def mk_caracoles():
A = np.array([[[ 0.5 ,-0.2 ],[ 0.2 , 0.6 ]],
[[ 0.75 , 0.5 ],[-0.6 , 0.4 ]]])
b = np.array([[-1.0 ,-2.0 ],
[-1.0 , 2.0 ]])
next_transform = rv(name='Caracoles',
values=((0,1),(0.42,0.58)))
return ChaosGame(A,b,next_transform)
def mk_sierpinski():
A = np.array([[[ 0.50, 0.00],[ 0.00, 0.50]],
[[ 0.50, 0.00],[ 0.00, 0.50]],
[[ 0.50, 0.00],[ 0.00, 0.50]]])
b = np.array([[ 0.00, 0.00],
[ 0.50, 0.00],
[ 0.25, 0.25]])
next_transform = rv(name='Sierpinski',values=((0,1,2),(0.33,0.33,0.33)))
return ChaosGame(A,b,next_transform)
def mk_cristales():
A = np.array([[[ 0.5 , 0.0 ],[ 0.0 ,-0.5 ]],
[[ 0.5 , 0.0 ],[ 0.0 ,-0.5 ]],
[[ 0.5 , 0.0 ],[ 0.0 ,-0.5 ]]])
b = np.array([[ 0.0 , 0.0 ],
[ 0.5 , 0.0 ],
[ 0.25 , 0.5 ]])
next_transform = rv(name='Cristales',
values=((0,1,2),(0.333,0.333,0.334)))
return ChaosGame(A,b,next_transform)
def mk_koch():
A = np.array([[[ 0.33, 0.00],[ 0.00, 0.33]],
[[ 0.33, 0.00],[ 0.00, 0.33]],
[[ 0.16,-0.28],[ 0.28, 0.16]],
[[-0.16, 0.28],[ 0.28, 0.16]]])
b = np.array([[ 0.00, 0.00],
[ 0.66, 0.00],
[ 0.33, 0.00],
[ 0.66, 0.00]])
next_transform = rv(name='Fern',values=((0,1,2,3),(0.25,0.25,0.25,0.25)))
return ChaosGame(A,b,next_transform)
def mk_fern():
A = np.array([[[ 0.00, 0.00],[ 0.00, 0.16]],
[[ 0.85, 0.04],[-0.04, 0.85]],
[[ 0.20,-0.26],[ 0.23, 0.22]],
[[-0.15, 0.28],[ 0.26, 0.24]]])
b = np.array([[ 0.00, 0.00],
[ 0.00, 1.60],
[ 0.00, 1.60],
[ 0.00, 0.44]])
next_transform = rv(name='Fern',values=((0,1,2,3),(0.01,0.85,0.07,0.07)))
return ChaosGame(A,b,next_transform)
def mk_bronchi():
A = np.array([[[ 0.05, 0.00],[ 0.00, 0.50]],
[[ 0.05, 0.00],[ 0.00,-0.50]],
[[ 0.00,-0.80],[ 0.60, 0.00]],
[[ 0.00, 0.80],[-0.65, 0.00]]])
b = np.array([[ 0.00, 0.00],
[ 0.00, 0.80],
[ 0.00, 0.80],
[ 0.00, 0.80]])
next_transform = rv(name='Bronchi',values=((0,1,2,3),(0.15,0.15,0.35,0.35)))
return ChaosGame(A,b,next_transform)
def mk_molinos():
A = np.array([[[ 0.02 , 0.0 ],[ 0.0 , 0.5 ]],
[[ 0.02 , 0.0 ],[ 0.0 ,-0.5 ]],
[[ 0.5303307,-0.5303307],[ 0.5303307, 0.5303307 ]],
[[ 0.0 , 0.5 ],[-0.5 , 0.0 ]]])
b = np.array([[ 0.0 , 0.0 ],
[ 0.0 , 0.5 ],
[ 0.0 , 1.0 ],
[ 0.0 , 1.2 ]])
next_transform = rv(name='Molinos',
values=((0,1,2,3),(0.145,0.145,0.426,0.284)))
return ChaosGame(A,b,next_transform)
def mk_hoja():
A = np.array([[[ 0.64987,-0.013 ],[ 0.013 , 0.64987]],
[[ 0.64948,-0.026 ],[ 0.026 , 0.64948]],
[[ 0.3182 ,-0.3182],[ 0.3182 , 0.3182 ]],
[[-0.3182 , 0.3182],[ 0.3182 , 0.3182 ]]])
b = np.array([[ 0.175, 0.00 ],
[ 0.165, 0.325],
[ 0.2 , 0.00 ],
[ 0.8 , 0.00 ]])
next_transform = rv(name='Helecho',
values=((0,1,2,3),(0.3333,0.3333,0.1667,0.1667)))
return ChaosGame(A,b,next_transform)
def mk_helecho():
A = np.array([[[ 0.00000, 0.0000],[ 0.00 , 0.17000]],
[[ 0.84962, 0.0255],[-0.0255 , 0.84962]],
[[-0.15540, 0.2350],[ 0.19583, 0.18648]],
[[ 0.1554 ,-0.235 ],[ 0.19583, 0.18648]]])
b = np.array([[ 0.00, 0.00],
[ 0.00, 3.00],
[ 0.00, 1.20],
[ 0.00, 3.00]])
next_transform = rv(name='Helecho',
values=((0,1,2,3),(0.0572,0.5724,0.1852,0.1852)))
return ChaosGame(A,b,next_transform)
def mk_vicsek():
A = np.array([[[ 0.333333, 0.0 ],[ 0.0 , 0.333333 ]],
[[ 0.333333, 0.0 ],[ 0.0 , 0.333333 ]],
[[ 0.333333, 0.0 ],[ 0.0 , 0.333333 ]],
[[ 0.333333, 0.0 ],[ 0.0 , 0.333333 ]],
