Eye of Ra :ellipse_self_similar
- To: mathgroup at smc.vnet.net
- Subject: [mg101320] Eye of Ra :ellipse_self_similar
- From: Roger Bagula <rlbagula at sbcglobal.net>
- Date: Wed, 1 Jul 2009 06:34:29 -0400 (EDT)
http://www.geocities.com/rlbagulatftn/ellipse_self_similar.jpg I orginially did this in the 60's inspired by the CBS logo of a eye. This is the first time I figured out a mathematical form for a self-similar ellipse of thios sort: The figure alternates ellipses and inscribed ellises. It also tiles a disk in an hyperbolic reduction scaling of scale of powers of two. I really doubt this is a new fractal, but it is pretty anyway. I call it the "Eye of Ra" as reading about Akhenaten made me think of it. Mathematica: Clear[x, y, i, t, g] x[i_, t_] = If[Mod[i, 2] == 0, Cos[t]/2^(i - 1), Cos[t]/2^i] y[i_, t_] = If[Mod[i, 2] == 0, Sin[t]/2^(i + 1), Sin[t]/2^i] g = Table[ParametricPlot[{x[i, t], y[i, t]}, {t, - Pi, Pi}, Axes -> False], {i, 0, 10}] Show[g, PlotRange -> All] Respectfully, Roger L. Bagula 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :http://www.geocities.com/rlbagulatftn/Index.html alternative email: rlbagula at sbcglobal.net
