Hénon Curves

- strange attractors

Each Hénon curve is generated from a pair of quadratic equations. One gives the new value of X, the other of Y. Both new values of X and Y are derived from previous values of X and Y, and are plotted as a single pixel dot.
Xnew = 1 - A*X2 + Y
Ynew = B*X

For first Hénon curve, make A=1.4 and B=0.3.

To New
  # set default screen, pen and turtle values
  ResetAll SetScreenSize [400 400] HideTurtle
  SetSC Black SetPC Green SetPS 1 PenUp

To Init
  Make "X 0 Make "Y Minus 0.2
  Make "XScale 128 Make "YScale 440
  Make "Alpha 1.4 Make "Beta 0.3

To AngCol :Theta
  Make "Red Abs 255 *Cos (:Theta)
  Make "Gre Abs 255 *Cos (:Theta + 120)
  Make "Blu Abs 255 *Cos (:Theta + 240)
  Output (List :Red :Gre :Blu)

To Hénon
  Make "Xnew 1 - :Alpha*(Power :X 2) + :Y
  Make "Y :Beta * :X
  Make "X :Xnew
  Dot List (:X*:XScale) (:Y*:YScale)

To Go
  New Init
  Repeat 4000 [
    # SetPC AngCol Integer RepCount/10     # comment in for color

Replace the Init procedure for a second type of Hénon curve.

To Init
  Make "X 0 Make "Y 0
  Make "XScale 40 Make "YScale 40
  Make "Alpha 0.2 Make "Beta 0.9991

Henon 1
Henon 1


Henon 2
Henon 2

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