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Random walks
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<iframe 
    src="http://jsxgraph.uni-bayreuth.de/share/iframe/random-walks" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Random walks" 
    allowfullscreen
></iframe>
This code has to 
Number of random walks: <select id="number">
    <option value="1">1</option>
    <option value="2">2</option>
    <option value="3">3</option>
    <option value="4">4</option>
    <option value="5">5</option>
    <option value="6">6</option>
    <option value="7">7</option>
    <option value="8">8</option>
    <option value="9">9</option>
    <option value="10">10</option>
    <option value="15">15</option>
    <option value="20" selected>20</option>
    <option value="30">30</option>
    <option value="50">50</option>
    <option value="100">100</option>
    <option value="200">200</option>
</select>
<input type="button" value="run simulation" onClick="run()">
<input type="button" value="clear screen" onClick="clearturtle()">
Average square of the distance between starting point and endpoint of the walks: <input type="text" value=""
    id="output">

<div id="board-0-wrapper" class="jxgbox-wrapper " style="width: 100%; ">
   <div id="board-0" class="jxgbox" style="aspect-ratio: 1 / 1; width: 100%;" data-ar="1 / 1"></div>
</div>

<script type = "text/javascript"> 
    /*
    This example is licensed under a 
    Creative Commons Attribution ShareAlike 4.0 International License.
    https://creativecommons.org/licenses/by-sa/4.0/
    
    Please note you have to mention 
    The Center of Mobile Learning with Digital Technology
    in the credits.
    */
    
    const BOARDID = 'board-0';

    var board = JXG.JSXGraph.initBoard(BOARDID, { boundingbox: [-100, 100, 100, -100], keepaspectratio: true });
    var t = board.create('turtle');
    
    function run() {
        var i, j, dist, sumdist = 0.0;
        var stepSize = 5;
        t.hideTurtle();
        board.suspendUpdate();
        var nr = document.getElementById('number').value * 1;
        for (i = 0; i < nr; i++) {
            t.setPenColor(JXG.hsv2rgb(Math.round(Math.random() * 255), Math.random(), Math.random()));
            for (j = 0; j < 100; j++) {
                var a = Math.floor(360 * Math.random());
                t.right(a);
                t.forward(stepSize);
            }
            dist = t.pos[0] * t.pos[0] + t.pos[1] * t.pos[1];
            sumdist += dist;
            t.home();
        }
        document.getElementById('output').value = (sumdist / nr).toFixed(3);
        board.unsuspendUpdate();
    }
    
    function clearturtle() {
        t.cs();
    }
 </script> 
/*
This example is licensed under a 
Creative Commons Attribution ShareAlike 4.0 International License.
https://creativecommons.org/licenses/by-sa/4.0/

Please note you have to mention 
The Center of Mobile Learning with Digital Technology
in the credits.
*/

const BOARDID = 'your_div_id'; // Insert your id here!

var board = JXG.JSXGraph.initBoard(BOARDID, { boundingbox: [-100, 100, 100, -100], keepaspectratio: true });
var t = board.create('turtle');

function run() {
    var i, j, dist, sumdist = 0.0;
    var stepSize = 5;
    t.hideTurtle();
    board.suspendUpdate();
    var nr = document.getElementById('number').value * 1;
    for (i = 0; i < nr; i++) {
        t.setPenColor(JXG.hsv2rgb(Math.round(Math.random() * 255), Math.random(), Math.random()));
        for (j = 0; j < 100; j++) {
            var a = Math.floor(360 * Math.random());
            t.right(a);
            t.forward(stepSize);
        }
        dist = t.pos[0] * t.pos[0] + t.pos[1] * t.pos[1];
        sumdist += dist;
        t.home();
    }
    document.getElementById('output').value = (sumdist / nr).toFixed(3);
    board.unsuspendUpdate();
}

function clearturtle() {
    t.cs();
}
Fixed values in this simulation are: * stepsize ${}=5$ and * Number of steps per walk ${}= 100$. Therefore, the expected squared distance from the starting point will be equal to * $100\cdot 5^2=2500$.
Number of random walks: Average square of the distance between starting point and endpoint of the walks: 
Number of random walks: <select id="number">
    <option value="1">1</option>
    <option value="2">2</option>
    <option value="3">3</option>
    <option value="4">4</option>
    <option value="5">5</option>
    <option value="6">6</option>
    <option value="7">7</option>
    <option value="8">8</option>
    <option value="9">9</option>
    <option value="10">10</option>
    <option value="15">15</option>
    <option value="20" selected>20</option>
    <option value="30">30</option>
    <option value="50">50</option>
    <option value="100">100</option>
    <option value="200">200</option>
</select>
<input type="button" value="run simulation" onClick="run()">
<input type="button" value="clear screen" onClick="clearturtle()">
Average square of the distance between starting point and endpoint of the walks: <input type="text" value=""
    id="output">
// Define the id of your board in BOARDID

var board = JXG.JSXGraph.initBoard(BOARDID, { boundingbox: [-100, 100, 100, -100], keepaspectratio: true });
var t = board.create('turtle');

function run() {
    var i, j, dist, sumdist = 0.0;
    var stepSize = 5;
    t.hideTurtle();
    board.suspendUpdate();
    var nr = document.getElementById('number').value * 1;
    for (i = 0; i < nr; i++) {
        t.setPenColor(JXG.hsv2rgb(Math.round(Math.random() * 255), Math.random(), Math.random()));
        for (j = 0; j < 100; j++) {
            var a = Math.floor(360 * Math.random());
            t.right(a);
            t.forward(stepSize);
        }
        dist = t.pos[0] * t.pos[0] + t.pos[1] * t.pos[1];
        sumdist += dist;
        t.home();
    }
    document.getElementById('output').value = (sumdist / nr).toFixed(3);
    board.unsuspendUpdate();
}

function clearturtle() {
    t.cs();
}

license

This example is licensed under a Creative Commons Attribution ShareAlike 4.0 International License.
Please note you have to mention The Center of Mobile Learning with Digital Technology in the credits.