jpayne@69: # File: tdemo_chaos.py
jpayne@69: # Author: Gregor Lingl
jpayne@69: # Date: 2009-06-24
jpayne@69: 
jpayne@69: # A demonstration of chaos
jpayne@69: 
jpayne@69: from turtle import *
jpayne@69: 
jpayne@69: N = 80
jpayne@69: 
jpayne@69: def f(x):
jpayne@69:     return 3.9*x*(1-x)
jpayne@69: 
jpayne@69: def g(x):
jpayne@69:     return 3.9*(x-x**2)
jpayne@69: 
jpayne@69: def h(x):
jpayne@69:     return 3.9*x-3.9*x*x
jpayne@69: 
jpayne@69: def jumpto(x, y):
jpayne@69:     penup(); goto(x,y)
jpayne@69: 
jpayne@69: def line(x1, y1, x2, y2):
jpayne@69:     jumpto(x1, y1)
jpayne@69:     pendown()
jpayne@69:     goto(x2, y2)
jpayne@69: 
jpayne@69: def coosys():
jpayne@69:     line(-1, 0, N+1, 0)
jpayne@69:     line(0, -0.1, 0, 1.1)
jpayne@69: 
jpayne@69: def plot(fun, start, color):
jpayne@69:     pencolor(color)
jpayne@69:     x = start
jpayne@69:     jumpto(0, x)
jpayne@69:     pendown()
jpayne@69:     dot(5)
jpayne@69:     for i in range(N):
jpayne@69:         x=fun(x)
jpayne@69:         goto(i+1,x)
jpayne@69:         dot(5)
jpayne@69: 
jpayne@69: def main():
jpayne@69:     reset()
jpayne@69:     setworldcoordinates(-1.0,-0.1, N+1, 1.1)
jpayne@69:     speed(0)
jpayne@69:     hideturtle()
jpayne@69:     coosys()
jpayne@69:     plot(f, 0.35, "blue")
jpayne@69:     plot(g, 0.35, "green")
jpayne@69:     plot(h, 0.35, "red")
jpayne@69:     # Now zoom in:
jpayne@69:     for s in range(100):
jpayne@69:         setworldcoordinates(0.5*s,-0.1, N+1, 1.1)
jpayne@69:     return "Done!"
jpayne@69: 
jpayne@69: if __name__ == "__main__":
jpayne@69:     main()
jpayne@69:     mainloop()