Cleaning up example mplot3d/lorenz_attractor.py.

matplotlib · WeatherGod · Apr 19, 2016 · Apr 2, 2016 · Apr 2, 2016 · Apr 3, 2016
commit dcc0d7cc3e8b8185398f2db640c6eec8bc3b6fce
diff --git a/examples/mplot3d/lorenz_attractor.py b/examples/mplot3d/lorenz_attractor.py
@@ -1,42 +1,54 @@
-# Plot of the Lorenz Attractor based on Edward Lorenz's 1963 "Deterministic
-# Nonperiodic Flow" publication.
-# http://journals.ametsoc.org/doi/abs/10.1175/1520-0469%281963%29020%3C0130%3ADNF%3E2.0.CO%3B2
-#
-# Note: Because this is a simple non-linear ODE, it would be more easily
-#       done using SciPy's ode solver, but this approach depends only
-#       upon NumPy.
+'''
+Plot of the Lorenz Attractor based on Edward Lorenz's 1963 "Deterministic
+Nonperiodic Flow" publication.
+http://journals.ametsoc.org/doi/abs/10.1175/1520-0469%281963%29020%3C0130%3ADNF%3E2.0.CO%3B2
+
+Note: Because this is a simple non-linear ODE, it would be more easily
+      done using SciPy's ode solver, but this approach depends only
+      upon NumPy.
+'''

 import numpy as np
 import matplotlib.pyplot as plt
 from mpl_toolkits.mplot3d import Axes3D


 def lorenz(x, y, z, s=10, r=28, b=2.667):
+    '''
+    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 = s*(y - x)
    y_dot = r*x - y - x*z
    z_dot = x*y - b*z
    return x_dot, y_dot, z_dot


 dt = 0.01
-stepCnt = 10000
+num_steps = 10000

 # Need one more for the initial values
-xs = np.empty((stepCnt + 1,))
-ys = np.empty((stepCnt + 1,))
-zs = np.empty((stepCnt + 1,))
+xs = np.empty((num_steps + 1,))
+ys = np.empty((num_steps + 1,))
+zs = np.empty((num_steps + 1,))

-# Setting initial values
+# Set initial values
 xs[0], ys[0], zs[0] = (0., 1., 1.05)

-# Stepping through "time".
-for i in range(stepCnt):
-    # Derivatives of the X, Y, Z state
+# 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 = lorenz(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')