Added a Lorenz Attractor example for mplot3d.

WeatherGod · WeatherGod · commit 3a68d1adacac · 2011-09-22T15:28:41.000-05:00
Why? Because butterflies are awesome!
diff --git a/examples/mplot3d/lorenz_attractor.py b/examples/mplot3d/lorenz_attractor.py
@@ -0,0 +1,49 @@
+# 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) :
+    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
+
+# Need one more for the initial values
+xs = np.empty((stepCnt + 1,))
+ys = np.empty((stepCnt + 1,))
+zs = np.empty((stepCnt + 1,))
+
+# Setting initial values
+xs[0], ys[0], zs[0] = (0., 1., 1.05)
+
+# Stepping through "time".
+for i in xrange(stepCnt) :
+    # Derivatives of the X, Y, Z state
+    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)
+
+fig = plt.figure()
+ax = fig.gca(projection='3d')
+
+ax.plot(xs, ys, zs)
+ax.set_xlabel("X Axis")
+ax.set_ylabel("Y Axis")
+ax.set_zlabel("Z Axis")
+
+plt.show()
+
