Nowhere differentiable continuous function

Reference

Wei-Chi Yang, "Technology has shaped up mathematics comunities", Proceedings of the Sixteenth Asian Technology Conference in Mathmatics (ATCM 16), pp 81-96.

The underlying JavaScript code

 var bd = JXG.JSXGraph.initBoard('box', {axis:true, boundingbox: [-5, 3, 5, -3]});
 var a = bd.create('slider', [[0.5,2],[2.5,2],[0,0.3,1]], {name:'a'});
 var b = bd.create('slider', [[0.5,1.5],[2.5,1.5],[0,20,100]], {name:'b'}); 
 var N = bd.create('slider', [[0.5,1.0],[2.5,1.0],[0,2,30]], {name:'N'}); 
 var f = function(x){
            var i, s=0.0, n = N.Value(), aa= a.Value(), bb = b.Value(); 
            for (i=0; i<n; i++) {
                s += Math.pow(aa,i)*Math.cos(Math.pow(bb,i)*Math.PI*x);
            }
            return s;
         };
 var c = bd.create('functiongraph', [f], {
                    doAdvancedPlot:false, 
                    numberPointsHigh:15000, numberPointsLow:1000, 
                    strokeWidth:1});