Nowhere differentiable continuous function - Revision history

A WASSERMANN at 15:11, 14 January 2021

2021-01-14T15:11:56Z

← Older revision		Revision as of 15:11, 14 January 2021
Line 3:		Line 3:
	:<math> f(x) = \sum_{k=1}^{N} a^k\cos(b^k\pi x), </math>		:<math> f(x) = \sum_{k=1}^{N} a^k\cos(b^k\pi x), </math>

	where <math>0<a<1</math> and <math>ab>1+3/2\pi</math>.		where <math>0< a <1</math> and <math>ab>1+3/2\pi</math>.
	<jsxgraph width="500" height="500" box="box">		<jsxgraph width="500" height="500" box="box">
	(function(){		(function(){

A WASSERMANN at 19:14, 22 September 2011

2011-09-22T19:14:24Z

@@ Line 1: / Line 1: @@
-This page shows the graph of the nowhere differentiable, but continuos function
+This page shows the graph of the nowhere differentiable, but continuous function
 :<math> f(x) = \sum_{k=1}^{N} a^k\cos(b^k\pi x), </math>
@@ Line 44: / Line 44: @@
 </source>
-=== Speed optimization ===
+== Speed optimization ==
 <jsxgraph width="500" height="500" box="box2">
@@ Line 55: / Line 55: @@
              var k, s=0.0;
              if (!suspendedUpdate) {
                  this.n = N.Value();
                  this.aa= a.Value();
@@ Line 75: / Line 74: @@
 </jsxgraph>
 [[Category:Examples]]
 [[Category:Curves]]

A WASSERMANN at 19:02, 22 September 2011

2011-09-22T19:02:29Z

← Older revision		Revision as of 19:02, 22 September 2011
Line 55:		Line 55:
	var k, s=0.0;		var k, s=0.0;
	if (!suspendedUpdate) {		if (!suspendedUpdate) {
			console.log("doit");
	this.n = N.Value();		this.n = N.Value();
	this.aa= a.Value();		this.aa= a.Value();

A WASSERMANN at 18:58, 22 September 2011

2011-09-22T18:58:47Z

← Older revision		Revision as of 18:58, 22 September 2011
Line 61:		Line 61:
	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;
	}		}
	}		}

A WASSERMANN at 18:57, 22 September 2011

2011-09-22T18:57:57Z

← Older revision		Revision as of 18:57, 22 September 2011
Line 57:		Line 57:
	this.n = N.Value();		this.n = N.Value();
	this.aa= a.Value();		this.aa= a.Value();
	this.bb = b.Value();		this.bb = b.Value();
			this.aArr = [1.0];
			this.bArr = [1.0*Math.PI];
			for (k=1; k<this.n; k++) {
			this.aArr[k] = this.aArr[k-1]*aa;
			this.bArr[k] = this.bArr[k-1]*bb;
			}
	}		}
	for (k=1; k<this.n; k++) {		for (k=1; k<this.n; k++) {
	s += ~~Math.pow(~~this.~~aa,~~k)Math.cos~~(Math.pow~~(this.~~bb,~~k~~)Math.PI~~*x);		s += this.aArr[k]Math.cos(this.bArr[k]x);
	}		}
	return s;		return s;

A WASSERMANN at 18:53, 22 September 2011

2011-09-22T18:53:35Z

← Older revision		Revision as of 18:53, 22 September 2011
Line 53:		Line 53:
	var N = bd.create('slider', [[0.5,1.0],[2.5,1.0],[0,2,30]], {name:'N'});		var N = bd.create('slider', [[0.5,1.0],[2.5,1.0],[0,2,30]], {name:'N'});
	var f = function(x, suspendedUpdate){		var f = function(x, suspendedUpdate){
	var k, s=0.0~~, n, aa, bb~~;		var k, s=0.0;
	if (!suspendedUpdate) {		if (!suspendedUpdate) {
	n = N.Value();		this.n = N.Value();
	aa= a.Value();		this.aa= a.Value();
	bb = b.Value();		this.bb = b.Value();
	}		}
	for (k=1; k<n; k++) {		for (k=1; k<this.n; k++) {
	s += Math.pow(aa,k)Math.cos(Math.pow(bb,k)Math.PI*x);		s += Math.pow(this.aa,k)Math.cos(Math.pow(this.bb,k)Math.PI*x);
	}		}
	return s;		return s;

