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Apr 29th, 2016
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  1. sol = RSolve[{x[n + 1] == 2.8*x[n]*(1 - x[n]), x[0] == 0.2}, x[n], n]
  2. ListPlot[Table[{n, x[n] /. sol[[1]]}, {n, 1, 5}],
  3. PlotStyle -> {Hue[1], PointSize[0.0125]}];
  4.  
  5. logistic[[Alpha]_, x0_] := Module[{f}, f[x_] := [Alpha] x (1 - x);
  6. seq = NestList[f, x0, 100];
  7. p = Join @@ ({{#, #}, {##}} & @@@ Partition[seq, 2, 1]);
  8. Plot[{f[x], x}, {x, 0, 1}, PlotRange -> {0, 1},
  9. Epilog -> {Thick, Opacity[0.6], Line[p]}, ImageSize -> 500]];
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