# Random walks

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Number of random walks:

Fixed values in this simulation are:

• stepsize $\displaystyle{ {}=5 }$ and
• Number of steps per walk $\displaystyle{ {}= 100 }$.

Therefore, the expected squared distance from the starting point will be equal to

• $\displaystyle{ 100\cdot 5^2=2500 }$.

Average square of the distance between starting point and endpoint of the walks:

### Source code

var brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-100, 100, 100, -100]});
var t = brd.create('turtle');

function run() {
var i,j,dist,sumdist=0.0;
var stepSize = 5;
brd.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);
brd.unsuspendUpdate();
}
function clearturtle() {
t.cs();
}