L-systems: Difference between revisions

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<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>
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<form><textarea id="inputtext0" rows=3 cols=35 wrap="off" style="width:600px;">
<form><textarea id="inputtext0" rows=3 cols=35 wrap="off" style="width:600px;">
var level = 6;
var level = 6;
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var brd = [];
var brd = [];
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brd[0] = JXG.JSXGraph.initBoard('box0', {originX: 300, originY: 300, unitX: 1, unitY: 1});
turtle[0] = new JSXTurtleObj(brd[0]);
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function expander(level,axiom,rules) {
function expander(level,axiom,rules) {
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<script language="JavaScript">
<script language="JavaScript">
brd[1] = JXG.JSXGraph.initBoard('box1', {originX: 300, originY: 300, unitX: 1, unitY: 1});
brd[1] = JXG.JSXGraph.initBoard('box1', {originX: 300, originY: 300, unitX: 1, unitY: 1});
turtle[1] = new JSXTurtleObj(brd[1]);
turtle[1] = brd[1].createElement('turtle');
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<script language="JavaScript">
<script language="JavaScript">
brd[2] = JXG.JSXGraph.initBoard('box2', {originX: 300, originY: 300, unitX: 1, unitY: 1});
brd[2] = JXG.JSXGraph.initBoard('box2', {originX: 300, originY: 300, unitX: 1, unitY: 1});
turtle[2] = new JSXTurtleObj(brd[2]);
turtle[2] = brd[2].createElement('turtle');
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<script language="JavaScript">
<script language="JavaScript">
brd[3] = JXG.JSXGraph.initBoard('box3', {originX: 300, originY: 300, unitX: 1, unitY: 1});
brd[3] = JXG.JSXGraph.initBoard('box3', {originX: 300, originY: 300, unitX: 1, unitY: 1});
turtle[3] = new JSXTurtleObj(brd[3]);
turtle[3] = brd[3].createElement('turtle');
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<script language="JavaScript">
<script language="JavaScript">
brd[4] = JXG.JSXGraph.initBoard('box4', {originX: 300, originY: 300, unitX: 1, unitY: 1});
brd[4] = JXG.JSXGraph.initBoard('box4', {originX: 300, originY: 300, unitX: 1, unitY: 1});
turtle[4] = new JSXTurtleObj(brd[4]);
turtle[4] = brd[4].createElement('turtle');
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<script language="JavaScript">
<script language="JavaScript">
brd[5] = JXG.JSXGraph.initBoard('box5', {originX: 300, originY: 300, unitX: 1, unitY: 1});
brd[5] = JXG.JSXGraph.initBoard('box5', {originX: 300, originY: 300, unitX: 1, unitY: 1});
turtle[5] = new JSXTurtleObj(brd[5]);
turtle[5] = brd[5].createElement('turtle');
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<script language="JavaScript">
<script language="JavaScript">
brd[6] = JXG.JSXGraph.initBoard('box6', {originX: 300, originY: 300, unitX: 1, unitY: 1});
brd[6] = JXG.JSXGraph.initBoard('box6', {originX: 300, originY: 300, unitX: 1, unitY: 1});
turtle[6] = new JSXTurtleObj(brd[6]);
turtle[6] = brd[6].createElement('turtle');
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<script language="JavaScript">
<script language="JavaScript">
brd[7] = JXG.JSXGraph.initBoard('box7', {originX: 300, originY: 300, unitX: 1, unitY: 1});
brd[7] = JXG.JSXGraph.initBoard('box7', {originX: 300, originY: 300, unitX: 1, unitY: 1});
turtle[7] = new JSXTurtleObj(brd[7]);
turtle[7] = brd[7].createElement('turtle');
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<script language="JavaScript">
<script language="JavaScript">
brd[8] = JXG.JSXGraph.initBoard('box8', {originX: 300, originY: 300, unitX: 1, unitY: 1});
brd[8] = JXG.JSXGraph.initBoard('box8', {originX: 300, originY: 300, unitX: 1, unitY: 1});
turtle[8] = new JSXTurtleObj(brd[8]);
turtle[8] = brd[8].createElement('turtle');
</script>
</script>
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<script language="JavaScript">
<script language="JavaScript">
brd[9] = JXG.JSXGraph.initBoard('box9', {originX: 300, originY: 300, unitX: 1, unitY: 1});
brd[9] = JXG.JSXGraph.initBoard('box9', {originX: 300, originY: 300, unitX: 1, unitY: 1});
turtle[9] = new JSXTurtleObj(brd[9]);
turtle[9] = brd[9].createElement('turtle');
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</script>
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<script language="JavaScript">
<script language="JavaScript">
brd[10] = JXG.JSXGraph.initBoard('box10', {originX: 300, originY: 300, unitX: 1, unitY: 1});
brd[10] = JXG.JSXGraph.initBoard('box10', {originX: 300, originY: 300, unitX: 1, unitY: 1});
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Revision as of 15:12, 21 January 2009

Online experiments with Lindenmayer Systems

A Lindenmayer System consists of

  • an initial string called axiom
  • a set of rewriting rules

This is an experimental page, where the Lindenmayer Systems can be changed online. The visualization is done by the JavaScript library JSXGraph. For each system a maximum level is defined. If this value is increased, the complexity of the drawing rises and running time increases, too.

Most of the examples are from the book by Przemyslaw Prusinkiewicz and James Hanan: Lindenmayer Systems, Fractals, and Plants, see the References.

Sierpinski curve



Quadratic snowflake variation


Dragon curve


Islands and lakes



Peano curve


Hexagonal Gosper curve


Plant 1


Plant 2


Hexagonal kolam


Mango kolam



Penrose tiling


The underlying JavaScript code

The underlying JavaScript code for producing Lindenmayer systems

References

Retrieved from "http://jsxgraph.org/wiki/index.php?title=L-systems&oldid=1060"