; Date: Mon, 06 Jan 2003 10:45:01 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 06-01-03 (Siegel Mandelbrot [4]) ; Id: <1.5.4.16.20030106104740.29cf5576@pop.mindspring.com> ; --------- ; FOTD -- November 06, 2003 (Rating 4) ; ; Fractal visionaries and enthusiasts: ; ; Two days ago I posted a FOTD that illustrates what I assume to ; be almost-Siegel Disks, or about as close as is possible to come ; to Siegel Disks this side of infinity. Then, yesterday, I began ; wondering about the appearance of the Mandelbrot set at a point ; so close to the Siegel-boundary. The area was extremely easy to ; find, but its maxiter of over 1-million made the rendering quite ; slow. ; ; What I found was an area of thin, wiry arms, so jagged that it ; is difficult to determine the direction from which they are ; coming. The coloring shows that the arm in the upper right part ; of the image is the lowest-iteration feature in the frame, but ; the tan-colored arm in the left half of the frame could just as ; easily be entering from the top as from the bottom. It actually ; enters from the top. ; ; I also noticed that the midgets are very plentiful this deep in ; the M-set. At least 30 become visible in the frame when the ; color mode is toggled. I assume that the smaller ones are ; surrounded by even wirier and more jagged arms in addition to ; taking even longer to render. ; ; Curiously, at this extreme location of the M-set, the normal ; 2-4-8... pattern has all but vanished. The pattern might be ; there, but if it is, it is so distorted as to be virtually ; beyond detection. ; ; I am also curious about the appearance of the odd planes and ; oblique slices of the Julibrot at this point, but without ; Fractint's fast Mandelbrot formula to speed up the rendering, ; such images would be extremely slow. Still, I might investigate ; this aspect in the near future, and if the results show anything ; unusual, it will appear as a FOTD. ; ; Like the Siegel Disk image of two days ago, the interest of ; today's image lies mostly in the mathematical aspect, and like ; the earlier image, it also rates a 4. I named the image "Siegel ; Mandelbrot" as a simple description. ; ; With its render time of almost 1-1/2 hours, the image is a very ; slow one, I recommend downloading it from one of the following ; two web sites: ; ; ; ; ; ; But before going for the download, give Paul and Scott a chance ; to render and post the image. ; ; Snow fell all day Sunday here at Fractal Central, piling up 5in ; 12cm by nightfall. The snow, combined with a temperature of 30F ; -1C, kept the dynamic fractal cats housebound. They put on ; their best pouts to let me know of their unhappiness, but ; knowing them as I do, I realized that their displeasure was ; mostly a show. ; ; It's another threatening day today, with talk of several more ; inches of snow by this evening. (We still measure length in ; inches, and temperature in degrees Fahrenheit here in the best ; educated ;-) nation in the world.) The cats were saddened by ; the news of still more snow. As for me, I've got enough ; supplies stocked and enough graphic work waiting that I have no ; time to be sad and no need to venture out on treacherous roads. ; ; The next glorious fractal will appear in only 24 hours. Until ; then, take care, and if you lift too much heavy snow, you might ; hurt a Siegel Disk. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Siegel_Mandelbrot { ; time=1:22:52.63--SF5 on a P200 reset=2002 type=mandel passes=1 center-mag=-0.3905\ 4756291390700/-0.58679532300884950/442757.7/1/102.\ 5/-2.48215537707041634e-009 params=0/0 float=y maxiter=1200000 inside=0 logmap=905 periodicity=10 colors=0008pe5rf7pg8ng9mhAkhBiiChiEfjFdjGckHakI_lJ\ ZlKXmMVmNUnOSnPQoQPoRNpTLpUKqVIqWGrXFrYDsYBuZCs_Cr\ _Cq`Cp`CoaCnaCmbDlbDjcDidDhdDgeDfeDefEdfEcgEagE`hE\ _iEZiEYjFXjFWkFVkFTlFSlFRmFQmGPnGOoGNoGMpGKpGJqGIq\ HHrHGrHFsHEtHDtHBuHAuI9vI8vI7wI6wI5xI4xI3tH7qGAnFD\ kEGgDJdDMaCPZBSVAWS9ZP8aM8dI7gF6jC5m94p53t64s75r86\ q97pA7oB8oC9nDAmEAlEBkFCjGDjHDiIEhJFgKGfLGfMHeNIdN\ JcOJbPKaQLaRM`SM_TNZUOYVPYWQXWQWXRVYSUZTT_TT`USaVR\ bWQcWPdXPdYOeZNfZMg_Lh`KiaKjaJkbIlcHmdGohCmdGk`KiY\ NgUReQVcNYaJa_FeYChW8lV5oU6pT6pS6pS7pR7pQ7pQ7pP8qO\ 8qO8qN8qM9qL9qL9qK9qJArJArIArHArHBrGBrFBrEAsFBrFCr\ FCrFDrFDrGEqGEqGFqGGqGGqHHpHHpHIpHIpHJpIKpIKoILoIL\ oIMoJMoJNnJOnJOnJPnKPnKQnKQmKRmKSmLSmLTmLTlLUlLUlM\ VlMWlMWkMXkMXkNYkNYkNZkN_jN_jO`jO`jOajOaiObiPciPci\ PdiPdiPehQehQfhQghQghQhgRhgRigRigRjgRjgSihThhTghUf\ hUehVehVdhWchWbhXahBpaApc } ; END PARAMETER FILE========================================= ; ;