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
|
"""
==============
Filled polygon
==============
`~.Axes.fill()` draws a filled polygon based on lists of point
coordinates *x*, *y*.
This example uses the `Koch snowflake`_ as an example polygon.
.. _Koch snowflake: https://en.wikipedia.org/wiki/Koch_snowflake
"""
import matplotlib.pyplot as plt
import numpy as np
def koch_snowflake(order, scale=10):
"""
Return two lists x, y of point coordinates of the Koch snowflake.
Parameters
----------
order : int
The recursion depth.
scale : float
The extent of the snowflake (edge length of the base triangle).
"""
def _koch_snowflake_complex(order):
if order == 0:
# initial triangle
angles = np.array([0, 120, 240]) + 90
return scale / np.sqrt(3) * np.exp(np.deg2rad(angles) * 1j)
else:
ZR = 0.5 - 0.5j * np.sqrt(3) / 3
p1 = _koch_snowflake_complex(order - 1) # start points
p2 = np.roll(p1, shift=-1) # end points
dp = p2 - p1 # connection vectors
new_points = np.empty(len(p1) * 4, dtype=np.complex128)
new_points[::4] = p1
new_points[1::4] = p1 + dp / 3
new_points[2::4] = p1 + dp * ZR
new_points[3::4] = p1 + dp / 3 * 2
return new_points
points = _koch_snowflake_complex(order)
x, y = points.real, points.imag
return x, y
# %%
# Basic usage:
x, y = koch_snowflake(order=5)
plt.figure(figsize=(8, 8))
plt.axis('equal')
plt.fill(x, y)
plt.show()
# %%
# Use keyword arguments *facecolor* and *edgecolor* to modify the colors
# of the polygon. Since the *linewidth* of the edge is 0 in the default
# Matplotlib style, we have to set it as well for the edge to become visible.
x, y = koch_snowflake(order=2)
fig, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(9, 3),
subplot_kw={'aspect': 'equal'})
ax1.fill(x, y)
ax2.fill(x, y, facecolor='lightsalmon', edgecolor='orangered', linewidth=3)
ax3.fill(x, y, facecolor='none', edgecolor='purple', linewidth=3)
plt.show()
# %%
#
# .. admonition:: References
#
# The use of the following functions, methods, classes and modules is shown
# in this example:
#
# - `matplotlib.axes.Axes.fill` / `matplotlib.pyplot.fill`
# - `matplotlib.axes.Axes.axis` / `matplotlib.pyplot.axis`
#
# .. tags::
#
# styling: shape
# level: beginner
# purpose: showcase
|
