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Takagi-Landsberg (Blancmange) curve
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<iframe 
    src="https://www.jsxgraph.uni-bayreuth.de/share/iframe/takagi-landsberg-curve" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Takagi-Landsberg (Blancmange) curve" 
    allowfullscreen
></iframe>
This code has to 
<div id="board-0-wrapper" class="jxgbox-wrapper " style="width: 100%; ">
   <div id="board-0" class="jxgbox" style="aspect-ratio: 1 / 1; width: 100%;" data-ar="1 / 1"></div>
</div>

<script type = "text/javascript"> 
    /*
    This example is licensed under a 
    Creative Commons Attribution ShareAlike 4.0 International License.
    https://creativecommons.org/licenses/by-sa/4.0/
    
    Please note you have to mention 
    The Center of Mobile Learning with Digital Technology
    in the credits.
    */
    
    const BOARDID = 'board-0';

     var board = JXG.JSXGraph.initBoard(BOARDID, { axis: true, boundingbox: [-0.05, 16, 1.27, -4] });
     var w = board.create('slider', [[0, 8], [0.8, 8], [0, 0.25, 1.5]], {
         name: 'w',
         snapWidth: 0.01,
         snapValues: [0.5, 0.25],
         snapValueDistance: 0.1
     });
     var N = board.create('slider', [[0, 7], [0.8, 7], [0, 5, 40]], { name: 'N' });
     var s = function(x) { return Math.abs(x - Math.round(x)); };
     var c = board.create('functiongraph', [
         function(x) {
             var n, su, wval;
             su = 0.0;
             wval = w.Value();
             for (n = 0; n < N.Value(); n++) {
                 su += Math.pow(wval, n) * s(Math.pow(2, n) * x);
             }
             return su;
         },
         0, 1], { strokeColor: 'red' });
 </script> 
/*
This example is licensed under a 
Creative Commons Attribution ShareAlike 4.0 International License.
https://creativecommons.org/licenses/by-sa/4.0/

Please note you have to mention 
The Center of Mobile Learning with Digital Technology
in the credits.
*/

const BOARDID = 'your_div_id'; // Insert your id here!

 var board = JXG.JSXGraph.initBoard(BOARDID, { axis: true, boundingbox: [-0.05, 16, 1.27, -4] });
 var w = board.create('slider', [[0, 8], [0.8, 8], [0, 0.25, 1.5]], {
     name: 'w',
     snapWidth: 0.01,
     snapValues: [0.5, 0.25],
     snapValueDistance: 0.1
 });
 var N = board.create('slider', [[0, 7], [0.8, 7], [0, 5, 40]], { name: 'N' });
 var s = function(x) { return Math.abs(x - Math.round(x)); };
 var c = board.create('functiongraph', [
     function(x) {
         var n, su, wval;
         su = 0.0;
         wval = w.Value();
         for (n = 0; n < N.Value(); n++) {
             su += Math.pow(wval, n) * s(Math.pow(2, n) * x);
         }
         return su;
     },
     0, 1], { strokeColor: 'red' });
<jsxgraph width="100%" aspect-ratio="1 / 1" title="Takagi-Landsberg (Blancmange) curve" description="This construction was copied from JSXGraph examples database: BTW HERE SHOULD BE A GENERATED LINKuseGlobalJS="false">
   /*
   This example is licensed under a 
   Creative Commons Attribution ShareAlike 4.0 International License.
   https://creativecommons.org/licenses/by-sa/4.0/
   
   Please note you have to mention 
   The Center of Mobile Learning with Digital Technology
   in the credits.
   */
   
    var board = JXG.JSXGraph.initBoard(BOARDID, { axis: true, boundingbox: [-0.05, 16, 1.27, -4] });
    var w = board.create('slider', [[0, 8], [0.8, 8], [0, 0.25, 1.5]], {
        name: 'w',
        snapWidth: 0.01,
        snapValues: [0.5, 0.25],
        snapValueDistance: 0.1
    });
    var N = board.create('slider', [[0, 7], [0.8, 7], [0, 5, 40]], { name: 'N' });
    var s = function(x) { return Math.abs(x - Math.round(x)); };
    var c = board.create('functiongraph', [
        function(x) {
            var n, su, wval;
            su = 0.0;
            wval = w.Value();
            for (n = 0; n < N.Value(); n++) {
                su += Math.pow(wval, n) * s(Math.pow(2, n) * x);
            }
            return su;
        },
        0, 1], { strokeColor: 'red' });
</jsxgraph>

Takagi-Landsberg (Blancmange) curve

Curves
The *blancmange* function is defined on the unit interval by $${\rm blanc}(x) = \sum_{n=0}^\infty {s(2^{n}x)\over 2^n},$$ where $s(x)$ is defined by $s(x)=\min_{n\in\mathbb{Z}}|x-n|$. That is, $s(x)$ is the distance from $x$ to the nearest integer. The infinite sum defining ${\rm blanc}(x)$ converges absolutely for all $x$, but the resulting curve is a fractal. The *blancmange* function is continuous but nowhere differentiable. The Takagi–Landsberg curve is a slight generalization, given by $$T_w(x) = \sum_{n=0}^\infty w^n s(2^{n}x)$$ for a parameter $w$; thus the *blancmange* curve is the special case $w = 1 / 2$. For $w = 1 / 4$, one obtains the parabola: the construction of the parabola by midpoint subdivision was described by Archimedes.
// Define the id of your board in BOARDID

 var board = JXG.JSXGraph.initBoard(BOARDID, { axis: true, boundingbox: [-0.05, 16, 1.27, -4] });
 var w = board.create('slider', [[0, 8], [0.8, 8], [0, 0.25, 1.5]], {
     name: 'w',
     snapWidth: 0.01,
     snapValues: [0.5, 0.25],
     snapValueDistance: 0.1
 });
 var N = board.create('slider', [[0, 7], [0.8, 7], [0, 5, 40]], { name: 'N' });
 var s = function(x) { return Math.abs(x - Math.round(x)); };
 var c = board.create('functiongraph', [
     function(x) {
         var n, su, wval;
         su = 0.0;
         wval = w.Value();
         for (n = 0; n < N.Value(); n++) {
             su += Math.pow(wval, n) * s(Math.pow(2, n) * x);
         }
         return su;
     },
     0, 1], { strokeColor: 'red' });

license

This example is licensed under a Creative Commons Attribution ShareAlike 4.0 International License.
Please note you have to mention The Center of Mobile Learning with Digital Technology in the credits.