# A realization of 1D Bessel process with n = 3, 10, 20 and time step dt = .0001  import matplotlib.pyplot as pl import numpy as np import matplotlib.patches as mpatches  t0 = 0.0 dt = 0.0001 t_final = 2.0 T = np.arange(t0, t_final, dt) ax = pl.figure().add_subplot(111) ax.set_xlabel('t') ax.set_ylabel('X')  def realize(ax, n, color):     B = [0.0 for _ in range(n)]     np.random.seed(1)      for t in T:         old_value = np.sqrt(sum([x*x for x in B]))         for i in range(len(B)):             B[i] += np.random.normal(0, dt)         new_value = np.sqrt(sum([x*x for x in B]))         ax.plot([t, t+dt], [old_value, new_value], color, linewidth=0.5)  realize(ax, 3, 'b-') realize(ax, 10, 'r-') realize(ax, 20, 'g-')  bluePatch = mpatches.Patch(color='blue', label='$n = 3$') redPatch = mpatches.Patch(color='red', label='$n = 10$') greenPatch = mpatches.Patch(color='green', label='$n = 20$') pl.legend(handles = [bluePatch, redPatch, greenPatch], loc=2)  pl.show()