View source for L-systems

===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 [http://jsxgraph.org 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.

===Examples===
Most of the examples are from the book by Przemyslaw Prusinkiewicz and James Hanan: ''Lindenmayer Systems, Fractals, and Plants'', see the References.
====First Example: Sierpinski curve====
<html>
<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/jsxgraphcore.js"></script>
<form><textarea id="inputtext0" rows=15 cols=35 wrap="off" style="width:600px;">
var level = 6;
var axiom = 'A';
var rules = {
    'A':'B-A-B',
    'B':'A+B+A',
    '+' : '+',
    '-' : '-'
};
var symbols = { 'A':'F', 
                'B':'F', 
                '+':'+', 
                '-':'-', 
                '[':'[', 
                ']':']'  
              }; 
var angle = 60; 
var len = 500/Math.pow(2,level); 
t.setPos(-250*Math.pow(-1,level),-250); 
t.rt(90*Math.pow(-1,level)); 
</textarea><br />
<input type="button" value="run" onClick="run(0)">
<input type="button" value="clear" onClick="clearturtle(0)">
</form>
</html>
<jsxgraph width="600" height="600" box="box0">
var t;
var turtle = [];
var brd = [];
brd[0] = JXG.JSXGraph.initBoard('box0', {boundingbox: [-300, 300, 300, -300]});
turtle[0] = brd[0].create('turtle');

function expander(level,axiom,rules) {
    this.axiom = axiom;
    this.rules = rules;
    this.source = (level>1) ? new expander(level-1,axiom,rules) : (new function() {
        // Axiom:
        this.code = axiom;
        this.pos = 0;
        this.next = function() {
            if (this.pos>=this.code.length) return null;
            return this.code.charAt(this.pos++);
        }
    });
    
    this.code = '';
    this.pos = 0;
    this.next = function() {
        while (this.pos>=this.code.length) { // produce new symbols from source
            this.pos = 0;
            var pattern = this.source.next();
            if (!pattern) return null // Finished
            this.code = this.rules[pattern];
        }
        return this.code.charAt(this.pos++);
    }
}

function plotter(generator,symbols,len,angle,t,shrink) {
    for (var c; c=generator.next(); c) {
        switch(symbols[c]) {
            case 'F':
                t.fd(len);
                break;
            case 'f':
                t.penUp();
                t.fd(len);
                t.penDown();
                break;
            case '+':
                t.lt(angle);
                break;
            case '-':
                t.rt(angle);
                break;
            case '[':
                t.pushTurtle();
                len *= shrink;
                break;
            case ']':
                t.popTurtle();
                len /= shrink;
                break;
            default:
                ;
        }
    }
    return null;
  }
var shrink = 1.0;
 
function run(nr) {
  brd[nr].suspendUpdate();
  var code = document.getElementById('inputtext'+nr).value;
  if (code=='') { return; }
  t = turtle[nr];
  t.cs();
  t.hideTurtle();
  eval(code);
  var generator = new expander(level,axiom,rules);
  plotter(generator,symbols,len,angle,t,shrink);
  brd[nr].unsuspendUpdate();
}

function clearturtle(nr) {
  turtle[nr].cs();
}
</jsxgraph>

====More examples====
* [[Quadratic snowflake variation]]
* [[Dragon curve]]
* [[Islands and lakes]]
* [[Peano curve]]
* [[Hexagonal Gosper curve]]
* [[Plant generation I]]
* [[Plant generation II]]
* [[Hexagonal kolam]]
* [[Mango kolam]]
* [[Penrose tiling]]

===The underlying JavaScript code===
The underlying [[JavaScript code for producing Lindenmayer systems]]

===References===
* Przemyslaw Prusinkiewicz, James Hanan: Lindenmayer Systems, Fractals, and Plants (Lecture Notes in Biomathematics). Springer-Verlag 1989, ISBN 0-387-97092-4
* [http://en.wikipedia.org/wiki/L-system http://en.wikipedia.org/wiki/L-system]
* [http://en.wikipedia.org/wiki/Space-filling_curve http://en.wikipedia.org/wiki/Space-filling_curve]
* [http://www.biologie.uni-hamburg.de/b-online/e28_3/lsys.html An Introduction to Lindenmayer Systems]


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