1  #!/usr/bin/env python3
       2  """      turtle-example-suite:
       3  
       4          tdemo_fractalCurves.py
       5  
       6  This program draws two fractal-curve-designs:
       7  (1) A hilbert curve (in a box)
       8  (2) A combination of Koch-curves.
       9  
      10  The CurvesTurtle class and the fractal-curve-
      11  methods are taken from the PythonCard example
      12  scripts for turtle-graphics.
      13  """
      14  from turtle import *
      15  from time import sleep, perf_counter as clock
      16  
      17  class ESC[4;38;5;81mCurvesTurtle(ESC[4;38;5;149mPen):
      18      # example derived from
      19      # Turtle Geometry: The Computer as a Medium for Exploring Mathematics
      20      # by Harold Abelson and Andrea diSessa
      21      # p. 96-98
      22      def hilbert(self, size, level, parity):
      23          if level == 0:
      24              return
      25          # rotate and draw first subcurve with opposite parity to big curve
      26          self.left(parity * 90)
      27          self.hilbert(size, level - 1, -parity)
      28          # interface to and draw second subcurve with same parity as big curve
      29          self.forward(size)
      30          self.right(parity * 90)
      31          self.hilbert(size, level - 1, parity)
      32          # third subcurve
      33          self.forward(size)
      34          self.hilbert(size, level - 1, parity)
      35          # fourth subcurve
      36          self.right(parity * 90)
      37          self.forward(size)
      38          self.hilbert(size, level - 1, -parity)
      39          # a final turn is needed to make the turtle
      40          # end up facing outward from the large square
      41          self.left(parity * 90)
      42  
      43      # Visual Modeling with Logo: A Structural Approach to Seeing
      44      # by James Clayson
      45      # Koch curve, after Helge von Koch who introduced this geometric figure in 1904
      46      # p. 146
      47      def fractalgon(self, n, rad, lev, dir):
      48          import math
      49  
      50          # if dir = 1 turn outward
      51          # if dir = -1 turn inward
      52          edge = 2 * rad * math.sin(math.pi / n)
      53          self.pu()
      54          self.fd(rad)
      55          self.pd()
      56          self.rt(180 - (90 * (n - 2) / n))
      57          for i in range(n):
      58              self.fractal(edge, lev, dir)
      59              self.rt(360 / n)
      60          self.lt(180 - (90 * (n - 2) / n))
      61          self.pu()
      62          self.bk(rad)
      63          self.pd()
      64  
      65      # p. 146
      66      def fractal(self, dist, depth, dir):
      67          if depth < 1:
      68              self.fd(dist)
      69              return
      70          self.fractal(dist / 3, depth - 1, dir)
      71          self.lt(60 * dir)
      72          self.fractal(dist / 3, depth - 1, dir)
      73          self.rt(120 * dir)
      74          self.fractal(dist / 3, depth - 1, dir)
      75          self.lt(60 * dir)
      76          self.fractal(dist / 3, depth - 1, dir)
      77  
      78  def main():
      79      ft = CurvesTurtle()
      80  
      81      ft.reset()
      82      ft.speed(0)
      83      ft.ht()
      84      ft.getscreen().tracer(1,0)
      85      ft.pu()
      86  
      87      size = 6
      88      ft.setpos(-33*size, -32*size)
      89      ft.pd()
      90  
      91      ta=clock()
      92      ft.fillcolor("red")
      93      ft.begin_fill()
      94      ft.fd(size)
      95  
      96      ft.hilbert(size, 6, 1)
      97  
      98      # frame
      99      ft.fd(size)
     100      for i in range(3):
     101          ft.lt(90)
     102          ft.fd(size*(64+i%2))
     103      ft.pu()
     104      for i in range(2):
     105          ft.fd(size)
     106          ft.rt(90)
     107      ft.pd()
     108      for i in range(4):
     109          ft.fd(size*(66+i%2))
     110          ft.rt(90)
     111      ft.end_fill()
     112      tb=clock()
     113      res =  "Hilbert: %.2fsec. " % (tb-ta)
     114  
     115      sleep(3)
     116  
     117      ft.reset()
     118      ft.speed(0)
     119      ft.ht()
     120      ft.getscreen().tracer(1,0)
     121  
     122      ta=clock()
     123      ft.color("black", "blue")
     124      ft.begin_fill()
     125      ft.fractalgon(3, 250, 4, 1)
     126      ft.end_fill()
     127      ft.begin_fill()
     128      ft.color("red")
     129      ft.fractalgon(3, 200, 4, -1)
     130      ft.end_fill()
     131      tb=clock()
     132      res +=  "Koch: %.2fsec." % (tb-ta)
     133      return res
     134  
     135  if __name__  == '__main__':
     136      msg = main()
     137      print(msg)
     138      mainloop()