FOTD -- August 16, 2008 (Rating 7) Fractal visionaries and enthusiasts: It is an inescapable mathematical fact that fractals with frac- tional powers of Z must have discontinuities. These discontinui- ties sometimes make interesting patterns in themselves, but just as often they spoil the perfection of the fractal in which they are found. The discontinuities cannot be avoided, but as the FOTD image for today unexpectedly shows, they can be minimized. The formula for today's image contains Z^(3.5), which demands that the image have discontinuities. The breaks are there indeed, but they are so few and so unobtrusive that they could easily be missed when the image is glanced at casually. With its one minor break on the left side, today's image is a scene in the East Valley area of its parent fractal, which is an oversized Mandelbrot set. I named it "Few Discontinuities" and rated it at a 7. The calculation time of just under 5 minutes is fast enough to hold boredom at bay, yet slow enough to allow ample time for anticipation. The image is also available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Pleasant temperatures and plenty sun made Friday an acceptable day here at Fractal Central. A sudden thunder-shower at 5pm was too brief to spoil things. The fractal cats agreed as they stretched in the returning sun. For me the day was acceptable. I could think of a few things that might have gone better, but why quibble with minutiae. The next in the apparently endless series of FOTD's will be posted in 24 hours. Until then, take care, and if life is all a dream, where will we be when we wake up? Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= FewDiscontinuities { ; time=0:04:53.03-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot center-mag=+3.798906332849346/-0.0029529560051977/\ 5.019158e+007/1/20/0 params=0/0/0/0/0/0/0/0/3.5/15 float=y maxiter=15000 inside=0 periodicity=10 colors=000jbjgciddhaegZefWfeTgdQhcNibKjaHk`Fk`Lh_Q\ fZVdY_bXd`WiZVnXUsVTxTTsWRnZQj`OecNafLXhKTkIOnHKpF\ FsEBuDApFAlHAhIAdKA`M9XN9TP9PR9LS9HU9DVBFXCGZEH_FJ\ aHKbILdJMeLOgMPiOQjPSlRTmSUoTVpUWoVXnWXnXYmYZlZZl_\ _k`_ja`jbaicahdbhebgfcfgdfhdeiediedhbeh_ehYfhVfhTg\ hQghOhhLhgIhgGigDigBjg8jg6kg3kg1ke2ic3ib4i`5hZ6hY7\ gW8gU9fTAfRBePCeODeMEeKFeJGeHHeFIeEJeBGi8Dl5Ao28r5\ Ar7CsADtCFuFGvHIwKJxMLyPMzROxTQvWRtYTr`UpbWpeXogZo\ j_olaonbom_nlYmlWmkTljRkjPkiNjhKihIigGhfEgfBge9fd7\ eb3gd5ee6cf8ag9`hBZiCXjEWkFUlHSmIRnKPoLNpNLqOKrQIs\ RGtTFuUDvVBvW1xZAwbJtfRrj_mmhlolknngmkdke`h`YfVUcQ\ Q`KNYFJV9HR3GT4FV5EX6EZ7D`8Cb9BdABfBAhC9jD8lE2Nn8m\ EAe9CY5AN0DQ1GS2JU3MW4PY5R_6Ua7Xc7_f8bh9djAglBjnCm\ pDprEtuFrtEptEotEmsDlsDjsDisDgrCerCdrCbqBaqB_qB`s9\ ZqBXpCVnDUmESkFQjGPhINgJLeKKdLIcMGaNE`ODZQBYR9WS8V\ T6TU4SV1PV3RW5TW7VW8WWmak } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================