Fractal Polygons - Revision history

Michael at 09:28, 31 January 2013

2013-01-31T09:28:07Z

← Older revision		Revision as of 09:28, 31 January 2013
Line 43:		Line 43:
	</html>		</html>
	<jsxgraph width="600" height="600" box="box">		<jsxgraph width="600" height="600" box="box">
	var brd = JXG.JSXGraph.initBoard('box', {boundingbox: [-~~200~~, ~~200~~, ~~200~~, -~~200~~]});		var brd = JXG.JSXGraph.initBoard('box', {boundingbox: [-250, 250, 250, -250]});
	var t = brd.create('turtle');		var t = brd.create('turtle');
	function run() {		function run() {

Michael at 09:27, 31 January 2013

2013-01-31T09:27:17Z

← Older revision		Revision as of 09:27, 31 January 2013
Line 43:		Line 43:
	</html>		</html>
	<jsxgraph width="600" height="600" box="box">		<jsxgraph width="600" height="600" box="box">
	var brd = JXG.JSXGraph.initBoard('box', {boundingbox: [-~~150~~, ~~150~~, ~~150~~, -~~150~~]});		var brd = JXG.JSXGraph.initBoard('box', {boundingbox: [-200, 200, 200, -200]});
	var t = brd.create('turtle');		var t = brd.create('turtle');
	function run() {		function run() {

Michael at 09:26, 31 January 2013

2013-01-31T09:26:51Z

← Older revision		Revision as of 09:26, 31 January 2013
Line 43:		Line 43:
	</html>		</html>
	<jsxgraph width="600" height="600" box="box">		<jsxgraph width="600" height="600" box="box">
	var brd = JXG.JSXGraph.initBoard('box', {~~originX~~: ~~300~~, ~~originY: 300~~, ~~unitX: 1~~, ~~unitY: 1~~});		var brd = JXG.JSXGraph.initBoard('box', {boundingbox: [-150, 150, 150, -150]});
	var t = brd.create('turtle');		var t = brd.create('turtle');
	function run() {		function run() {

A WASSERMANN at 09:51, 25 March 2011

2011-03-25T09:51:54Z

← Older revision		Revision as of 09:51, 25 March 2011
Line 44:		Line 44:
	<jsxgraph width="600" height="600" box="box">		<jsxgraph width="600" height="600" box="box">
	var brd = JXG.JSXGraph.initBoard('box', {originX: 300, originY: 300, unitX: 1, unitY: 1});		var brd = JXG.JSXGraph.initBoard('box', {originX: 300, originY: 300, unitX: 1, unitY: 1});
	var t = brd.~~createElement~~('turtle');		var t = brd.create('turtle');
	function run() {		function run() {
	brd.suspendUpdate();		brd.suspendUpdate();

A WASSERMANN at 09:45, 25 March 2011

2011-03-25T09:45:19Z

← Older revision		Revision as of 09:45, 25 March 2011
Line 42:		Line 42:
	</form>		</form>
	</html>		</html>
	<jsxgraph width="600" height="~~400~~" box="box">		<jsxgraph width="600" height="600" box="box">
	var brd = JXG.JSXGraph.initBoard('box', {originX: 300, originY: 300, unitX: 1, unitY: 1});		var brd = JXG.JSXGraph.initBoard('box', {originX: 300, originY: 300, unitX: 1, unitY: 1});
	var t = brd.createElement('turtle');		var t = brd.createElement('turtle');

A WASSERMANN at 09:45, 25 March 2011

2011-03-25T09:45:02Z

New page

With turtle graphics it is quite easy to construct regular polygons in a recursive manner.

It is possible to play around with this example:
In the last line of the input window there is the command
<source lang="javascript">
fracPolygon(5,100,0.4,5);
</source>
The meaning of the parameters is
* 5: number of vertices of the regular polygon,
* 100: length of a side of the initial polygon,
* 0.4: shrink factor from one level to the next,
* 5: number of recursion steps.

