# Difference between revisions of "Nowhere differentiable continuous function"

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this.bArr = [1.0*Math.PI]; | this.bArr = [1.0*Math.PI]; | ||

for (k=1; k<this.n; k++) { | for (k=1; k<this.n; k++) { | ||

− | this.aArr[k] = this.aArr[k-1]*aa; | + | this.aArr[k] = this.aArr[k-1]*this.aa; |

− | this.bArr[k] = this.bArr[k-1]*bb; | + | this.bArr[k] = this.bArr[k-1]*this.bb; |

} | } | ||

} | } |

## Revision as of 20:58, 22 September 2011

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

- [math] f(x) = \sum_{k=1}^{N} a^k\cos(b^k\pi x), [/math]

where [math]0\lta\lt1[/math] and [math]ab\gt1+3/2\pi[/math].

### 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], {
doAdvancedPlot:false,
numberPointsHigh:15000, numberPointsLow:1000,
strokeWidth:1});
```