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