; Date: Thu, 08 Aug 2002 11:24:37 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 08-08-02 (Odd Mandelbrot [5]) ; Id: <1.5.4.16.20020808112523.29af7c38@pop.mindspring.com> ; --------- ; 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: ; ; ; ; and at: ; ; ; ; 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 PARAMETER 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 PARAMETER FILE================================== ; ;