random_walk1.py

# -*- coding: utf-8 -*-
"""Random Walk1.ipynb

Automatically generated by Colaboratory.

Original file is located at
    https://colab.research.google.com/drive/1ORkwEqoi33Qt9Bh0UGVNZhrxNBbkpSos
"""

#1D

import matplotlib.pyplot as plt
import random

def random_walk_1d(steps):
    walk = [0]  # start from position 0
    for i in range(steps):
        step = -1 if random.randint(0, 1) == 0 else 1  # either step -1 or 1
        walk.append(walk[-1] + step)  # add the step to the last position
    return walk

steps = 1000  # for example, a walk of 1000 steps
walk = random_walk_1d(steps)

plt.figure(figsize=(10,6))
plt.plot(walk)
plt.title('1D Random Walk')
plt.xlabel('Steps')
plt.ylabel('Position')
plt.show()

def random_walk_2d(steps):
    x, y = [0], [0]  # start from position (0, 0)
    for _ in range(steps):
        dx = random.choice([-1, 0, 1])
        dy = random.choice([-1, 0, 1])
        x.append(x[-1] + dx)
        y.append(y[-1] + dy)
    return x, y

x, y = random_walk_2d(1000)

plt.figure(figsize=(10,6))
plt.plot(x, y)
plt.title('2D Random Walk')
plt.xlabel('X Position')
plt.ylabel('Y Position')
plt.axis('equal')  # make the axes equal, so the walk appears unbiased
plt.show()

import matplotlib.pyplot as plt
import random
from mpl_toolkits.mplot3d import Axes3D

def random_walk_3d(steps):
    x, y, z = [0], [0], [0]  # start from position (0, 0, 0)
    for _ in range(steps):
        dx, dy, dz = random.choice(
            [(1, 0, 0), (-1, 0, 0), (0, 1, 0), (0, -1, 0), (0, 0, 1), (0, 0, -1), (0, 0, 0)]
        )
        x.append(x[-1] + dx)
        y.append(y[-1] + dy)
        z.append(z[-1] + dz)
    return x, y, z

x, y, z = random_walk_3d(1000)

fig = plt.figure(figsize=(10,6))
ax = fig.add_subplot(111, projection='3d')
ax.plot(x, y, z)
ax.set_title('3D Random Walk')
ax.set_xlabel('X Position')
ax.set_ylabel('Y Position')
ax.set_zlabel('Z Position')
plt.show()