Demo/turtle/tdemo_chaos.py

   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, colour):
  33     pencolor(colour)
  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()