{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def random_coordinate(z):\n",
    "    x_arr = np.random.randint(-1,2,z)\n",
    "    y_arr = np.random.randint(-1,2,z)\n",
    "    steps = np.vstack((x_arr,y_arr))\n",
    "    steps = steps.T\n",
    "    random_coordinate = np.empty([z+1,2],dtype=int)\n",
    "    random_coordinate[0] = [0,0]\n",
    "    for i in range(0,z):\n",
    "        random_coordinate[i+1] = random_coordinate[i] + steps[i]\n",
    "    random_coordinate = random_coordinate.T\n",
    "    return random_coordinate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0, -1, -2, -2, -3, -3, -3, -4, -3, -2, -3],\n",
       "       [ 0, -1, -1,  0,  1,  2,  1,  0, -1, -2, -1]])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "random_coordinate(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def random_walk_final(z):\n",
    "    x = random_coordinate(z)\n",
    "    ax = plt.subplot()\n",
    "    out = ax.plot(x[0],x[1])\n",
    "    out = ax.plot([0],[0],marker = \"o\",color = 'green')\n",
    "    out = ax.plot(x[0,z],x[1,z],marker = 'o',color = 'red')\n",
    "    out = ax.plot([0,0],[x[1].min()-1,x[1].max()+1],color = 'black',lw = 0.5,ls = '--')\n",
    "    out = ax.plot([x[0].min()-1,x[0].max()+1],np.zeros_like([x[0].min()-1,x[0].max()+1]),color = 'black',lw = 0.5,ls = '--')\n",
    "    out = plt.xlim(x[0].min()-1,x[0].max()+1)\n",
    "    out = plt.ylim(x[1].min()-1,x[1].max()+1)\n",
    "    out = ax.get_xaxis().set_visible(False)\n",
    "    out = ax.get_yaxis().set_visible(False)\n",
    "    return out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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XtyNxjrDd6SYl8Vb1gw+Ajz7yOW516UJ/gOnTaQwTKmzZwoaG6Ghg4sSsj78O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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f9b3c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "random_walk_final(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def rand_walk_9_test2(y):\n",
    "    fig1,ax = plt.subplots(3,3,figsize=(12,6))\n",
    "    flag = 0\n",
    "    for i in range(0,3):\n",
    "        for j in range(0,3):\n",
    "            x = random_coordinate(y)\n",
    "            flag += 1\n",
    "            out = ax[i][j].get_xaxis().set_visible(False)\n",
    "            out = ax[i][j].get_yaxis().set_visible(False)\n",
    "            out = ax[i][j].set_title('Random Walk %d' %flag )\n",
    "            out = ax[i][j].plot(x[0],x[1])\n",
    "            out = ax[i][j].plot([0],[0],marker = \"o\",color = 'green')\n",
    "            out = ax[i][j].plot(x[0,y],x[1,y],marker = 'o',color = 'red')\n",
    "            out = ax[i][j].plot([0,0],[x[1].min()-1,x[1].max()+1],color = 'black',lw = 0.5,ls = '--')\n",
    "            out = ax[i][j].plot([x[0].min()-1,x[0].max()+1],np.zeros_like([x[0].min()-1,x[0].max()+1]),color = 'black',lw = 0.5,ls = '--')\n",
    "            out = plt.xlim(x[0].min()-1,x[0].max()+1)\n",
    "            out = plt.ylim(x[1].min()-1,x[1].max()+1)\n",
