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: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> 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=========================================