def simulate_escape_with_trajectory(M):\ box_length = 50\ step = 2\ escapes = 0\ last_trajectory = []\ for i in range(M):\ x_corr, y_corr = box_length // 2, box_length // 2\ trajectory = [(x_corr, y_corr)] #Store initial position\ \ for t in range(600):\ u = np.random.uniform(low = 0, high = 1)\ \ if u < 0.25:\ x_corr -= step\ elif u < 0.5:\ x_corr += step\ elif u < 0.75:\ y_corr += step\ else:\ y_corr -= step\ \ x_corr = max(0, min(box_length, x_corr))\ y_corr = max(0, min(box_length, y_corr))\ \ trajectory.append((x_corr, y_corr)) #Store current position\ \ if y_corr >= box_length and 20 <= x_corr <= 30:\ escapes += 1\ #print("escaped!", i)\ last_trajectory = trajectory #Update last trajectory\ break\ probability = escapes / M\ return escapes, probability, last_trajectory\ \ attempts = np.linspace(10, 1000, 19)\ data = {"attempts": [], "escapes": [], "probability": []}\ for M in attempts:\ escapes, probability, last_trajectory = simulate_escape_with_trajectory(M)\ data["attempts"].append(M)\ data["escapes"].append(escapes)\ data["probability"].append(probability)