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Eye of Ra :ellipse_self_similar

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  • Subject: [mg101320] Eye of Ra :ellipse_self_similar
  • From: Roger Bagula <rlbagula at>
  • Date: Wed, 1 Jul 2009 06:34:29 -0400 (EDT)

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.
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 
alternative email: rlbagula at

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