/usr/lib/python3.5/turtledemo/fractalcurves.py is in python3.5-examples 3.5.3-1+deb9u1.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 | #! /usr/bin/python3.5
""" turtle-example-suite:
tdemo_fractalCurves.py
This program draws two fractal-curve-designs:
(1) A hilbert curve (in a box)
(2) A combination of Koch-curves.
The CurvesTurtle class and the fractal-curve-
methods are taken from the PythonCard example
scripts for turtle-graphics.
"""
from turtle import *
from time import sleep, clock
class CurvesTurtle(Pen):
# example derived from
# Turtle Geometry: The Computer as a Medium for Exploring Mathematics
# by Harold Abelson and Andrea diSessa
# p. 96-98
def hilbert(self, size, level, parity):
if level == 0:
return
# rotate and draw first subcurve with opposite parity to big curve
self.left(parity * 90)
self.hilbert(size, level - 1, -parity)
# interface to and draw second subcurve with same parity as big curve
self.forward(size)
self.right(parity * 90)
self.hilbert(size, level - 1, parity)
# third subcurve
self.forward(size)
self.hilbert(size, level - 1, parity)
# fourth subcurve
self.right(parity * 90)
self.forward(size)
self.hilbert(size, level - 1, -parity)
# a final turn is needed to make the turtle
# end up facing outward from the large square
self.left(parity * 90)
# Visual Modeling with Logo: A Structural Approach to Seeing
# by James Clayson
# Koch curve, after Helge von Koch who introduced this geometric figure in 1904
# p. 146
def fractalgon(self, n, rad, lev, dir):
import math
# if dir = 1 turn outward
# if dir = -1 turn inward
edge = 2 * rad * math.sin(math.pi / n)
self.pu()
self.fd(rad)
self.pd()
self.rt(180 - (90 * (n - 2) / n))
for i in range(n):
self.fractal(edge, lev, dir)
self.rt(360 / n)
self.lt(180 - (90 * (n - 2) / n))
self.pu()
self.bk(rad)
self.pd()
# p. 146
def fractal(self, dist, depth, dir):
if depth < 1:
self.fd(dist)
return
self.fractal(dist / 3, depth - 1, dir)
self.lt(60 * dir)
self.fractal(dist / 3, depth - 1, dir)
self.rt(120 * dir)
self.fractal(dist / 3, depth - 1, dir)
self.lt(60 * dir)
self.fractal(dist / 3, depth - 1, dir)
def main():
ft = CurvesTurtle()
ft.reset()
ft.speed(0)
ft.ht()
ft.getscreen().tracer(1,0)
ft.pu()
size = 6
ft.setpos(-33*size, -32*size)
ft.pd()
ta=clock()
ft.fillcolor("red")
ft.begin_fill()
ft.fd(size)
ft.hilbert(size, 6, 1)
# frame
ft.fd(size)
for i in range(3):
ft.lt(90)
ft.fd(size*(64+i%2))
ft.pu()
for i in range(2):
ft.fd(size)
ft.rt(90)
ft.pd()
for i in range(4):
ft.fd(size*(66+i%2))
ft.rt(90)
ft.end_fill()
tb=clock()
res = "Hilbert: %.2fsec. " % (tb-ta)
sleep(3)
ft.reset()
ft.speed(0)
ft.ht()
ft.getscreen().tracer(1,0)
ta=clock()
ft.color("black", "blue")
ft.begin_fill()
ft.fractalgon(3, 250, 4, 1)
ft.end_fill()
ft.begin_fill()
ft.color("red")
ft.fractalgon(3, 200, 4, -1)
ft.end_fill()
tb=clock()
res += "Koch: %.2fsec." % (tb-ta)
return res
if __name__ == '__main__':
msg = main()
print(msg)
mainloop()
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