1  # File: tdemo_chaos.py
       2  # Author: Gregor Lingl
       3  # Date: 2009-06-24
       4  
       5  # A demonstration of chaos
       6  
       7  from turtle import *
       8  
       9  N = 80
      10  
      11  def f(x):
      12      return 3.9*x*(1-x)
      13  
      14  def g(x):
      15      return 3.9*(x-x**2)
      16  
      17  def h(x):
      18      return 3.9*x-3.9*x*x
      19  
      20  def jumpto(x, y):
      21      penup(); goto(x,y)
      22  
      23  def line(x1, y1, x2, y2):
      24      jumpto(x1, y1)
      25      pendown()
      26      goto(x2, y2)
      27  
      28  def coosys():
      29      line(-1, 0, N+1, 0)
      30      line(0, -0.1, 0, 1.1)
      31  
      32  def plot(fun, start, color):
      33      pencolor(color)
      34      x = start
      35      jumpto(0, x)
      36      pendown()
      37      dot(5)
      38      for i in range(N):
      39          x=fun(x)
      40          goto(i+1,x)
      41          dot(5)
      42  
      43  def main():
      44      reset()
      45      setworldcoordinates(-1.0,-0.1, N+1, 1.1)
      46      speed(0)
      47      hideturtle()
      48      coosys()
      49      plot(f, 0.35, "blue")
      50      plot(g, 0.35, "green")
      51      plot(h, 0.35, "red")
      52      # Now zoom in:
      53      for s in range(100):
      54          setworldcoordinates(0.5*s,-0.1, N+1, 1.1)
      55      return "Done!"
      56  
      57  if __name__ == "__main__":
      58      main()
      59      mainloop()