; Date: Sun, 08 Feb 2009 19:47:02 -0500 ; ; To: fractint@mailman.xmission.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 09-02-09 (Siegels on Parade [6]) ; ; Id: <1.5.4.16.20090208194640.2ba7dcd0@pop.mindspring.com> ; --------- ; ; FOTD -- February 09, 2009 (Rating 6) ; ; Fractal visionaries and enthusiasts: ; ; In yesterday's discussion I mentioned Siegel Disks. Actually, ; I'm not sure of the significance of Siegel Disks. The math ; encyclopedia defines the Siegel Disk Fractal as a Julia set (of ; the Mandelbrot set) with c=-0.390541,-0.586788i. But why this ; particular fractal is special is a mystery. I can see nothing ; unusual or unique about it. The corresponding point of the ; Mandelbrot set lies exactly on the boundary of the main bay, but ; other points on the boundary give similar fractals. The answer ; must lie somewhere in one of the fractal books I have not yet ; come upon. ; ; Today's image is an extension of the Siegel Disk idea, a Julia ; set of a point on the boundary of the Z^6+C Mandeloid. It is ; filled with things that closely resemble Z^2+C Siegel Disks, ; with six large disks and an infinity of smaller ones, their ; position made obvious by the coloring. The fractal is rather ; attractive, though its familiarity prevents it from earning a ; rating above a 6. ; ; I named the image "Siegels on Parade", and why not? After all, ; a parade with an infinity of marching Siegel Disks would take ; forever to pass the reviewing stand. Luckily, the march is only ; symbolic, and the fractal takes only 3-3/4 minutes to calculate. ; And even better, the already-calculated image is or soon will be ; posted on the FOTD web site for immediate and intense gratifica- ; tion. The web site may be accessed at: ; ; ; ; Sunday brought a prelude of spring to Fractal Central, with ; total sun and a temperature of 55F 13C. The wind was a bit ; higher than ideal, but the fractal cats didn't mind a bit. ; ; My day was uneventful, though I heard that a rather sizable job ; will be coming in sometime Monday. The next FOTD will be posted ; in 24 hours. Until then, take care, and is skepticism always ; the most rational approach? ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Siegels_on_Parade { ; time=0:03:45.73-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=JuliaN passes=1 center-mag=0/0/0.928 params=6/0/0/0/-0.4241305333947207/0.6631595440171\ 235 float=y maxiter=3200 inside=bof60 logmap=yes symmetry=origin periodicity=0 colors=000A4fA5eA6dA7cA8bA9aAA`AB_ACZADYAEXAFWAGVA\ HUBITBKSCMRDNQEPPoROpTLqUIrWFsYCtZAu_9v`9wa9xa8yb8\ zc8zc8zd7ze7ze7zf7zg6zh6zh6zi6zj5zj5zk5zl5zl4zm4zn\ 4zpUzqZztczwhzzjsZKgVOfRSfNWfJ_iFbfGcdGdbGe_GeYGfW\ GgTGgRGhPGiLDjNGiOJiPMhRPhSSgTVgVYgW`fXcfZfe_ie_ng\ `keaidbfccdadb`e__fYZgWXhTWiRVjPTkMSlKRlHNmIQmITmI\ WmIZnIanIcnIfnIioIloIooIrpJvoItnIrmHqlHokHmjGliGjh\ GihFggFefFdeEbdEacE_bDYaDX`DV`CT_CSZCQYBPXBNWBLVAK\ UAIW7GUAHTDIRGJQIKPLKNOLMQMLTNJWOIZOH`PFcQEfRPvUDh\ REgTEfUFfVFeWGeXGdYHdZHc_Ib`IbaJacJadK`eK`fL_gL_hM\ ZiMYjNYkNXlOXmOWoPWpPVqQUrQUsRTtRTuSSvSSwTRxTRyQWt\ N_oLdjIheEmZGl`HlaJkbKkcMkdNjePjfQigSihTiiVhkWhlYh\ mZgn`goafpcfqdfrfesgetheugctfbsf`se_rdZrdXqcWqbUpb\ TpaSo`Qo`Pn_Nn_MmZLlYJlYIkXGkWFjWEjVCiUBiU9hT8hS7g\ S5gR4fR3fO5dL7bJ9aGB_DDYBEXFFYIGYLGYOHYRHYUIY7Jh6I\ j6Hk6Gl6Fm6En5Do5Cp5Bq5Ar } frm:JuliaN {; Jim Muth b=p1, z=p2+pixel, c=p3: z=z^(b)+c, |z| <= 16 } ; END PARAMETER FILE========================================= ; ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint