Difference between revisions of "Random walks"

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Line 36: Line 36:
  
 
<jsxgraph width="600" height="600">
 
<jsxgraph width="600" height="600">
var brd = JXG.JSXGraph.initBoard('jxgbox', {originX: 300, originY: 300, unitX: 3, unitY: 3});
+
var brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-100, 100, 100, -100]});
var t = brd.createElement('turtle');
+
var t = brd.create('turtle');
  
 
function run() {
 
function run() {
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===Source code===
 
===Source code===
<source lang="html4strict">
+
<source lang="javascript">
<jsxgraph width="600" height="600">
+
var brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-100, 100, 100, -100]});
var brd = JXG.JSXGraph.initBoard('jxgbox', {originX: 300, originY: 300, unitX: 3, unitY: 3});
+
var t = brd.create('turtle');
var t = brd.createElement('turtle');
 
  
 
function run() {
 
function run() {
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   t.cs();
 
   t.cs();
 
}
 
}
</jsxgraph>
 
 
</source>
 
</source>
  

Latest revision as of 14:19, 8 June 2011

Number of random walks:

Fixed values in this simulation are:

  • stepsize [math]{}=5[/math] and
  • Number of steps per walk [math] {}= 100[/math].

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

  • [math]100\cdot 5^2=2500[/math].

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();
}

External links