summaryrefslogtreecommitdiffstats
path: root/Lib/turtledemo/fractalcurves.py
blob: c49f8b88ea128d5e8fd12ba1ea65dcc278b78d07 (plain)
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/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()