    "    return out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-3, 2)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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BFwObZd3fkrX8X4Edg9+H479ZfSu4PhpYDnwiuH43/ttP5rH3AhcEv08C/gGM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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f9bb0d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rand_walk_9_test2(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def rand_walk_9_test3(y):\n",
    "    fig1,ax = plt.subplots(3,3,figsize=(12,6))\n",
    "    flag = 0\n",
    "    for i in range(0,3):\n",
    "        for j in range(0,3):\n",
    "            flag += 1\n",
    "            out = ax[i][j].set_title('Random Walk %d' %flag )\n",
    "            out = random_walk_final(y)\n",
    "\n",
    "    return out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Sqailp6dHhw4dsvb+RKpdrsarC8FKpKIaV4KVSLXL5Xj1KliJVNRrcHBQg4OD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\nAAAAOO3/AwgwU+CAlKLsAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1101029d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rand_walk_9_test3(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'NoneType' object has no attribute 'plot'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-40-09fac5447519>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      9\u001b[0m         \u001b[0max\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_title\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Random Walk %d'\u001b[0m \u001b[0;34m%\u001b[0m\u001b[0mflag\u001b[0m \u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     10\u001b[0m         \u001b[0max\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mrandom_walk_final\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 11\u001b[0;31m         \u001b[0max\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     12\u001b[0m         \u001b[0max\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mmarker\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m\"o\"\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mcolor\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m'green'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     13\u001b[0m         \u001b[0max\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mmarker\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m'o'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mcolor\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m'red'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mAttributeError\u001b[0m: 'NoneType' object has no attribute 'plot'"
     ]
    },
    {
     "data": {
      "image/png": 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swui5UIDaGPnDONlZBS7LqQHUwlf+wOUIq0AS1QD6ZeQPbEQNAFhHNYC9YuTPPE2nUycC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\nUC1hFQCAav0/qV7bwutKWmwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110a10410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig1,ax = plt.subplots(3,3,figsize=(12,6))\n",
    "y = 10\n",
    "flag = 0\n",
    "for i in range(0,3):\n",
    "    for j in range(0,3):\n",
    "        flag += 1\n",
    "        ax[i][j].get_xaxis().set_visible(False)\n",
    "        ax[i][j].get_yaxis().set_visible(False)\n",
    "        ax[i][j].set_title('Random Walk %d' %flag )\n",
    "        ax[i][j] = random_walk_final(10)\n",
    "        ax[i][j].plot(x[0],x[1])\n",
    "        ax[i][j].plot([0],[0],marker = \"o\",color = 'green')\n",
