JSXGraph
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Spirograph
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<iframe 
    src="https://www.jsxgraph.uni-bayreuth.de/share/iframe/spirograph" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Spirograph" 
    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,{boundingbox:[-5,5,5,-5], keepaspectratio: true});
    var R = 2.0;
    var r = board.create('slider',[[-3,4],[3,4],[-5,1,5]],{name:'r'});
    var a = board.create('slider',[[-3,3],[3,3],[-5,1,5]],{name:'a'});
    
    var c = board.create('curve',[
         function(t){ 
            var r1 = Math.round(100.0*r.Value())/100.0; 
            var a1 = Math.round(100.0*a.Value())/100.0; 
            return (R-r1)*Math.cos(r1/R*t)+a1*Math.cos((1-r1/R)*t); 
         },
         function(t){ 
            var r1 = Math.round(100.0*r.Value())/100.0; 
            var a1 = Math.round(100.0*a.Value())/100.0; 
            return (R-r1)*Math.sin(r1/R*t)+a1*Math.sin((1-r1/R)*t); 
         }, 
         -40*Math.PI,40*Math.PI
         ], {strokeWidth:3, strokeColor:'#3355ff', strokeOpacity:0.7});
 </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,{boundingbox:[-5,5,5,-5], keepaspectratio: true});
var R = 2.0;
var r = board.create('slider',[[-3,4],[3,4],[-5,1,5]],{name:'r'});
var a = board.create('slider',[[-3,3],[3,3],[-5,1,5]],{name:'a'});

var c = board.create('curve',[
     function(t){ 
        var r1 = Math.round(100.0*r.Value())/100.0; 
        var a1 = Math.round(100.0*a.Value())/100.0; 
        return (R-r1)*Math.cos(r1/R*t)+a1*Math.cos((1-r1/R)*t); 
     },
     function(t){ 
        var r1 = Math.round(100.0*r.Value())/100.0; 
        var a1 = Math.round(100.0*a.Value())/100.0; 
        return (R-r1)*Math.sin(r1/R*t)+a1*Math.sin((1-r1/R)*t); 
     }, 
     -40*Math.PI,40*Math.PI
     ], {strokeWidth:3, strokeColor:'#3355ff', strokeOpacity:0.7});
<jsxgraph width="100%" aspect-ratio="1 / 1" title="Spirograph" 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,{boundingbox:[-5,5,5,-5], keepaspectratio: true});
   var R = 2.0;
   var r = board.create('slider',[[-3,4],[3,4],[-5,1,5]],{name:'r'});
   var a = board.create('slider',[[-3,3],[3,3],[-5,1,5]],{name:'a'});
   
   var c = board.create('curve',[
        function(t){ 
           var r1 = Math.round(100.0*r.Value())/100.0; 
           var a1 = Math.round(100.0*a.Value())/100.0; 
           return (R-r1)*Math.cos(r1/R*t)+a1*Math.cos((1-r1/R)*t); 
        },
        function(t){ 
           var r1 = Math.round(100.0*r.Value())/100.0; 
           var a1 = Math.round(100.0*a.Value())/100.0; 
           return (R-r1)*Math.sin(r1/R*t)+a1*Math.sin((1-r1/R)*t); 
        }, 
        -40*Math.PI,40*Math.PI
        ], {strokeWidth:3, strokeColor:'#3355ff', strokeOpacity:0.7});
</jsxgraph>

Spirograph

Curves
Interactive parametric curve (epicycloid/hypotrochoid) with sliders *r* and *a* controlling radius and amplitude. Drawn on a \[-5,5] board, using $$x(t)=(R-r)\cos(r/R t)+a\cos((1-r/R)t),$$ $$y(t)=(R-r)\sin(r/R t)+a\sin((1-r/R)t)$$ for $t\in[-40\pi,40\pi]$. 
// Define the id of your board in BOARDID

var board = JXG.JSXGraph.initBoard(BOARDID,{boundingbox:[-5,5,5,-5], keepaspectratio: true});
var R = 2.0;
var r = board.create('slider',[[-3,4],[3,4],[-5,1,5]],{name:'r'});
var a = board.create('slider',[[-3,3],[3,3],[-5,1,5]],{name:'a'});

var c = board.create('curve',[
     function(t){ 
        var r1 = Math.round(100.0*r.Value())/100.0; 
        var a1 = Math.round(100.0*a.Value())/100.0; 
        return (R-r1)*Math.cos(r1/R*t)+a1*Math.cos((1-r1/R)*t); 
     },
     function(t){ 
        var r1 = Math.round(100.0*r.Value())/100.0; 
        var a1 = Math.round(100.0*a.Value())/100.0; 
        return (R-r1)*Math.sin(r1/R*t)+a1*Math.sin((1-r1/R)*t); 
     }, 
     -40*Math.PI,40*Math.PI
     ], {strokeWidth:3, strokeColor:'#3355ff', strokeOpacity:0.7});

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.