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: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> 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 20.0 PAR-FORMULA 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 20.0 PAR-FORMULA FILE==================================