[[ 0.333333, 0.0 ],[ 0.0 , 0.333333 ]]])
b = np.array([[ 0.0 , 0.0 ],
[ 2.0 , 0.0 ],
[ 1.0 , 1.0 ],
[ 0.0 , 2.0 ],
[ 2.0 , 2.0 ]])
next_transform = rv(name='Vicsek',
values=((0,1,2,3,4),(0.2,0.2,0.2,0.2,0.2)))
return ChaosGame(A,b,next_transform)
class Fern:
A = np.array([[[0.0, 0.0], [0.00, 0.16]], [[0.85, 0.04], [-0.04, 0.85]],
[[0.2, -0.26], [0.23, 0.22]], [[-0.15, 0.28], [0.26, 0.24]]])
b = np.array([[0.00, 0.00], [0.00, 1.60], [0.00, 1.60], [0.00, 0.44]])
#next_transform = rv(name='Fern',values=((0,1,2,3),(0.01,0.85,0.0,0.14)))
next_transform = rv(name='Fern',
values=((0, 1, 2, 3), (0.01, 0.85, 0.07, 0.07)))
def simplify_axes(self, ax):
ax.set_yticklabels([])
ax.set_xticklabels([])
ax.set_yticks([])
ax.set_xticks([])
ax.set_xlim(-2.3, 2.8)
ax.set_ylim(-0.1, 10.1)
def next_point(self, last_point):
transform = self.next_transform.rvs()
return np.dot(self.A[transform], last_point) + self.b[transform]
def plot(self):
current = np.array([0.0, 0.0])
fig = plt.figure()
ax = fig.add_subplot(111)
self.simplify_axes(ax)
# Don't plot the first few iterations.
for x in range(15):
current = self.next_point(current)
ax.plot(current[0], current[1], 'go', markersize=1)
xs, ys = [], []
line_fern, = ax.plot(xs, ys, 'go', markersize=1)
for x in range(60000):
current = self.next_point(current)
xs.append(current[0])
ys.append(current[1])
line_fern.set_data(xs, ys)
plt.show()
def mk_arbol():
A = np.array([[[ 0.05 , 0.00 ],[ 0.00 , 0.6 ]],
[[ 0.05 , 0.00 ],[ 0.00 ,-0.5 ]],
[[ 0.46 ,-0.32 ],[ 0.39 , 0.38 ]],
[[ 0.47 ,-0.15 ],[ 0.17 , 0.42 ]],
[[ 0.43 , 0.28 ],[-0.25 , 0.45 ]],
[[ 0.42 , 0.26 ],[-0.35 , 0.31 ]]])
b = np.array([[ 0.00 , 0.00 ],
[ 0.00 , 1.00 ],
[ 0.00 , 0.60 ],
[ 0.00 , 1.10 ],
[ 0.00 , 1.00 ],
[ 0.00 , 0.70 ]])
next_transform = rv(name='Arbol',
values=((0,1,2,3,4,5),(0.1,0.1,0.2,0.2,0.2,0.2)))
return ChaosGame(A,b,next_transform)
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import rv_discrete as rv
A = np.array([[[0.0,0.0],[0.00,0.16]],
[[0.85,0.04],[-0.04,0.85]],
[[0.2,-0.26],[0.23,0.22]],
[[-0.15,0.28],[0.26,0.24]]])
b = np.array([[0.00,0.00],
[0.00,1.60],
[0.00,1.60],
[0.00,0.44]])
#next_transform = rv(name='Fern',values=((0,1,2,3),(0.01,0.85,0.0,0.14)))
next_transform = rv(name='Fern',values=((0,1,2,3),(0.01,0.85,0.07,0.07)))
def simplify_axes(ax):
ax.set_yticklabels([])
ax.set_xticklabels([])
ax.set_yticks([])
ax.set_xticks([])
ax.set_xlim(-2.3,2.8)
ax.set_ylim(-0.1,10.1)
def next_point(last_point):
transform = next_transform.rvs()
return np.dot(A[transform],last_point) + b[transform]
def main():
"""
Animated construction of the Sierpinski gasket using the chaos game.
"""
import random
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.animation as animation
from scipy.stats import rv_discrete as rv
A = np.array([[[0.0, 0.0], [0.00, 0.16]], [[0.85, 0.04], [-0.04, 0.85]],
[[0.2, -0.26], [0.23, 0.22]], [[-0.15, 0.28], [0.26, 0.24]]])
b = np.array([[0.00, 0.00], [0.00, 1.60], [0.00, 1.60], [0.00, 0.44]])
next_transform = rv(name='Fern',
values=((0, 1, 2, 3), (0.01, 0.85, 0.07, 0.07)))
xs, ys = [], []
def simplify_axes(ax):
ax.set_yticklabels([])
ax.set_xticklabels([])
ax.set_yticks([])
ax.set_xticks([])
ax.set_xlim(-2.3, 2.8)
ax.set_ylim(-0.1, 10.1)
# int(last_point):
# transform = next_transform.rvs()
