jpayne@69: #!/usr/bin/env python3
jpayne@69: """      turtle-example-suite:
jpayne@69: 
jpayne@69:         tdemo_fractalCurves.py
jpayne@69: 
jpayne@69: This program draws two fractal-curve-designs:
jpayne@69: (1) A hilbert curve (in a box)
jpayne@69: (2) A combination of Koch-curves.
jpayne@69: 
jpayne@69: The CurvesTurtle class and the fractal-curve-
jpayne@69: methods are taken from the PythonCard example
jpayne@69: scripts for turtle-graphics.
jpayne@69: """
jpayne@69: from turtle import *
jpayne@69: from time import sleep, perf_counter as clock
jpayne@69: 
jpayne@69: class CurvesTurtle(Pen):
jpayne@69:     # example derived from
jpayne@69:     # Turtle Geometry: The Computer as a Medium for Exploring Mathematics
jpayne@69:     # by Harold Abelson and Andrea diSessa
jpayne@69:     # p. 96-98
jpayne@69:     def hilbert(self, size, level, parity):
jpayne@69:         if level == 0:
jpayne@69:             return
jpayne@69:         # rotate and draw first subcurve with opposite parity to big curve
jpayne@69:         self.left(parity * 90)
jpayne@69:         self.hilbert(size, level - 1, -parity)
jpayne@69:         # interface to and draw second subcurve with same parity as big curve
jpayne@69:         self.forward(size)
jpayne@69:         self.right(parity * 90)
jpayne@69:         self.hilbert(size, level - 1, parity)
jpayne@69:         # third subcurve
jpayne@69:         self.forward(size)
jpayne@69:         self.hilbert(size, level - 1, parity)
jpayne@69:         # fourth subcurve
jpayne@69:         self.right(parity * 90)
jpayne@69:         self.forward(size)
jpayne@69:         self.hilbert(size, level - 1, -parity)
jpayne@69:         # a final turn is needed to make the turtle
jpayne@69:         # end up facing outward from the large square
jpayne@69:         self.left(parity * 90)
jpayne@69: 
jpayne@69:     # Visual Modeling with Logo: A Structural Approach to Seeing
jpayne@69:     # by James Clayson
jpayne@69:     # Koch curve, after Helge von Koch who introduced this geometric figure in 1904
jpayne@69:     # p. 146
jpayne@69:     def fractalgon(self, n, rad, lev, dir):
jpayne@69:         import math
jpayne@69: 
jpayne@69:         # if dir = 1 turn outward
jpayne@69:         # if dir = -1 turn inward
jpayne@69:         edge = 2 * rad * math.sin(math.pi / n)
jpayne@69:         self.pu()
jpayne@69:         self.fd(rad)
jpayne@69:         self.pd()
jpayne@69:         self.rt(180 - (90 * (n - 2) / n))
jpayne@69:         for i in range(n):
jpayne@69:             self.fractal(edge, lev, dir)
jpayne@69:             self.rt(360 / n)
jpayne@69:         self.lt(180 - (90 * (n - 2) / n))
jpayne@69:         self.pu()
jpayne@69:         self.bk(rad)
jpayne@69:         self.pd()
jpayne@69: 
jpayne@69:     # p. 146
jpayne@69:     def fractal(self, dist, depth, dir):
jpayne@69:         if depth < 1:
jpayne@69:             self.fd(dist)
jpayne@69:             return
jpayne@69:         self.fractal(dist / 3, depth - 1, dir)
jpayne@69:         self.lt(60 * dir)
jpayne@69:         self.fractal(dist / 3, depth - 1, dir)
jpayne@69:         self.rt(120 * dir)
jpayne@69:         self.fractal(dist / 3, depth - 1, dir)
jpayne@69:         self.lt(60 * dir)
jpayne@69:         self.fractal(dist / 3, depth - 1, dir)
jpayne@69: 
jpayne@69: def main():
jpayne@69:     ft = CurvesTurtle()
jpayne@69: 
jpayne@69:     ft.reset()
jpayne@69:     ft.speed(0)
jpayne@69:     ft.ht()
jpayne@69:     ft.getscreen().tracer(1,0)
jpayne@69:     ft.pu()
jpayne@69: 
jpayne@69:     size = 6
jpayne@69:     ft.setpos(-33*size, -32*size)
jpayne@69:     ft.pd()
jpayne@69: 
jpayne@69:     ta=clock()
jpayne@69:     ft.fillcolor("red")
jpayne@69:     ft.begin_fill()
jpayne@69:     ft.fd(size)
jpayne@69: 
jpayne@69:     ft.hilbert(size, 6, 1)
jpayne@69: 
jpayne@69:     # frame
jpayne@69:     ft.fd(size)
jpayne@69:     for i in range(3):
jpayne@69:         ft.lt(90)
jpayne@69:         ft.fd(size*(64+i%2))
jpayne@69:     ft.pu()
jpayne@69:     for i in range(2):
jpayne@69:         ft.fd(size)
jpayne@69:         ft.rt(90)
jpayne@69:     ft.pd()
jpayne@69:     for i in range(4):
jpayne@69:         ft.fd(size*(66+i%2))
jpayne@69:         ft.rt(90)
jpayne@69:     ft.end_fill()
jpayne@69:     tb=clock()
jpayne@69:     res =  "Hilbert: %.2fsec. " % (tb-ta)
jpayne@69: 
jpayne@69:     sleep(3)
jpayne@69: 
jpayne@69:     ft.reset()
jpayne@69:     ft.speed(0)
jpayne@69:     ft.ht()
jpayne@69:     ft.getscreen().tracer(1,0)
jpayne@69: 
jpayne@69:     ta=clock()
jpayne@69:     ft.color("black", "blue")
jpayne@69:     ft.begin_fill()
jpayne@69:     ft.fractalgon(3, 250, 4, 1)
jpayne@69:     ft.end_fill()
jpayne@69:     ft.begin_fill()
jpayne@69:     ft.color("red")
jpayne@69:     ft.fractalgon(3, 200, 4, -1)
jpayne@69:     ft.end_fill()
jpayne@69:     tb=clock()
jpayne@69:     res +=  "Koch: %.2fsec." % (tb-ta)
jpayne@69:     return res
jpayne@69: 
jpayne@69: if __name__  == '__main__':
jpayne@69:     msg = main()
jpayne@69:     print(msg)
jpayne@69:     mainloop()