; Date: Tue, 24 Jun 2003 10:19:33 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 24-06-03 (Good Fortune [6]) ; Id: <1.5.4.16.20030624101924.2ab7921a@pop.mindspring.com> ; --------- ; ; FOTD -- June 24, 2003 (Rating 6) ; ; Fractal visionaries and enthusiasts: ; ; The formula that created today's image is one of the simplest -- ; Z+Z^3+C. Yet it creates a parent with scenes that rate at least ; a 6, as in today's picture, and likely with scenes that would ; rate a 9, if only they could be found. ; ; Curiously, adding Z to Z^2 makes no change in the appearance of ; the Mandelbrot image, though it does move it to the west, but ; adding Z to Z^3 totally changes the appearance of the resulting ; fractal. ; ; The parent fractal of today's scene consists of an obvious ; Mandelbrot set standing on its nose, with much interesting ; detail beyond its East (or North) Valley, and an almost ; completely obscured Mandelbrot set hidden beneath the detail ; beyond the first Mandeloid's East Valley. This second M-set is ; visible only with carefully chosen coloring. ; ; Today's image is located in a spiral in a valley near the ; northern extremity of the parent. The unusually-well-defined ; pattern surrounding the midget is a result of the coloring. ; With other palettes the pattern vanishes. ; ; I named today's image "Good Fortune". When I gave it this name, ; I had an idea in mind, but whatever it was, it has eluded me. ; So let's just say the scene in the image is very lucky to have ; been found. The odds against it ever having seen the light of ; day are at least one-googol-to-one. ; ; The image takes 1/2 hour to render on my machine. This is a bit ; of a drag for busy fractalists. So I recommend downloading the ; completed GIF image from: ; ; ; ; or from: ; ; ; ; Summer weather finally arrived at Fractal Central on Monday, as ; the temperature reached 89F 32C and the hot sun beamed down on ; the fractal cats, who were pleased with the turn of events and ; showed their pleasure by playing like kittens. Tippy actually ; scampered up a holly tree, while Thomas watched with amusement. ; No tuna was needed. ; ; Since today will be a repeat, I expect a repeat performance from ; the dynamic duo. I'll do my part by finishing the work early. ; But to finish the work, I must first start it, so until next ; FOTD, take care, and wait until the fractals come home. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE================================ Good_Fortune { ; time=0:29:42.99--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.00290337839407/+1.12763603161069/6.4\ 25424e+008/1/-177.5/-0.00023613749 params=1/1/1/3/\ 0/0 float=y maxiter=4200 inside=0 periodicity=10 colors=000AVK8TK6TM6RM4PM2PM0OM0MM0MM0KM0IM0GI0IM0\ IO0IP4IR6ITAIVCIXGIYIIbMIdOIeRIgTIiXIkYIlbIndIpgIs\ iIulIwnIxrIzsIzwIzxIzzIzzIzzIzzIzzIzzIzzIzzIzzIzzI\ zzKzzMzzOzwPzpRziTzbVzVXzOYzG_z4XzA_zGdzKgzPkzVnzY\ rzduzixwlzunwwpswrpwslwuiwwewx_wzXwzTwzPwzMwzIwzCw\ z8wz4wz0wz0wz0wz0sz0wz0xz0zs8zkEzbKzTRzKXzCbzI_zMY\ zPXzTVxXTu_RrePniOllMipKesIbwG_zEXzCTzAPz8Oz6Kz4Gz\ 2Cz2Az08z06z06z04z02z02x00u00p00l00i00e00_00X00T00\ P00K00G00C008006006006004004204602A02C02G02K00O00P\ 00T00X00Y00b00e00i00k00n00r00u00w00z00z00z00z00z00\ z00z04z4IsEVgPgXYsKgz6rz0zz0zz0zz0zz0zz0xz0uz0sz0p\ x0nu0kr0in2ek4dg6_d8Y_AXXCTTERPGOMIMIKIEMGAOC6PA2R\ 60T40V00X00Y00_00b00_00Y00X00V00V22T46R6AP8COAGOCK\ MEOKGRIIVGKYGMbEOdCPgARk8Tn8Vr6Xu4Yx2_z0bz0dz0iz0n\ z0sz0xz0zz0zz0zz0zz0zz2zw6zrCzlGzgKzbOzXRzRVzM_zGd\ zAgz4kz0nz0rzG_KEYKCXKCXK } 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 PARAMETER FILE================================== ;