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#!/usr/bin/env python3
""" 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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