    "        ax[i][j].plot(x[0,y],x[1,y],marker = 'o',color = 'red')\n",
    "        ax[i][j].plot([0,0],[x[1].min()-1,x[1].max()+1],color = 'black',lw = 0.5,ls = '--')\n",
    "        ax[i][j].plot([x[0].min()-1,x[0].max()+1],np.zeros_like([x[0].min()-1,x[0].max()+1]),color = 'black',lw = 0.5,ls = '--')\n",
    "        plt.xlim(x[0].min()-1,x[0].max()+1)\n",
    "        plt.ylim(x[1].min()-1,x[1].max()+1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4zjl3b3Dfu8BC59zC4PoHQTu6cyewd/Bp6xDgBGAvM9sI35luz9i2GnjJ/KH7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\nCqwiIiIiEmn/H5nZvVru4RgnAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c9c4ad0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "    y = 10\n",
    "    fig1,ax = plt.subplots(3,3,figsize=(12,6))\n",
    "    flag = 0\n",
    "    for i in range(0,3):\n",
    "        for j in range(0,3):\n",
    "            x = random_coordinate(y)\n",
    "            flag += 1\n",
    "            out = ax[i][j].get_xaxis().set_visible(False)\n",
    "            out = ax[i][j].get_yaxis().set_visible(False)\n",
    "            out = ax[i][j].set_title('Random Walk %d' %flag )\n",
    "            out = ax[i][j].plot(x[0],x[1])\n",
    "            out = ax[i][j].plot([0],[0],marker = \"o\",color = 'green')\n",
    "            out = ax[i][j].plot(x[0,y],x[1,y],marker = 'o',color = 'red')\n",
    "            out = ax[i][j].plot([0,0],[x[1].min()-1,x[1].max()+1],color = 'black',lw = 0.5,ls = '--')\n",
    "            out = ax[i][j].plot([x[0].min()-1,x[0].max()+1],np.zeros_like([x[0].min()-1,x[0].max()+1]),color = 'black',lw = 0.5,ls = '--')\n",
    "            out = plt.xlim(x[0].min()-1,x[0].max()+1)\n",
    "            out = plt.ylim(x[1].min()-1,x[1].max()+1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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S4nstpC0iStONj2dXsE8/Vd3CfvmF199SIqLeflut37gxL/e+ciXw11+sNU2bZtx/jRq8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\nECJCVxAEIYSI0BUEQQgh/w+JRFC0Nb6BigAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x103a775d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "random_walk_final(100000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "NoneType"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV0AAADtCAYAAAAcNaZ2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nGV2AgowuQEFGF6Cg/wAYi0IFuYvgeAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fdd4e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "type(random_walk_final(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV0AAADtCAYAAAAcNaZ2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAACiVJREFUeJzt3T+I3GUex/HvrIkEgpfrhFiY3Gg6tYmICpILhPMEWy1c\n8E9hIWeEtLK4YbEIQoQ7tVNX8AoVRasUKRzEu068E+yyTMLhIsEDyWGhYuaKicmazOw+s/vM8/v3\nelXH7hw8IHx4M/v8fumNRqMAoIyFqg8A0CVGF6AgowtQkNEFKMjoAhRkdAEK2rXZL3u9nvtkANsw\nGo16k36+6ehe+T/mPw3QOoPBII4cOVL1MWqh15u4txHh6wUgk8FgUPURGsHoAhRkdAEKMroABRld\ngIKMLpCFmwtpeptdCev1eiNXxgBm0+v1pt7TVboABRldgIKMLkBBRhegIKMLZOEx4DRGF8jC6KYx\nugAFGV2AgowuQEFGF6Agowtk4d0Labx7ASAz714AqAmjC1CQ0QUoyOgCFGR0gSw8BpzG6AJZGN00\nRhegIKMLUJDRBSjI6AIUZHSBLLx7IY13LwBk5t0LADVhdAEKMroABRldgIKMLpCFx4DTGF0gC6Ob\nxugCFGR0AQoyusCODM8PY/H4Yqx+vBqLxxdjeH5Y9ZFqzRNpwLYNzw/j2F+Oxdo9axH/iIgHI