Nowhere differentiable continuous function: Difference between revisions

This page shows the graph of the nowhere differentiable, but continuos function

$\displaystyle{ f(x) = \sum_{k=1}^{N} a^k\cos(b^k\pi x), }$

where $\displaystyle{ 0\lt a\lt 1 }$ and $\displaystyle{ ab\gt 1+3/2\pi }$.

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 k, s=0.0, n = N.Value(), aa= a.Value(), bb = b.Value();
for (k=1; k<n; k++) {
s += Math.pow(aa,k)*Math.cos(Math.pow(bb,k)*Math.PI*x);
}
return s;
};
var c = bd.create('functiongraph', [f], {