Random walks - Revision history

Michael at 12:19, 8 June 2011

2011-06-08T12:19:49Z

← Older revision		Revision as of 12:19, 8 June 2011
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() {
Line 65:		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 92:		Line 91:
	t.cs();		t.cs();
	}		}
	~~</jsxgraph>~~
	</source>		</source>

A WASSERMANN at 17:25, 29 October 2009

2009-10-29T17:25:02Z

← Older revision		Revision as of 17:25, 29 October 2009
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();
	}		}

Michael: Undo revision 3145 by Annie (Talk), Reason: Spam

2009-10-09T17:11:39Z

Undo revision 3145 by Annie (Talk), Reason: Spam

New page

<html>
<form>
Number of random walks: <select id="number">
<option value="1">1</option>
<option value="2">2</option>
<option value="3">3</option>
<option value="4">4</option>
<option value="5">5</option>
<option value="6">6</option>
<option value="7">7</option>
<option value="8">8</option>
<option value="9">9</option>
<option value="10">10</option>
<option value="15">15</option>
<option value="20" selected>20</option>
<option value="30">30</option>
<option value="50">50</option>
<option value="100">100</option>
<option value="200">200</option>
</select> <br />
<input type="button" value="run simulation" onClick="run()">
<input type="button" value="clear screen" onClick="clearturtle()">
<br />
</form></html>
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>.
<html>
<form>
Average square of the distance between starting point and endpoint of the walks: <input type="text" value="" id="output">
</form>
</html>

<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;
t.hideTurtle();
brd.suspendUpdate();
var nr = $('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();
}
$('output').value = (sumdist/nr).toFixed(3);
brd.unsuspendUpdate();
}
function clearturtle() {
t.cs();
}
</jsxgraph>

===Source code===
<source lang="html4strict">
<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++) {
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();
}
$('output').value = (sumdist/nr).toFixed(3);
brd.unsuspendUpdate();
}
function clearturtle() {
t.cs();
}
</jsxgraph>
</source>

===External links===
* [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://www.bookrags.com/research/random-walks-and-brownian-motion-wop/ http://www.bookrags.com/research/random-walks-and-brownian-motion-wop/]

[[Category:Examples]]
[[Category:Turtle Graphics]]
[[Category:Statistics]]

A WASSERMANN at 17:44, 22 June 2009

2009-06-22T17:44:30Z

@@ Line 38: / Line 38: @@
 var brd = JXG.JSXGraph.initBoard('jxgbox', {originX: 300, originY: 300, unitX: 3, unitY: 3});
 var t = brd.createElement('turtle');
 function run() {
@@ Line 84: / Line 46: @@
    var nr = $('number').value*1;
    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++) {
          var a = Math.floor(360*Math.random());
@@ Line 114: / Line 76: @@
    var nr = $('number').value*1;
    for (i=0;i<nr;i++) {
       for (j=0;j<100;j++) {
          var a = Math.floor(360*Math.random());

A WASSERMANN at 13:14, 27 May 2009

2009-05-27T13:14:13Z

← Older revision		Revision as of 13:14, 27 May 2009
Line 127:		Line 127:
	}		}
	function clearturtle() {		function clearturtle() {
	~~sumist = 0.0~~
	t.cs();		t.cs();
	}		}

A WASSERMANN at 13:13, 27 May 2009

2009-05-27T13:13:46Z

← Older revision		Revision as of 13:13, 27 May 2009
Line 98:		Line 98:
	}		}
	function clearturtle() {		function clearturtle() {
	~~sumist = 0.0~~
	t.cs();		t.cs();
	}		}

A WASSERMANN at 13:11, 27 May 2009

2009-05-27T13:11:59Z

← Older revision		Revision as of 13:11, 27 May 2009
Line 137:		Line 137:
	* [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]]

A WASSERMANN at 13:11, 27 May 2009

2009-05-27T13:11:14Z

← Older revision		Revision as of 13:11, 27 May 2009
Line 27:		Line 27:
	* 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>

A WASSERMANN at 13:10, 27 May 2009

2009-05-27T13:10:54Z

← Older revision		Revision as of 13:10, 27 May 2009
Line 24:		Line 24:
	</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>.

A WASSERMANN at 13:10, 27 May 2009

2009-05-27T13:10:24Z

← Older revision		Revision as of 13:10, 27 May 2009
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 <math>100\cdot 5^2=2500</math>.