| 1 | n/a | #!/usr/bin/env python3 |
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| 2 | n/a | """ turtle-example-suite: |
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| 3 | n/a | |
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| 4 | n/a | xtx_lindenmayer_indian.py |
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| 5 | n/a | |
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| 6 | n/a | Each morning women in Tamil Nadu, in southern |
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| 7 | n/a | India, place designs, created by using rice |
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| 8 | n/a | flour and known as kolam on the thresholds of |
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| 9 | n/a | their homes. |
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| 10 | n/a | |
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| 11 | n/a | These can be described by Lindenmayer systems, |
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| 12 | n/a | which can easily be implemented with turtle |
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| 13 | n/a | graphics and Python. |
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| 14 | n/a | |
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| 15 | n/a | Two examples are shown here: |
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| 16 | n/a | (1) the snake kolam |
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| 17 | n/a | (2) anklets of Krishna |
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| 18 | n/a | |
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| 19 | n/a | Taken from Marcia Ascher: Mathematics |
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| 20 | n/a | Elsewhere, An Exploration of Ideas Across |
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| 21 | n/a | Cultures |
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| 22 | n/a | |
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| 23 | n/a | """ |
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| 24 | n/a | ################################ |
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| 25 | n/a | # Mini Lindenmayer tool |
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| 26 | n/a | ############################### |
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| 27 | n/a | |
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| 28 | n/a | from turtle import * |
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| 29 | n/a | |
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| 30 | n/a | def replace( seq, replacementRules, n ): |
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| 31 | n/a | for i in range(n): |
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| 32 | n/a | newseq = "" |
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| 33 | n/a | for element in seq: |
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| 34 | n/a | newseq = newseq + replacementRules.get(element,element) |
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| 35 | n/a | seq = newseq |
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| 36 | n/a | return seq |
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| 37 | n/a | |
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| 38 | n/a | def draw( commands, rules ): |
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| 39 | n/a | for b in commands: |
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| 40 | n/a | try: |
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| 41 | n/a | rules[b]() |
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| 42 | n/a | except TypeError: |
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| 43 | n/a | try: |
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| 44 | n/a | draw(rules[b], rules) |
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| 45 | n/a | except: |
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| 46 | n/a | pass |
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| 47 | n/a | |
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| 48 | n/a | |
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| 49 | n/a | def main(): |
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| 50 | n/a | ################################ |
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| 51 | n/a | # Example 1: Snake kolam |
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| 52 | n/a | ################################ |
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| 53 | n/a | |
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| 54 | n/a | |
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| 55 | n/a | def r(): |
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| 56 | n/a | right(45) |
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| 57 | n/a | |
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| 58 | n/a | def l(): |
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| 59 | n/a | left(45) |
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| 60 | n/a | |
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| 61 | n/a | def f(): |
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| 62 | n/a | forward(7.5) |
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| 63 | n/a | |
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| 64 | n/a | snake_rules = {"-":r, "+":l, "f":f, "b":"f+f+f--f--f+f+f"} |
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| 65 | n/a | snake_replacementRules = {"b": "b+f+b--f--b+f+b"} |
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| 66 | n/a | snake_start = "b--f--b--f" |
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| 67 | n/a | |
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| 68 | n/a | drawing = replace(snake_start, snake_replacementRules, 3) |
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| 69 | n/a | |
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| 70 | n/a | reset() |
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| 71 | n/a | speed(3) |
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| 72 | n/a | tracer(1,0) |
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| 73 | n/a | ht() |
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| 74 | n/a | up() |
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| 75 | n/a | backward(195) |
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| 76 | n/a | down() |
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| 77 | n/a | draw(drawing, snake_rules) |
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| 78 | n/a | |
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| 79 | n/a | from time import sleep |
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| 80 | n/a | sleep(3) |
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| 81 | n/a | |
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| 82 | n/a | ################################ |
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| 83 | n/a | # Example 2: Anklets of Krishna |
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| 84 | n/a | ################################ |
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| 85 | n/a | |
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| 86 | n/a | def A(): |
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| 87 | n/a | color("red") |
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| 88 | n/a | circle(10,90) |
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| 89 | n/a | |
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| 90 | n/a | def B(): |
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| 91 | n/a | from math import sqrt |
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| 92 | n/a | color("black") |
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| 93 | n/a | l = 5/sqrt(2) |
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| 94 | n/a | forward(l) |
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| 95 | n/a | circle(l, 270) |
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| 96 | n/a | forward(l) |
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| 97 | n/a | |
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| 98 | n/a | def F(): |
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| 99 | n/a | color("green") |
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| 100 | n/a | forward(10) |
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| 101 | n/a | |
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| 102 | n/a | krishna_rules = {"a":A, "b":B, "f":F} |
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| 103 | n/a | krishna_replacementRules = {"a" : "afbfa", "b" : "afbfbfbfa" } |
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| 104 | n/a | krishna_start = "fbfbfbfb" |
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| 105 | n/a | |
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| 106 | n/a | reset() |
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| 107 | n/a | speed(0) |
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| 108 | n/a | tracer(3,0) |
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| 109 | n/a | ht() |
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| 110 | n/a | left(45) |
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| 111 | n/a | drawing = replace(krishna_start, krishna_replacementRules, 3) |
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| 112 | n/a | draw(drawing, krishna_rules) |
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| 113 | n/a | tracer(1) |
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| 114 | n/a | return "Done!" |
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| 115 | n/a | |
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| 116 | n/a | if __name__=='__main__': |
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| 117 | n/a | msg = main() |
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| 118 | n/a | print(msg) |
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| 119 | n/a | mainloop() |
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