<html>
<form><textarea id="inputtext" rows=3 cols=35 wrap="off" style="width:600px;">
function fracPolygon(corner,len,shrink,recurs) {
if (recurs>0) {
if (arguments.length==4) { // initial call
t.rt(180);
fracPolygon(corner,len*shrink,shrink,recurs-1,1);
t.lt(180);
}
t.fd(len);
t.rt(360/corner);
for(var i=0;i<corner-1;i++) {
t.rt(180);
fracPolygon(corner,len*shrink,shrink,recurs-1,1);
t.lt(180);
t.fd(len);
t.rt(360/corner);
}
};
}
t.cs();
t.hideTurtle();
t.setPos(-100,0);
t.setPenColor('blue');
fracPolygon(5,100,0.4,5);
</textarea><br />
<input type="button" value="run" onClick="run()">
<input type="button" value="clear" onClick="clearturtle()">
</form>
</html>
<jsxgraph width="600" height="400" box="box">
var brd = JXG.JSXGraph.initBoard('box', {originX: 300, originY: 300, unitX: 1, unitY: 1});
var t = brd.createElement('turtle');
function run() {
brd.suspendUpdate();
var code = document.getElementById('inputtext').value;
if (code=='') { return; }
eval(code);
brd.unsuspendUpdate();
}
function clearturtle() {
t.cs();
}
</jsxgraph>

===References===
* Peter Baptist, Wolfgang Neidhardt, Alfred Wassermann:'' Symmetry and Regular Polygons'', Prispevki k poucevanju Matematike, The Improvement of Mathematics Education in Secondary Schools: A Tempus Project, Maribor 1996.

[[Category:Examples]]
[[Category:Turtle Graphics]]
[[Category:Fractals]]

A WASSERMANN at 19:41, 29 October 2009

2009-10-29T19:41:44Z

← Older revision		Revision as of 19:41, 29 October 2009
Line 49:		Line 49:
	function run() {		function run() {
	brd.suspendUpdate();		brd.suspendUpdate();
	var code = $('inputtext').value;		var code = document.getElementById('inputtext').value;
	if (code=='') { return; }		if (code=='') { return; }
	eval(code);		eval(code);

A WASSERMANN at 16:37, 29 October 2009

2009-10-29T16:37:22Z

← Older revision		Revision as of 16:37, 29 October 2009
Line 14:		Line 14:
	<html>		<html>
	<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />		<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
	~~<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script>~~
	<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>		<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
	<form><textarea id="inputtext" rows=3 cols=35 wrap="off" style="width:600px;">		<form><textarea id="inputtext" rows=3 cols=35 wrap="off" style="width:600px;">

A WASSERMANN at 15:09, 21 January 2009

2009-01-21T15:09:24Z

← Older revision		Revision as of 15:09, 21 January 2009
Line 16:		Line 16:
	<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script>		<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script>
	<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>		<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
	~~<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxturtle.js"></script>~~
	<form><textarea id="inputtext" rows=3 cols=35 wrap="off" style="width:600px;">		<form><textarea id="inputtext" rows=3 cols=35 wrap="off" style="width:600px;">
	function fracPolygone(corner,len,shrink,recurs) {		function fracPolygone(corner,len,shrink,recurs) {
Line 48:		Line 47:
	<script language="JavaScript">		<script language="JavaScript">
	var brd = JXG.JSXGraph.initBoard('box', {originX: 300, originY: 300, unitX: 1, unitY: 1});		var brd = JXG.JSXGraph.initBoard('box', {originX: 300, originY: 300, unitX: 1, unitY: 1});
	var t = ~~new JSXTurtleObj~~(~~brd~~);		var t = brd.createElement('turtle');
	function run() {		function run() {
	brd.suspendUpdate();		brd.suspendUpdate();

A WASSERMANN at 12:04, 21 December 2008

2008-12-21T12:04:19Z

← Older revision		Revision as of 12:04, 21 December 2008
Line 8:		Line 8:
	The meaning of the parameters is		The meaning of the parameters is
	* 5: number of vertices of the regular polygone,		* 5: number of vertices of the regular polygone,
	* 100: length of a side of the initial ~~poylgone~~,		* 100: length of a side of the initial polygone,
	* 0.4: shrink factor from one level to the next,		* 0.4: shrink factor from one level to the next,
	* 5: number of recursion steps.		* 5: number of recursion steps.