jpayne@69: #!/usr/bin/env python3
jpayne@69: """       turtle-example-suite:
jpayne@69: 
jpayne@69:         xtx_lindenmayer_indian.py
jpayne@69: 
jpayne@69: Each morning women in Tamil Nadu, in southern
jpayne@69: India, place designs, created by using rice
jpayne@69: flour and known as kolam on the thresholds of
jpayne@69: their homes.
jpayne@69: 
jpayne@69: These can be described by Lindenmayer systems,
jpayne@69: which can easily be implemented with turtle
jpayne@69: graphics and Python.
jpayne@69: 
jpayne@69: Two examples are shown here:
jpayne@69: (1) the snake kolam
jpayne@69: (2) anklets of Krishna
jpayne@69: 
jpayne@69: Taken from Marcia Ascher: Mathematics
jpayne@69: Elsewhere, An Exploration of Ideas Across
jpayne@69: Cultures
jpayne@69: 
jpayne@69: """
jpayne@69: ################################
jpayne@69: # Mini Lindenmayer tool
jpayne@69: ###############################
jpayne@69: 
jpayne@69: from turtle import *
jpayne@69: 
jpayne@69: def replace( seq, replacementRules, n ):
jpayne@69:     for i in range(n):
jpayne@69:         newseq = ""
jpayne@69:         for element in seq:
jpayne@69:             newseq = newseq + replacementRules.get(element,element)
jpayne@69:         seq = newseq
jpayne@69:     return seq
jpayne@69: 
jpayne@69: def draw( commands, rules ):
jpayne@69:     for b in commands:
jpayne@69:         try:
jpayne@69:             rules[b]()
jpayne@69:         except TypeError:
jpayne@69:             try:
jpayne@69:                 draw(rules[b], rules)
jpayne@69:             except:
jpayne@69:                 pass
jpayne@69: 
jpayne@69: 
jpayne@69: def main():
jpayne@69:     ################################
jpayne@69:     # Example 1: Snake kolam
jpayne@69:     ################################
jpayne@69: 
jpayne@69: 
jpayne@69:     def r():
jpayne@69:         right(45)
jpayne@69: 
jpayne@69:     def l():
jpayne@69:         left(45)
jpayne@69: 
jpayne@69:     def f():
jpayne@69:         forward(7.5)
jpayne@69: 
jpayne@69:     snake_rules = {"-":r, "+":l, "f":f, "b":"f+f+f--f--f+f+f"}
jpayne@69:     snake_replacementRules = {"b": "b+f+b--f--b+f+b"}
jpayne@69:     snake_start = "b--f--b--f"
jpayne@69: 
jpayne@69:     drawing = replace(snake_start, snake_replacementRules, 3)
jpayne@69: 
jpayne@69:     reset()
jpayne@69:     speed(3)
jpayne@69:     tracer(1,0)
jpayne@69:     ht()
jpayne@69:     up()
jpayne@69:     backward(195)
jpayne@69:     down()
jpayne@69:     draw(drawing, snake_rules)
jpayne@69: 
jpayne@69:     from time import sleep
jpayne@69:     sleep(3)
jpayne@69: 
jpayne@69:     ################################
jpayne@69:     # Example 2: Anklets of Krishna
jpayne@69:     ################################
jpayne@69: 
jpayne@69:     def A():
jpayne@69:         color("red")
jpayne@69:         circle(10,90)
jpayne@69: 
jpayne@69:     def B():
jpayne@69:         from math import sqrt
jpayne@69:         color("black")
jpayne@69:         l = 5/sqrt(2)
jpayne@69:         forward(l)
jpayne@69:         circle(l, 270)
jpayne@69:         forward(l)
jpayne@69: 
jpayne@69:     def F():
jpayne@69:         color("green")
jpayne@69:         forward(10)
jpayne@69: 
jpayne@69:     krishna_rules = {"a":A, "b":B, "f":F}
jpayne@69:     krishna_replacementRules = {"a" : "afbfa", "b" : "afbfbfbfa" }
jpayne@69:     krishna_start = "fbfbfbfb"
jpayne@69: 
jpayne@69:     reset()
jpayne@69:     speed(0)
jpayne@69:     tracer(3,0)
jpayne@69:     ht()
jpayne@69:     left(45)
jpayne@69:     drawing = replace(krishna_start, krishna_replacementRules, 3)
jpayne@69:     draw(drawing, krishna_rules)
jpayne@69:     tracer(1)
jpayne@69:     return "Done!"
jpayne@69: 
jpayne@69: if __name__=='__main__':
jpayne@69:     msg = main()
jpayne@69:     print(msg)
jpayne@69:     mainloop()