hy6iz6jz6kz6lz5mz5nz5oz5pz5qz5rz4sz4tz4\ uz4vz4wz4xz3yz3zz3zz3zz3zz2zz2zz2zz2zz2zz2zz1zz1zz\ 1zz1zz1zz1zz0zz0zz0zz0zz0zz9zz8zz8zz8zz8zz7zz7zz7z\ z7zz7zz6zz6zz6zz6zz6zz5zz5zz5zzdzzczzbzz`zz_zzZzzY\ zzWzzVzzUzzSzzRzzQzzPzzNz } 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==================================