L-systems: Difference between revisions

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For each system a maximum ''level'' is defined. If this value is increased, the complexity of the drawing rises and running time increases, too.
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.
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====
===Sierpinski curve===
<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="inputtext0" rows=3 cols=35 wrap="off" style="width:600px;">
<form><textarea id="inputtext0" rows=15 cols=35 wrap="off" style="width:600px;">
var level = 6;
var level = 6;
var axiom = 'A';
var axiom = 'A';
Line 38: Line 37:
<input type="button" value="clear" onClick="clearturtle(0)">
<input type="button" value="clear" onClick="clearturtle(0)">
</form>
</form>
<div id="box0" class="jxgbox" style="width:600px; height:600px;"></div>
</html>
<script language="JavaScript">
<jsxgraph width="600" height="600" box="box0">
var t;
var t;
var turtle = [];
var turtle = [];
var brd = [];
var brd = [];
brd[0] = JXG.JSXGraph.initBoard('box0', {originX: 300, originY: 300, unitX: 1, unitY: 1});
brd[0] = JXG.JSXGraph.initBoard('box0', {boundingbox: [-300, 300, 300, -300]});
turtle[0] = brd[0].createElement('turtle');
turtle[0] = brd[0].create('turtle');


function expander(level,axiom,rules) {
function expander(level,axiom,rules) {
Line 107: Line 106:
function run(nr) {
function run(nr) {
   brd[nr].suspendUpdate();
   brd[nr].suspendUpdate();
   var code = $('inputtext'+nr).value;
   var code = document.getElementById('inputtext'+nr).value;
   if (code=='') { return; }
   if (code=='') { return; }
   t = turtle[nr];
   t = turtle[nr];
Line 121: Line 120:
   turtle[nr].cs();
   turtle[nr].cs();
}
}
</script>
</jsxgraph>
</html>
 
 
===Quadratic snowflake variation===
 
<html>
<form><textarea id="inputtext1" rows=3 cols=35 wrap="off" style="width:600px;">
var level = 5;
var axiom = '+F';
var rules = {
    'F':'F-F+F+F-F',
    '+' : '+',
    '-' : '-'
};
var symbols = { 'F':'F',
                '+':'+',
                '-':'-',
                '[':'[',
                ']':']'
              } ;
var angle = 90;
var len = 500/Math.pow(3,level);
t.setPos(250,0);
</textarea><br />
<input type="button" value="run" onClick="run(1)">
<input type="button" value="clear" onClick="clearturtle(1)">
</form>
<div id="box1" class="jxgbox" style="width:600px; height:600px;"></div>
<script language="JavaScript">
brd[1] = JXG.JSXGraph.initBoard('box1', {originX: 300, originY: 300, unitX: 1, unitY: 1});
turtle[1] = brd[1].createElement('turtle');
</script>
</html>
 
===Dragon curve===
 
<html>
<form><textarea id="inputtext2" rows=3 cols=35 wrap="off" style="width:600px;">
var level = 8;
var axiom = 'Fl';
var rules = {
    'F' : 'F',
    'l' : 'l+rF+',
    'r' : '-Fl-r',
    '+' : '+',
    '-' : '-'
};
var symbols = { 'F':'F',
                'l':' ',
                'r':' ',
                '+':'+',
                '-':'-',
                '[':'[',
                ']':']'
              } ;
             
var angle = 90;
var len = 500/(level*level);
</textarea><br />
<input type="button" value="run" onClick="run(2)">
<input type="button" value="clear" onClick="clearturtle(2)">
</form>
<div id="box2" class="jxgbox" style="width:600px; height:600px;"></div>
<script language="JavaScript">
brd[2] = JXG.JSXGraph.initBoard('box2', {originX: 300, originY: 300, unitX: 1, unitY: 1});
turtle[2] = brd[2].createElement('turtle');
</script>
</html>
 
===Islands and lakes===
 
<html>
<form><textarea id="inputtext3" rows=3 cols=35 wrap="off" style="width:600px;">
var level = 2;
var axiom = 'F-F-F-F';
var rules = {
    'F' : 'F-f+FF-F-FF-Ff-FF+f-FF+F+FF+Ff+FFF',
    'f' : 'ffffff',
    '+' : '+',
    '-' : '-'
};
var symbols = { 'F':'F',
                'f':'f',
                '+':'+',
                '-':'-',
                '[':'[',
                ']':']'
              } ;
             
var angle = 90;
var len = 20/Math.pow(2,level);
</textarea><br />
<input type="button" value="run" onClick="run(3)">
<input type="button" value="clear" onClick="clearturtle(3)">
</form>
<div id="box3" class="jxgbox" style="width:600px; height:600px;"></div>
<script language="JavaScript">
brd[3] = JXG.JSXGraph.initBoard('box3', {originX: 300, originY: 300, unitX: 1, unitY: 1});
turtle[3] = brd[3].createElement('turtle');
</script>
</html>
 
