Page - 73 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python 3.6, Volume Second Edition

3.3 Branching(if,elifandelse) 73 d = 1 # step length (e.g., in meter) x = np.zeros(N+1) # x coordinates y = np.zeros(N+1) # y coordinates x[0] = 0; y[0] = 0 # set initial position for i in range(0, N, 1): r = random.random() # random number in [0,1) if 0 <= r < 0.25: # move north y[i+1] = y[i] + d x[i+1] = x[i] elif 0.25 <= r < 0.5: # move east x[i+1] = x[i] + d y[i+1] = y[i] elif 0.5 <= r < 0.75: # move south y[i+1] = y[i] - d x[i+1] = x[i] else: # move west x[i+1] = x[i] - d y[i+1] = y[i] # plot path (mark start and stop with blue o and *, respectively) plt.plot(x, y, ’r--’, x[0], y[0], ’bo’, x[-1], y[-1], ’b*’) plt.xlabel(’x’); plt.ylabel(’y’) plt.show() Here, the initial position is explicitly set, even if x[0] and y[0] are known to be zero already. We do this, since the initial position is important, and by setting it explicitly, it is clearlynotaccidentalwhat thestartingposition is.Note that if a step is taken in thex-direction, they-coordinate is unchanged,andviceversa. Executing the program produces the plot seen in Fig.3.2, where the initial and final positions are marked in blue with a circle and a star, respectively. Remember that pseudo-randomnumbersare involvedhere, meaning that two consecutive runs will generallyproducetotallydifferentpaths. Fig. 3.2 Onerealizationofarandomwalk(N-E-S-W)witha1000steps. Initialandfinalpositions are marked inblue witha circle and a star, respectively