FOTD -- January 14, 2003 (Rating 6) Fractal visionaries and enthusiasts: While at least one member of the Fractint list appears to perhaps be losing a bit of enthusiasm for fractals, there is no danger of a similar fate befalling myself. The only thing I regret is that I lack the time to explore more of the infinitely infinite world of fractals. Perhaps the first sign of impending boredom with fractals is the desire to add multiple layers, as if a single-layer fractal needed something to give it more interest. Then again, perhaps my devotion to single-layer fractals is an individual quirk of mine, caused perhaps by my typical male tendency to concentrate on one task at a time. After all, multiple layers works very well in the case of music, which is candy for the ears; why not in the case of fractals, which are candy for the eyes? I named today's image "Polytope Paradise". I can give no logical reason why I chose such a name, since a polytope is a geometrical figure, existing in n-dimensional space and enclosed by a finite number of planes or hyperplanes. The strings of bubbles in today's image are enclosed by curved 2-D surfaces rather than planes, and therefore cannot truthfully be consid- ered polytopes. As a matter of interest, the word 'polytope' was invented by Alicia Boole, the daughter of logician George Boole. In 1-space and 2-space, an infinity of regular polytopes are possible. In our everyday 3-space, only 5 regular polytopes are possible. In 4-space, 6 are possible, but in 5-space and all higher spaces, only 3 regular polytopes can exist. Today's image is another ghostly one, consisting entirely of trapped points whose orbits have been made visible by the bof60 inside fill. The generating formula combines 1/Z and Z^(-2), then adds 1/C. The image itself rates a 6. The render time of 41 minutes for today's image is admittedly slow. The wait can be avoided by 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> The fractal weather was actually not too bad on Monday, with warm sun, little wind, and a temperature of 43F 6C. The fractal cats found the outdoors reasonably comfortable. Tippy, the lean lanky tabby, spent nearly two hours in the yard. Thomas, the overweight yellow, returned indoors after one hour. No treats were needed. Today however is much colder, and the dynamic pair will not find it so pleasant out of doors. I will not find it pleasant until the work is finished. The next FOTD will appear in 24 hours, so take care, and see you then. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ Polytope_Paradise { ; time=0:41:12.86--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.84049791931695570/+0.257654873112327\ 50/235620.6/1/-65/5.48976843151027794e-010 params=1/-1/1/-2/-32/1e+100 float=y maxiter=900 inside=bof60 logmap=yes periodicity=10 colors=000zzzzwyzuxzswyqvyouymtxlsxksxjrwirwhqwgqv\ fpqepldjgbcb`YYZRTXLNWGOVFPUFPTEQSEQRERQDRPDSODTNC\ TMCULBUKBVJBVIAWHAXH7YGAZFD_FF`EIaELbDNcCQeCTfBVhB\ YiA`i9bhAbgAaeA_cAZaAY_AWXAVUAUSBSPBRNBPLBOJBNGBME\ BKD8KCBJBDI000AIHALG9NG8PF8SE7UE7XD6ZD6aC5cB4eB4hA\ 3j93m92o82q84o96mA7kB9jCAhDCfDEeEFcFHaGI_HKZHMXINV\ JPUKQSLSQMUPMVNNXLOYJP_IQaGQbERdDSeBTg9Uj6Vh8Ug9Uf\ BUeCUdEUcFUbHUaIU`KUZLUYNUXOUWQUVRUUSTTUTSVTRXTPYT\ O_TN`TMbTLcTKeTJfTIhTHiTIqNGjTEcZCXdAQj8Jp5Dx7Cv9C\ uACtCBsEBrFBqHBpJAoKAnMAmNAlMBkMBkMCkLCkLCkLDjLDjK\ EjKEjKEjKFiJFiJGiJGiJGiIHhIHhIIhHIhHIhHJgHJgGKgGKg\ GKgGLfFLfFMfFMfFMfENdEOcDPbDQ`CR_CSZCSYBTWBUVAVUAW\ T9XR9XQ9YP8ZO8_M7`L7aK7aJ6bH6cG5dF5eE4fC4fB4gA3h93\ i72j62k50m22k44j66i88g99fBBeDDcEFbGGaII`JKZLMYNOXO\ PVQRUSTTTVSVWQXYPY_O_aMacLbdKdfJfhHgjGikFkmDloCnqB\ prAqVNIXPLYQN_RP`SRaTTcUV } 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==================================