 
===Peano curve===
 
<html>
<form><textarea id="inputtext4" rows=3 cols=35 wrap="off" style="width:600px;">
var level = 4;
var axiom = 'X';
var rules = {
    'F' : 'F',
    'X' : 'XFYFX+F+YFXFY-F-XFYFX',
    'Y' : 'YFXFY-F-XFYFX+F+YFXFY',
    '+' : '+',
    '-' : '-'
};
var symbols = { 'F':'F',
                'X':' ',
                'Y':' ',
                '+':'+',
                '-':'-',
                '[':'[',
                ']':']'
              } ;
             
var angle = 90;
var len = 500/Math.pow(3,level);
t.setPos(250,-250);
</textarea><br />
<input type="button" value="run" onClick="run(4)">
<input type="button" value="clear" onClick="clearturtle(4)">
</form>
<div id="box4" class="jxgbox" style="width:600px; height:600px;"></div>
<script language="JavaScript">
brd[4] = JXG.JSXGraph.initBoard('box4', {originX: 300, originY: 300, unitX: 1, unitY: 1});
turtle[4] = brd[4].createElement('turtle');
</script>
</html>
 
===Hexagonal Gosper curve===
 
<html>
<form><textarea id="inputtext5" rows=3 cols=35 wrap="off" style="width:600px;">
var level = 3;
var axiom = 'XF';
var rules = {
    'F' : 'F',
    'X' : 'X+YF++YF-FX--FXFX-YF+',
    'Y' : '-FX+YFYF++YF+FX--FX-Y',
    '+' : '+',
    '-' : '-'
};
var symbols = { 'F':'F',
                'X':' ',
                'Y':' ',
                '+':'+',
                '-':'-',
                '[':'[',
                ']':']'
              } ;
             
var angle = 60;
var len = 500/Math.pow(3,level);
t.setPos(250,0);
</textarea><br />
<input type="button" value="run" onClick="run(5)">
<input type="button" value="clear" onClick="clearturtle(5)">
</form>
<div id="box5" class="jxgbox" style="width:600px; height:600px;"></div>
<script language="JavaScript">
brd[5] = JXG.JSXGraph.initBoard('box5', {originX: 300, originY: 300, unitX: 1, unitY: 1});
turtle[5] = brd[5].createElement('turtle');
</script>
</html>
 
===Plant 1===
 
<html>
<form><textarea id="inputtext6" rows=3 cols=35 wrap="off" style="width:600px;">
var level = 3;
var axiom = 'F';
var rules = {
    'F' : 'F[+F]F[-F]F',
    '[' : '[',
    ']' : ']',
    '+' : '+',
    '-' : '-'
};
var symbols = { 'F':'F',
                '+':'+',
                '-':'-',
                '[':'[',
                ']':']'
              } ;
             
var angle = 25.7;
var len = 500/Math.pow(3,level);
t.setPos(0,-250);
var shrink = 1.0;
t.setProperty({strokeColor:'green',strokeWidth:2});
</textarea><br />
<input type="button" value="run" onClick="run(6)">
<input type="button" value="clear" onClick="clearturtle(6)">
</form>
<div id="box6" class="jxgbox" style="width:600px; height:600px;"></div>
<script language="JavaScript">
brd[6] = JXG.JSXGraph.initBoard('box6', {originX: 300, originY: 300, unitX: 1, unitY: 1});
turtle[6] = brd[6].createElement('turtle');
</script>
</html>
 
===Plant 2===
 
<html>
<form><textarea id="inputtext7" rows=3 cols=35 wrap="off" style="width:600px;">
var level = 4;
var axiom = 'X';
var rules = {
    'F' : 'FF',
    'X' : 'F-[[X]+X]+F[+FX]-X',
    '[' : '[',
    ']' : ']',
    '+' : '+',
    '-' : '-'
};
var symbols = { 'F':'F',
                'X':' ',
                '+':'+',
                '-':'-',
                '[':'[',
                ']':']'
              } ;
             
var angle = 22.5;
var len = 800/Math.pow(3,level);
t.setPos(0,-250);
t.setProperty({strokeColor:'green',strokeWidth:2});
</textarea><br />
<input type="button" value="run" onClick="run(7)">
<input type="button" value="clear" onClick="clearturtle(7)">
</form>
<div id="box7" class="jxgbox" style="width:600px; height:600px;"></div>
<script language="JavaScript">
brd[7] = JXG.JSXGraph.initBoard('box7', {originX: 300, originY: 300, unitX: 1, unitY: 1});
turtle[7] = brd[7].createElement('turtle');
</script>
</html>
 