/r/\n7sfZ187GwQMHqz5eZTyRRjaXLkV8+23Vp6Aulk4vjQf35og4EBE3R6zdsxZLp5cqPll97drqA8vL\nyzf87MiRIxNfbjEYDCb+BdPn2/H5U6cG8fLLg/j554iHHoq4776IhYXmnN/n83/+888+j/j9hh+e\nj4gDEeux3ojzz/Pz0/h6gS19/33EiRMRn34a8eabEbffHvHMMxG//BLx1lsRhw5VfUKqcPFixOE/\nLcZ/Hvn7uHR/9VPEE/97It7967uVna1qvl5g286cibjrrog9eyK++iri6NGIfn88wI8/HvHAAxGv\nvjoeYLphNIp4772Iu++O+PN9K/GHf/Ujfrryy5/G3+munFip9Ix1pnSZ6Pq6PXp08ufW1lRvl1y8\nGPHccxFffx2xujr+iml4fhhLp5di/dJ67P/d/lg5sdLpP6JFbF66RpcbnDkT8eyzEY8+GnHqVMQt\nt2z++cuXI15/PeLkyYgXX4w4fjzippvKnJUyRqOI99+PeOGFiCefHP+33rOn6lPVl9ElSWrdTqN6\n22lS3U4yGAz86xFX+E6XLU367nZWvuttl43f3fb7EV9+OX1wI7x7IdWWV8Zot411+8472xvbjRYW\nIp5/PuKRR8bV++GHqreJNtbtJ59sPrbMRul2WI66nUb1NtOsdcvslG4H5a7baVRvs6jbMpRux8yz\nbqdRvfWmbstye6EjdnozIRc3HOol9WZCCrcXrnF7oeOqqNtpVG89zKNuDW4apdtidanbaVRvNXLW\nLZMp3Q6qU91Oo3rL8t1tPSjdlql73U6zthbx9NPjR4pVb37qtiyl2xFNqNtp+v2IwSDiscdUb07q\ntn6Ubgs0tW6nOXdu/F2v6t2Z0nXr9sI1SrfFmly309xxh+rdiarq1rsX0ngiraFKPVVWlYWF8Ssi\nPc02G0+V1Z/SbaA21u00qjeN726bQ+k2SNvrdhrVuzl12yxKtyG6VLfTqN7fUrfN5PZCzbXtZkIu\nG284vP12xJ13Vn2isup479bthWvcXmgodTvdxuq9//7uVG+d69bgplG6NaRuZ9OV6q1j3TKZ0m0Q\ndTu7tldvneuW2SndmlC3ebStetVtMyndmlO3+bSletVteyndCqnb+Wpq9Ta1bt1euEbp1pC6nb+m\nVW/T69a7F9J4Iq2wrj5VVpVJT7PVsXo9VdYdSrcgdVudulZv0+uW2SndAtRtPdStetVtNyndOVO3\n9VN19arbbnN7YU7cTGiG0jccmnozIYXbC9e4vVCYum2OUtXbhbo1uGmUbkbqttnmVb1trlsmU7oF\nqNvmy129XahbZqd0d0jdttNOq1fddpvSnRN1217brV51y1aU7jao225Jrd6u163bC9co3YzUbfds\nVb3qdsy7F9J4Ii2Rp8q6bdrTbPv2eaqM2SjdBOfOqVvGNlbvoUMRt97a7bpldko3wRdfRNx7b8Qb\nb1R9Eurgu+8iPvts/L8PH444dara89AsSjfR7t1Vn4CqXf/d7SuvqFtmp3QhwaQ3gr32WtWnqhc3\nF9IoXdiEmwnpjG4apQtTeN8t86B04TrqlnlSurCBumXelC6EuqUcpUvnqds8vHshjdKls9RtXt69\nkEbp0knqlqooXTpF3VI1pUtnqFvqQOnSeuqWOlG6tJq6LcfNhTRKl1ZSt+UZ3TRKl9ZRt9SZ0qU1\n1C1NoHRpBXVLUyhdGk3d0jRKl8ZSt/Xi3QtplC6No27rybsX0ihdGkXd0nRKl0ZQt7SF0qX21C1t\nonSpLXVLGyldakndNo+bC2mULrWibpvL6KZRutSGuqULlC6VU7d0idKlUuqWrlG6VELd0lVKl+LU\nbTt590IapUsx6rbdvHshjdKlCHULY0qXuVK38FtKl7lRt3AjpUt26hamU7pkpW67y82FNEqXLNQt\nRjeN0mXH1C2kU7psm7qF2SldtkXdwvYoXWaibmFnlG6CffsiPvgg4qOPqj5J9UajiEOH1C038u6F\nNEY3wcMPR/z4Y9WnqI9duyJ6vapPQd0Y3TRGN9Hu3VWfAGgD3+kCFGR0AQoyugAFGV0gC39ES2N0\ngSyMbhqjC1CQ0QUoyOgCFGR0AQoyukAW/gn2NEYXyMLopjG6AAUZXYCCjC5AQUYXoCCjC2ThMeA0\nRhfIwuimMboABRldgIKMLkBBRhegIKMLZOEx4DRGF8jC6KYxugAFGV2AgowuQEFGF6Agowtk4THg\nNEYXyMLopjG6AAUZXYCCjC5AQUYXoCCjC2ThMeA0RhfIwuimMboABRldgIKMLkBBRhegIKML23Bh\nOIx/vrMY//34j3FycTEuDIdVH6lyHgNO0xuNRtN/2euNNvs9dNGF4TD+duxYnFxbi70R8UNEvNTv\nx/Nnz8btBw9WfTxqoNfrxWg06k36ndKFGa0uLV0d3IiIvRFxcm0tVpeWqjwWDWF0YUaXv/nm6uD+\nam9EXF5fr+I4NIzRhRkt3HZb/HDdz36IiIX9+6s4Dg1jdGFGT62sxEv9/tXh/fU73adWVqo8Fg3h\nD2mwDReGw1hdWorL6+uxsH9/PLWy0vk/og0GAzcYrtjsD2lGF8hieXk5lpeXqz5GLbi9AFATRheg\nIKMLUJDRBSjI6AJZuLmQxu0FgMzcXgCoCaMLUJDRBSjI6AIUZHSBLPwT7GmMLpCF0U1jdAEKMroA\nBRldgIKMLkBBRhfIwrsX0nj3AkBm3r0AUBNGF6AgowtQkNEFKMjoAll4DDiN0QWyMLppjC5AQUYX\noCCjC1CQ0QUoyOgCWXj3QhrvXgDIzLsXAGrC6AIUZHQBCjK6AAUZXSALjwGnMbpAFkY3jdEFKMjo\nAhRkdAEKMroABW35GHDBswC0xrTHgDcdXQDy8vUCQEFGF6AgowtQkNEFKMjoAhT0f79okG6gaGgK\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f7af650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "random_walk_final(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [Root]",
   "language": "python",
   "name": "Python [Root]"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}