; Date: Fri, 15 Aug 2008 21:22:37 -0400 ; ; To: fractint@mailman.xmission.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 16-08-08 (Few Discontinuities [7]) ; ; Id: <1.5.4.16.20080815212323.2b9fc1d2@pop.mindspring.com> ; --------- ; ; 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: ; ; ; ; 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========================================= ; ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint