Difference between revisions of "Random walks"

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Line 19: Line 19:
 
<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 equal to
 +
* <math>100\cdot 5^2=2500</math>.
 
<html>
 
<html>
 
<form>
 
<form>
Line 35: 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');
−
 
 
−
HSV2RGB = function(H,S,V) {
 
−
    var R,G,B, f,i,hTemp, p,q,t;
 
−
    if (S==0) {
 
−
        if (isNaN(H)) {
 
−
            R = V;
 
−
            G = V;
 
−
            B = V;
 
−
        } else {
 
−
            return '#000000';
 
−
        }
 
−
    } else {
 
−
        if (H>=360) {
 
−
            hTemp = 0.0;
 
−
        } else {
 
−
            hTemp = H;
 
−
        }
 
−
        hTemp = hTemp / 60;    // h is now IN [0,6)
 
−
        i = Math.floor(hTemp);        // largest integer <= h
 
−
        f = hTemp - i;                  // fractional part of h
 
−
        p = V * (1.0 - S);
 
−
        q = V * (1.0 - (S * f));
 
−
        t = V * (1.0 - (S * (1.0 - f)));
 
−
        switch (i) {
 
−
            case 0: R = V; G = t;  B = p; break;
 
−
            case 1: R = q; G = V;  B = p; break;
 
−
            case 2: R = p; G = V;  B = t; break;
 
−
            case 3: R = p; G = q;  B = V; break;
 
−
            case 4: R = t; G = p;  B = V; break;
 
−
            case 5: R = V; G = p;  B = q; break;
 
−
        }
 
−
    }
 
−
    R = Math.round(R*255).toString(16); R = (R.length==0)?'00':((R.length==1)?'0'+R:R);
 
−
    G = Math.round(G*255).toString(16); G = (G.length==0)?'00':((G.length==1)?'0'+G:G);
 
−
    B = Math.round(B*255).toString(16); B = (B.length==0)?'00':((B.length==1)?'0'+B:B);
 
−
    return '#'+R+G+B;
 
−
}
 
−
 
 
  
 
function run() {
 
function run() {
Line 81: 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(HSV2RGB(Math.round(Math.random()*255),Math.random(),Math.random()));
+
     t.setPenColor(JXG.hsv2rgb(Math.round(Math.random()*255),Math.random(),Math.random()));
 
     for (j=0;j<100;j++) {
 
     for (j=0;j<100;j++) {
 
         var a = Math.floor(360*Math.random());  
 
         var a = Math.floor(360*Math.random());  
Line 93: Line 56:
 
     t.home();
 
     t.home();
 
   }
 
   }
−
   $('output').value = (sumdist/nr).toFixed(3);
+
   document.getElementById('output').value = (sumdist/nr).toFixed(3);
 
   brd.unsuspendUpdate();
 
   brd.unsuspendUpdate();
 
}
 
}
 
function clearturtle() {
 
function clearturtle() {
−
  sumist = 0.0
 
 
   t.cs();
 
   t.cs();
 
}
 
}
Line 103: Line 65:
  
 
===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() {
Line 112: Line 73:
 
   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()));
 
     for (j=0;j<100;j++) {
 
     for (j=0;j<100;j++) {
 
         var a = Math.floor(360*Math.random());  
 
         var a = Math.floor(360*Math.random());  
Line 123: Line 85:
 
     t.home();
 
     t.home();
 
   }
 
   }
−
   $('output').value = (sumdist/nr).toFixed(3);
+
   document.getElementById('output').value = (sumdist/nr).toFixed(3);
 
   brd.unsuspendUpdate();
 
   brd.unsuspendUpdate();
 
}
 
}
 
function clearturtle() {
 
function clearturtle() {
−
  sumist = 0.0
 
 
   t.cs();
 
   t.cs();
 
}
 
}
−
</jsxgraph>
 
 
</source>
 
</source>
  
Line 136: Line 96:
 
* [http://en.wikipedia.org/wiki/Random_walk http://en.wikipedia.org/wiki/Random_walk]
 
* [http://en.wikipedia.org/wiki/Random_walk http://en.wikipedia.org/wiki/Random_walk]
 
* [http://mathworld.wolfram.com/RandomWalk.html http://mathworld.wolfram.com/RandomWalk.html]
 
* [http://mathworld.wolfram.com/RandomWalk.html http://mathworld.wolfram.com/RandomWalk.html]
 +
* [http://www.bookrags.com/research/random-walks-and-brownian-motion-wop/ http://www.bookrags.com/research/random-walks-and-brownian-motion-wop/]
  
 
[[Category:Examples]]
 
[[Category:Examples]]
 
[[Category:Turtle Graphics]]
 
[[Category:Turtle Graphics]]
 
[[Category:Statistics]]
 
[[Category:Statistics]]

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

Retrieved from "http://jsxgraph.org/wiki/index.php?title=Random_walks&oldid=5283"