rand_walk_2d.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "79165627-749a-418c-8fae-10f7cd17cbed",
   "metadata": {},
   "source": [
    "# random walk 2-d"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab3f4353-3a05-434d-a5d7-e1cb15a5db63",
   "metadata": {},
   "source": [
    "## mean distance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3300ca43-c50e-49ec-b170-c9304f67f56d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import random as rnd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "Nrep = 50\n",
    "Nstep = 101\n",
    "\n",
    "mean_r = [0.0] * Nstep\n",
    "\n",
    "# simulate random walks\n",
    "for j in range(Nrep):\n",
    "    x = 0.0\n",
    "    y = 0.0\n",
    "    for i in range(Nstep):\n",
    "        # random step: one of four directions (N, S, E, W)\n",
    "        direction = rnd.randint(0, 3)\n",
    "        if direction == 0:\n",
    "            x += 1\n",
    "        elif direction == 1:\n",
    "            x -= 1\n",
    "        elif direction == 2:\n",
    "            y += 1\n",
    "        else:\n",
    "            y -= 1\n",
    "\n",
    "        r2 = x*x + y*y\n",
    "        mean_r[i] += r2**0.5      # accumulate distance\n",
    "\n",
    "# average over repetitions\n",
    "for i in range(Nstep):\n",
    "    mean_r[i] /= Nrep\n",
    "\n",
    "# Plot results\n",
    "plt.figure(figsize=(8,5))\n",
    "plt.plot(mean_r)\n",
    "plt.xlabel('steps')\n",
    "plt.ylabel('mean distance')\n",
    "plt.grid(True)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3c72c6f-d1b3-42b7-9b6c-f06c16f2a661",
   "metadata": {},
   "source": [
    "## assignment 3\n",
    "1. Use above code to complete following plot.\n",
    "2. Explain the influence of `Nrep` on the value of `mean distance`.\n",
    "3. Cite a reference about it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e47ce471-6ce8-4299-abcd-821b1232e4ac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# mean distance for Nrep = 50\n",
    "sx_050 = []\n",
    "\n",
    "# mean distance for Nrep = 100\n",
    "sx_100 = []\n",
    "\n",
    "# mean distance for Nrep = 200\n",
    "sx_200 = []\n",
    "\n",
    "# mean distance for Nrep = 400\n",
    "sx_400 = []\n",
    "\n",
    "# mean distance for Nrep = 800\n",
    "sx_800 = []\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "plt.xlabel('steps')\n",
    "plt.ylabel('mean distance')\n",
    "plt.grid()\n",
    "plt.plot(sx_050, label='Nrep=050')\n",
    "plt.plot(sx_100, label='Nrep=100')\n",
    "plt.plot(sx_200, label='Nrep=200')\n",
    "plt.plot(sx_400, label='Nrep=400')\n",
    "plt.plot(sx_800, label='Nrep=800')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38daa23d-f3d5-4231-ba8a-cedd4e7b7f38",
   "metadata": {},
   "source": [
    "## mean squared distance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "80a900d4-5843-4f78-a5bc-738d01b10e06",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import random as rnd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "Nrep = 50\n",
    "Nstep = 101\n",
    "\n",
    "mean_r2 = [0.0] * Nstep\n",
    "\n",
    "# simulate random walks\n",
    "for j in range(Nrep):\n",
    "    x = 0.0\n",
    "    y = 0.0\n",
    "    for i in range(Nstep):\n",
    "        # random step: one of four directions (N, S, E, W)\n",
    "        direction = rnd.randint(0, 3)\n",
    "        if direction == 0:\n",
    "            x += 1\n",
    "        elif direction == 1:\n",
    "            x -= 1\n",
    "        elif direction == 2:\n",
    "            y += 1\n",
    "        else:\n",
    "            y -= 1\n",
    "\n",
    "        r2 = x*x + y*y\n",
    "        mean_r2[i] += r2      # accumulate squared distance\n",
    "\n",
    "# average over repetitions\n",
    "for i in range(Nstep):\n",
    "    mean_r2[i] /= Nrep\n",
    "\n",
    "# Plot results\n",
    "plt.figure(figsize=(8,5))\n",
    "plt.plot(mean_r2)\n",
    "plt.xlabel('steps')\n",
    "plt.ylabel('mean distance')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59e98db3-fc43-437a-8c3c-58a0fd4cbbaf",
   "metadata": {},
   "source": [
    "## assignment 4\n",
    "1. Use above code to complete following plot.\n",
    "2. Explain the influence of `Nrep` on the value of `mean squared distance`.\n",
    "3. Cite a reference about it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ac023e13-82c0-4d81-9fe2-4bf6d9e6e332",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# mean squared distance for Nrep = 50\n",
    "sx2_050 = []\n",
    "\n",
    "# mean squared distance for Nrep = 100\n",
    "sx2_100 = []\n",
    "\n",
    "# mean squared distance for Nrep = 200\n",
    "sx2_200 = []\n",
    "\n",
    "# mean squared distance for Nrep = 400\n",
    "sx2_400 = []\n",
    "\n",
    "# mean squared distance for Nrep = 800\n",
    "sx2_800 = []\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "plt.xlabel('steps')\n",
    "plt.ylabel('mean squared distance')\n",
    "plt.grid()\n",
    "plt.plot(sx2_050, label='Nrep=050')\n",
    "plt.plot(sx2_100, label='Nrep=100')\n",
    "plt.plot(sx2_200, label='Nrep=200')\n",
    "plt.plot(sx2_400, label='Nrep=400')\n",
    "plt.plot(sx2_800, label='Nrep=800')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ce73218f-9212-4c11-a137-9c2dcf2bc3a5",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.12.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}