chapter_2/random_walk_2D.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# https://www.codingem.com/random-walk-in-python/\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import random\n",
    "\n",
    "def randomwalk2D(n):\n",
    "    # [0, 0, 0, ... ,0]\n",
    "    x = np.zeros(n)\n",
    "    y = np.zeros(n)\n",
    "\n",
    "    # jodi sob dike jawar probablity same hoy\n",
    "    directions = [\"UP\", \"DOWN\", \"LEFT\", \"RIGHT\"]\n",
    "    for i in range(1, n):\n",
    "        # Pick a direction at random\n",
    "        step = random.choice(directions)\n",
    "        \n",
    "        # Move the object according to the direction\n",
    "        if step == \"RIGHT\":\n",
    "            x[i] = x[i - 1] + 1\n",
    "            y[i] = y[i - 1]\n",
    "        elif step == \"LEFT\":\n",
    "            x[i] = x[i - 1] - 1\n",
    "            y[i] = y[i - 1]\n",
    "        elif step == \"UP\":\n",
    "            x[i] = x[i - 1]\n",
    "            y[i] = y[i - 1] + 1\n",
    "        elif step == \"DOWN\":\n",
    "            x[i] = x[i - 1]\n",
    "            y[i] = y[i - 1] - 1\n",
    "    \n",
    "    # Return all the x and y positions of the object\n",
    "    return x, y\n",
    "\n",
    "x_data, y_data = randomwalk2D(1000)\n",
    "\n",
    "plt.title(\"2D Random Walk in Python\")\n",
    "plt.plot(x_data, y_data)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.0"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}