{ "cells": [ { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [], "source": [ "from numpy import random\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "def walk():\n", " x=0\n", " while x !=1 :\n", " x+=random.choice([-1,1]) \n", " yield x" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[-1, 0, -1, 0, -1, 0, 1]" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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AN0XkMPAPoKDmCqpa1dRgVLVCRGYBHwCRwFJV3SEiDwGpqlqdcK4HXlVV31LX6cBiEanC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\nx/hjTZpTZw+Fkoyvq8fFENu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A14FF+VkGwHkRcWuJMTVqKDAjj2LcCrguIpp6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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "random.seed(288) # set seed for reproducibility\n", "s = list(walk()) # generate the random steps\n", "fig,ax=plt.subplots()\n", "ax.plot(s)\n", "ax.set_ylabel(\"particle's x-position\",fontsize=16)\n", "ax.set_xlabel('step index k',fontsize=16)\n", "ax.set_title('Example of random walk',fontsize=16)\n", "s" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5,1,'average length=20.36')" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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dPEPd0EmaXmqlG5QaJZZLy4eOP3/mRoLXFrJcXszx+WtxLs6kmYwXmVgt0Bd0E/IeQqsp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cFOuoJdlEs525q3FdtEo4TxNflcRC4CfgBMAy8AbwJcidCNwM/iiCQaRcQbx4hGo9TX11NdXU04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\ntt2lH/gij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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "random.seed(123) \n", "s = [list(walk()) for i in range(50)] # generate 50 random walks\n", "len_walk=list(map(len,s)) # lengths of each walk\n", "\n", "\n", "fig,ax=plt.subplots()\n", "for i in s:\n", " ax.plot(i)\n", "ax.set_ylabel(\"particle's x-position\",fontsize=16)\n", "ax.set_xlabel('step index k',fontsize=16)\n", "ax.set_title('average length=%3.2f'%(np.mean(len_walk)))\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "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": "3.6.2" } }, "nbformat": 4, "nbformat_minor": 1 }