2次元のランダムウォーク（python）

import numpy as np
import matplotlib.pyplot as plt

time = 2000

state = np.zeros(2)
orbit = np.zeros(2)
for t in range(time):
    speed =  1
    randomvec = np.random.random(2) - 0.5
    randomvec *= speed/np.linalg.norm(randomvec)
    state += randomvec
    orbit = np.vstack([orbit, state])

orbit = orbit.T

plt.scatter(0, 0, color="r")
plt.plot(*orbit, lw=0.5)
plt.scatter(*state, color="r")
plt.axis("equal")
plt.show()