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