===Hexagonal kolam===
 
<html>
<form><textarea id="inputtext8" rows=3 cols=35 wrap="off" style="width:600px;">
var level = 4;
var axiom = 'X';
var rules = {
    'F' : 'F',
    'X' : '[-F+F[Y]+F][+F-F[X]-F]',
    'Y' : '[-F+F[Y]+F][+F-F-F]',
    '[' : '[',
    ']' : ']',
    '+' : '+',
    '-' : '-'
};
var symbols = { 'F':'F',
                'X':' ',
                'Y':' ',
                '+':'+',
                '-':'-',
                '[':'[',
                ']':']'
              } ;
             
var angle = 60;
var len = 300/(level);
t.setPos(0,-250);
</textarea><br />
<input type="button" value="run" onClick="run(8)">
<input type="button" value="clear" onClick="clearturtle(8)">
</form>
<div id="box8" class="jxgbox" style="width:600px; height:600px;"></div>
<script language="JavaScript">
brd[8] = JXG.JSXGraph.initBoard('box8', {originX: 300, originY: 300, unitX: 1, unitY: 1});
turtle[8] = brd[8].createElement('turtle');
</script>
</html>
 
===Mango kolam===
 
<html>
<form><textarea id="inputtext9" rows=3 cols=35 wrap="off" style="width:600px;">
var level = 5;
var axiom = 'A---A';
var rules = {
    'F' : 'F',
    'f' : 'f',
    'A' : 'f-F+Z+F-fA',
    'Z' : 'F-FF-F--[--Z]F-FF-F--F-FF-F--',
    '[' : '[',
    ']' : ']',
    '+' : '+',
    '-' : '-'
};
var symbols = { 'F':'F',
                'f':'f',
                'A':' ',
                'Z':' ',
                '+':'+',
                '-':'-',
                '[':'[',
                ']':']'
              } ;
             
var angle = 60;
var len = 100/(level);
</textarea><br />
<input type="button" value="run" onClick="run(9)">
<input type="button" value="clear" onClick="clearturtle(9)">
</form>
<div id="box9" class="jxgbox" style="width:600px; height:600px;"></div>
<script language="JavaScript">
brd[9] = JXG.JSXGraph.initBoard('box9', {originX: 300, originY: 300, unitX: 1, unitY: 1});
turtle[9] = brd[9].createElement('turtle');
</script>
</html>


 
====More examples====
===Penrose tiling===
* [[Quadratic snowflake variation]]
 
* [[Dragon curve]]
<html>
* [[Islands and lakes]]
<form><textarea id="inputtext10" rows=3 cols=35 wrap="off" style="width:600px;">
* [[Peano curve]]
var level = 2;
* [[Hexagonal Gosper curve]]
var axiom = '[7]++[7]++[7]++[7]++[7]';
* [[Plant generation I]]
var rules = {
* [[Plant generation II]]
    '6' : '81++91----71[-81----61]++',
* [[Hexagonal kolam]]
    '7' : '+81--91[---61--71]+',
* [[Mango kolam]]
    '8' : '-61++71[+++81++91]-',
* [[Penrose tiling]]
    '9' : '--81++++61[+91++++71]--71',
    '1' : '',
    '+' : '+',
    '-' : '-',
    '[' : '[',
    ']' : ']'
  };
var symbols = {
                '1':'F',
                '6':' ',
                '7':' ',
                '8':' ',
                '9':' ',
                '+':'+',
                '-':'-',
                '[':'[',
                ']':']'
              };
var angle = 36.0;
var len = 100/(level);
t.setProperty({fillcolor:'#abff00'});
</textarea><br />
<input type="button" value="run" onClick="run(10)">
<input type="button" value="clear" onClick="clearturtle(10)">
</form>
<div id="box10" class="jxgbox" style="width:600px; height:600px;"></div>
<script language="JavaScript">
brd[10] = JXG.JSXGraph.initBoard('box10', {originX: 300, originY: 300, unitX: 1, unitY: 1});
turtle[10] = brd[10].createElement('turtle');
</script>
</html>


===The underlying JavaScript code===
===The underlying JavaScript code===
Line 497: Line 141:
* [http://en.wikipedia.org/wiki/L-system http://en.wikipedia.org/wiki/L-system]
* [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://en.wikipedia.org/wiki/Space-filling_curve http://en.wikipedia.org/wiki/Space-filling_curve]
* [http://en.wikipedia.org/wiki/Penrose_tiling http://en.wikipedia.org/wiki/Penrose_tiling]
* [http://www.biologie.uni-hamburg.de/b-online/e28_3/lsys.html An Introduction to Lindenmayer Systems]
* [http://en.wikipedia.org/wiki/Kolam http://en.wikipedia.org/wiki/Kolam]




Line 504: Line 147:
[[Category:Fractals]]
[[Category:Fractals]]
[[Category:Turtle Graphics]]
[[Category:Turtle Graphics]]
[[Category:Lindenmayer systems]]

Latest revision as of 07:59, 8 June 2011

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.

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


More examples

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=5223"