Random walks

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Revision as of 13:10, 27 May 2009 by A WASSERMANN (talk | contribs)

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