A WASSERMANN at 18:52, 22 September 2011

2011-09-22T18:52:01Z

← Older revision		Revision as of 18:52, 22 September 2011
Line 5:		Line 5:
	where <math>0<a<1</math> and <math>ab>1+3/2\pi</math>.		where <math>0<a<1</math> and <math>ab>1+3/2\pi</math>.
	<jsxgraph width="500" height="500" box="box">		<jsxgraph width="500" height="500" box="box">
			(function(){
	var bd = JXG.JSXGraph.initBoard('box', {axis:true, boundingbox: [-5, 3, 5, -3]});		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 a = bd.create('slider', [[0.5,2],[2.5,2],[0,0.3,1]], {name:'a'});
Line 17:		Line 18:
	};		};
	var c = bd.create('functiongraph', [f], {doAdvancedPlot:false, numberPointsHigh:6000, numberPointsLow:500, strokeWidth:1});		var c = bd.create('functiongraph', [f], {doAdvancedPlot:false, numberPointsHigh:6000, numberPointsLow:500, strokeWidth:1});
			})();
	</jsxgraph>		</jsxgraph>

Line 45:		Line 47:

	<jsxgraph width="500" height="500" box="box2">		<jsxgraph width="500" height="500" box="box2">
			(function(){
	var bd = JXG.JSXGraph.initBoard('box2', {axis:true, boundingbox: [-5, 3, 5, -3]});		var bd = JXG.JSXGraph.initBoard('box2', {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 a = bd.create('slider', [[0.5,2],[2.5,2],[0,0.3,1]], {name:'a'});
Line 62:		Line 65:
	};		};
	var c = bd.create('functiongraph', [f], {doAdvancedPlot:false, numberPointsHigh:6000, numberPointsLow:500, strokeWidth:1});		var c = bd.create('functiongraph', [f], {doAdvancedPlot:false, numberPointsHigh:6000, numberPointsLow:500, strokeWidth:1});
			})();
	</jsxgraph>		</jsxgraph>

	[[Category:Examples]]		[[Category:Examples]]
	[[Category:Curves]]		[[Category:Curves]]

A WASSERMANN at 18:50, 22 September 2011

2011-09-22T18:50:42Z

@@ Line 42: / Line 42: @@
 </source>
 [[Category:Examples]]
 [[Category:Curves]]

A WASSERMANN at 14:59, 22 September 2011

2011-09-22T14:59:47Z

← Older revision		Revision as of 14:59, 22 September 2011
Line 16:		Line 16:
	return s;		return s;
	};		};
	var c = bd.create('functiongraph', [f], {doAdvancedPlot:false, numberPointsHigh:~~8000~~, numberPointsLow:500, strokeWidth:1});		var c = bd.create('functiongraph', [f], {doAdvancedPlot:false, numberPointsHigh:6000, numberPointsLow:500, strokeWidth:1});
	</jsxgraph>		</jsxgraph>

A WASSERMANN at 14:59, 22 September 2011

2011-09-22T14:59:15Z

← Older revision		Revision as of 14:59, 22 September 2011
Line 16:		Line 16:
	return s;		return s;
	};		};
	var c = bd.create('functiongraph', [f], {doAdvancedPlot:false, numberPointsHigh:~~5000~~, numberPointsLow:500, strokeWidth:1});		var c = bd.create('functiongraph', [f], {doAdvancedPlot:false, numberPointsHigh:8000, numberPointsLow:500, strokeWidth:1});
	</jsxgraph>		</jsxgraph>