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