mirror of https://github.com/python/cpython
136 lines
3.3 KiB
Python
136 lines
3.3 KiB
Python
"""turtledemo/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, perf_counter as 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()
|