Random walks: Difference between revisions

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<option value="200">200</option>
<option value="200">200</option>
</select> <br />
</select> <br />
<input type="button" value="run" onClick="run()">
<input type="button" value="run simulation" onClick="run()">
<input type="button" value="clear" onClick="clearturtle()">
<input type="button" value="clear screen" onClick="clearturtle()">
<br />
<br />
</form></html>
</form></html>
Fixed values in this simulation are:
Fixed values in this simulation are:
  * stepsize <math>{}=5</math> and  
  * stepsize <math>{}=5</math> and  
  * Number of steps per walk <math> {}= 100</math>.  
  * Number of steps per walk <math> {}= 100</math>.  
Therefore, the expected  
Therefore, the expected  
squared distance from the starting point will be <math>100\cdot 5^2=2500</math>.
squared distance from the starting point will be <math>100\cdot 5^2=2500</math>.

Revision as of 13:10, 27 May 2009

Number of random walks:

Fixed values in this simulation are:

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

Therefore, the expected squared distance from the starting point will be [math]\displaystyle{ 100\cdot 5^2=2500 }[/math].

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

Source code

<jsxgraph width="600" height="600">
var brd = JXG.JSXGraph.initBoard('jxgbox', {originX: 300, originY: 300, unitX: 3, unitY: 3});
var t = brd.createElement('turtle');

function run() {
  var i,j,dist,sumdist=0.0;
  var stepSize = 5; 
  brd.suspendUpdate();
  var nr = $('number').value*1;
  for (i=0;i<nr;i++) {
     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();
  }
  $('output').value = (sumdist/nr).toFixed(3);
  brd.unsuspendUpdate();
}
function clearturtle() {
  sumist = 0.0
  t.cs();
}
</jsxgraph>

External links