Cardioid plus circles...?
I have read that the Mandelbrot Set can also be though of as a cardioid (the main body) with circles attached to it. Looks likely to me. Does anyone know the ratio of sizes of successive circles to each other, and of the largest of them to, say, the "vertical diameter" of the cardioid? It isn't Fiegenbaum's first Constant by any chance, is it? Next: Is the arrangement (position) of the circles something which might be programmed, knowing size ratios, avoiding the standard z->z^2+c programming entirely? Tony Hanmer Tbilisi, Republic of Georgia _________________________________________________________________ The new MSN 8: smart spam protection and 2 months FREE* http://join.msn.com/?page=features/junkmail
Tony, there are quite a few sites on the web regarding these questions. Professor Robert L. Devaney's: http://math.bu.edu/DYSYS/explorer/index.html http://math.bu.edu/DYSYS/FRACGEOM/FRACGEOM.html http://math.bu.edu/DYSYS/FRACGEOM2/FRACGEOM2.html Especially the last URL has chapters you are interested in, i.e. "Period of the Bulbs" (bulbs = circles attached to the cardioid or to other attached circles), but I'd recommend visiting all of the above. Evgeny Demidov's: http://www.people.nnov.ru/fractal/MSet/Contents.htm or http://www.ibiblio.org/e-notes/MSet/Contents.htm Robert Munafo's site with everything M-Set: http://www.mrob.com/pub/muency.html Linas Vepstas site: http://linas.org/art-gallery/index.html ("Bud Sizes" near the end of the page) I'd say these are enough for a first round :-) Regards, Gerald
participants (2)
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Gerald K. Dobiasovsky -
Tony (Anthony) Hanmer