Multiple logarithmic spirals

Eight logarithmic spirals defined by

[math]\displaystyle{ r = ae^{b\theta + k\cdot\pi/4 + \tau}\,. }[/math]

 board = JXG.JSXGraph.initBoard('box1', {boundingbox: [-12, 12, 12, -12]});
 var a = board.create('slider', [[1,-1],[5,-1],[0,0.3,1]], {name:'a'});
 var b = board.create('slider', [[1,-2],[5,-2],[0,0.7,1]], {name:'b'});
 var tau = board.create('slider', [[-5,-3],[5,-3],[0,0,2]], {name:'τ'});
 for (var i=0;i<8;i++) {
   (function(x) { return board.create('curve', [function(phi){return a.Value()*Math.exp(b.Value()*(phi+Math.PI*x*0.25+tau.Value()*Math.PI)); }, [0, 0], -4*Math.PI, 8*Math.PI],
             {curveType:'polar', strokewidth:1});        
   })(i);
 }