# A realization of 1D Fractional Brownian motion with time step dt = .5  import matplotlib.pyplot as pl import numpy as np  t0 = 0.0 dt = 0.5 t_final = 1000.0 T = np.arange(t0, t_final+dt, dt) H = .75 ax = pl.figure().add_subplot(111) ax.set_xlabel('t') ax.set_ylabel('X')  np.random.seed(2)  Gamma = [[0.0 for _ in T] for _ in T] for i in range(len(T)):     for j in range(len(T)):         Gamma[i][j] = 0.5*(T[i]**(2*H) + T[j]**(2*H) - abs(T[j]-T[i])**(2*H))  eigens, P = np.linalg.eig(Gamma)  Lambda = [[0.0 for _ in T] for _ in T] for i in range(len(Lambda)):     Lambda[i][i] = eigens[i]**0.5  Sigma = np.matmul(np.matmul(P, Lambda), np.matrix.transpose(P))  path = [np.random.normal(0, 1) for _ in T]  path = np.matmul(Sigma, path)  for i in range(1, len(T)):     ax.plot([T[i-1], T[i]], [path[i-1], path[i]], 'k-', linewidth=0.5)  pl.show()