Exploring Chaotic Attractors - The Arneodo Attractor
Posted: Fri Aug 14, 2020 1:56 pm- Code: Select all
#!/usr/bin/env python
# coding: utf-8
get_ipython().magic(u'matplotlib inline')
import numpy as np
import matplotlib.pyplot as plt
# This import registers the 3D projection, but is otherwise unused.
from mpl_toolkits.mplot3d import Axes3D # noqa: F401 unused import
def arneodo(x, y, z, a=-5.5, b=3.5, c=-1):
'''
Given:
x, y, z: a point of interest in three dimensional space
s, r, b: parameters defining the lorenz attractor
Returns:
x_dot, y_dot, z_dot: values of the lorenz attractor's partial
derivatives at the point x, y, z
'''
x_dot = y
y_dot = z
z_dot = -a*x-b*y-z+c*(x**3)
return x_dot, y_dot, z_dot
dt = 0.01
num_steps = 7000
# Need one more for the initial values
xs = np.empty(num_steps + 1)
ys = np.empty(num_steps + 1)
zs = np.empty(num_steps + 1)
# Set initial values
xs[0], ys[0], zs[0] = (0.1, 0, 0.1)
# Step through "time", calculating the partial derivatives at the current point
# and using them to estimate the next point
for i in range(num_steps):
x_dot, y_dot, z_dot = arneodo(xs[i], ys[i], zs[i])
xs[i + 1] = xs[i] + (x_dot * dt)
ys[i + 1] = ys[i] + (y_dot * dt)
zs[i + 1] = zs[i] + (z_dot * dt)
# Plot
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot(xs, ys, zs, lw=0.5)
ax.set_xlabel("X Axis")
ax.set_ylabel("Y Axis")
ax.set_zlabel("Z Axis")
ax.set_title("Arneodo Plot")
plt.show()
plt.plot(xs)
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