Lissajous curves

Lissajous curve (Lissajous figure or Bowditch curve) is the graph of the system of parametric equations

[math]\displaystyle{ x=A\sin(at+\delta),\quad y=B\sin(bt). }[/math]

<jsxgraph board="brd" width="1000" height="500">
var brd = JXG.JSXGraph.initBoard('jxgbox',{axis:true,originX:300,originY:250,unitX:25,unitY:25});
var a = brd.createElement('slider',[[2,8],[6,8],[0,3,6]]); brd.createElement('text',[1,8,'a:']);
var b = brd.createElement('slider',[[2,7],[6,7],[0,2,6]]); brd.createElement('text',[1,7,'b:']);
var A = brd.createElement('slider',[[2,6],[6,6],[0,3,6]]); brd.createElement('text',[1,6,'A:']);
var B = brd.createElement('slider',[[2,5],[6,5],[0,3,6]]); brd.createElement('text',[1,5,'B:']);
var delta = brd.createElement('slider',[[2,4],[6,4],[0,0,Math.PI]]); brd.createElement('text',[1,4,'&delta;:']);

var c = brd.createElement('curve',[
          function(t){return A.Value()*Math.sin(a.Value()*t+delta.Value());},
          function(t){return B.Value()*Math.sin(b.Value()*t);},
          0, 2*Math.PI],{strokeColor:'#aa2233',strokeWidth:3});
</jsxgraph>