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MathGroup Archive 2006

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fractal based on modular form solution using Fibonacci numbers

  • To: mathgroup at smc.vnet.net
  • Subject: [mg64963] fractal based on modular form solution using Fibonacci numbers
  • From: Roger Bagula <rlbagulatftn at yahoo.com>
  • Date: Fri, 10 Mar 2006 05:14:55 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

I call it the Fibonacci Modular eye:
Notebook:
F[0] = 0; F[1] = 1;
F[n_] := F[n] = F[n - 1] + F[n - 2]
a = Table[F[n], {n, 0, 50}];
xroot[k_, m_, n_] := (Exp[I*2*Pi*k/(2*m)] - a[[n]])/a[[n + 1]] - 1
aout = Table[Table[Table[{Re[xroot[k, m, n]], Im[xroot[k, m,
    n]]}, {k, 1, 2*m}], {n, 1, m}], {m, 1, 25}];
b = Flatten[Flatten[aout, 1], 1];
ListPlot[b, PlotRange -> All]


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