Initial import

bernoulli.py

+'''
+This python script should demonstrate
+that the logarithmic spiral has
+(multiple, discrete) scale invariances.
+Also visible in animation:
+Scale + Rotation = continuous symmetry
+Since theta only covers a finite range,
+the symmetry is 'broken' (especially
+visbible at the end of the animation cycle)
+'''
+#module load psi-python27/4.4.0
+
+import numpy as np
+import matplotlib.pyplot as plt
+from matplotlib.animation import FuncAnimation 
+#Scale paramerts to cover in animtion
+beta = np.linspace(0.0, 2*np.pi, 100)
+#angular array
+theta = np.linspace(-6*np.pi, 6*np.pi, 800)
+#Plot settings
+fig = plt.figure(figsize=(6,6))
+# Next two lines (values) from https://de.wikipedia.org/wiki/Datei:Logarithmic_Spiral_Pylab.svg
+ax = plt.axes([0.1, 0.1, 0.8, 0.8], polar = True)
+kappa = np.log(1.19)
+#Reference r(theta)
+r = np.exp(kappa*theta)
+#Plot reference Spiral
+ax.plot(theta, r)
+line, = ax.plot([],[])
+
+#Plot scaled spirals
+def update(b):
+    r_s = np.exp(b)*r #scales reference spiral
+    line.set_xdata(theta) #update data in plot (theta unchanged)
+    line.set_ydata(r_s)   #      "
+    return line,
+
+#Define and run animation
+a = FuncAnimation(fig, update, frames=beta, blit=True)
+plt.show()
+