Difference between revisions of "Random walks"

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m (Undo revision 3145 by Annie (Talk), Reason: Spam)
 
Line 44: Line 44:
 
   t.hideTurtle();
 
   t.hideTurtle();
 
   brd.suspendUpdate();
 
   brd.suspendUpdate();
   var nr = $('number').value*1;
+
   var nr = document.getElementById('number').value*1;
 
   for (i=0;i<nr;i++) {
 
   for (i=0;i<nr;i++) {
 
     t.setPenColor(JXG.hsv2rgb(Math.round(Math.random()*255),Math.random(),Math.random()));
 
     t.setPenColor(JXG.hsv2rgb(Math.round(Math.random()*255),Math.random(),Math.random()));
Line 56: Line 56:
 
     t.home();
 
     t.home();
 
   }
 
   }
   $('output').value = (sumdist/nr).toFixed(3);
+
   document.getElementById('output').value = (sumdist/nr).toFixed(3);
 
   brd.unsuspendUpdate();
 
   brd.unsuspendUpdate();
 
}
 
}
Line 74: Line 74:
 
   var stepSize = 5;  
 
   var stepSize = 5;  
 
   brd.suspendUpdate();
 
   brd.suspendUpdate();
   var nr = $('number').value*1;
+
   var nr = document.getElementById('number').value*1;
 
   for (i=0;i<nr;i++) {
 
   for (i=0;i<nr;i++) {
 
     t.setPenColor(JXG.hsv2rgb(Math.round(Math.random()*255),Math.random(),Math.random()));
 
     t.setPenColor(JXG.hsv2rgb(Math.round(Math.random()*255),Math.random(),Math.random()));
Line 86: Line 86:
 
     t.home();
 
     t.home();
 
   }
 
   }
   $('output').value = (sumdist/nr).toFixed(3);
+
   document.getElementById('output').value = (sumdist/nr).toFixed(3);
 
   brd.unsuspendUpdate();
 
   brd.unsuspendUpdate();
 
}
 
}

Revision as of 19:25, 29 October 2009

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

<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 = 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();
}
</jsxgraph>

External links