import numpy as np
import matplotlib.pyplot as plt

# Random Walk
def randomWalks(n=100, nsteps=10000):
    plt.figure(figsize=(16,10))
    for i in range(n):
        steps = np.random.choice([-1, 1], nsteps)
        positions = np.cumsum(steps)
        plt.plot(positions)
    plt.show()
randomWalks()

# 2D Random Walk
def randomWalks2D(nsteps=25000):
    x, y = np.zeros(nsteps), np.zeros(nsteps)

    for step in range(1, nsteps):
        val = random.randint(1, 4)
        if val == 1:
            x[step], y[step] = x[step - 1] + 5, y[step - 1]
        elif val == 2:
            x[step], y[step] = x[step - 1] - 5, y[step - 1]
        elif val == 3:
            x[step], y[step] = x[step - 1], y[step - 1] + 5
        else:
            x[step], y[step] = x[step - 1], y[step - 1] - 5

    plt.figure(figsize=(16,10))
    plt.title("2D Random Walk ($n = " + str(nsteps) + "$ steps)")
    plt.plot(x, y)
    plt.show()

def main():
    randomWalks2D()

if __name__ == '__main__': main()