JSXGraph
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Rose
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<iframe 
    src="https://www.jsxgraph.uni-bayreuth.de/share/iframe/rose" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Rose" 
    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: [-10, 10, 10, -10],
         keepaspectratio: true
     });
    
     var f = board.create('slider', [[1, 8], [6, 8], [0, 4, 8]]);
     var len = board.create('slider', [[1, 7], [6, 7], [0, 2, 8]], { snapWidth: 0.2, name: 'len' });
     var k = board.create('slider', [[1, 6], [6, 6], [0, 2, 12]], { snapWidth: 1, name: 'k' });
    
     var c = board.create('curve', [
         (phi) => f.Value() * Math.cos(k.Value() * phi), // polar curve term
         [0, 0], // center
         0, // start phi
         () => len.Value() * Math.PI // end phi
    ], { curveType: 'polar', strokewidth: 2 });
 </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: [-10, 10, 10, -10],
     keepaspectratio: true
 });

 var f = board.create('slider', [[1, 8], [6, 8], [0, 4, 8]]);
 var len = board.create('slider', [[1, 7], [6, 7], [0, 2, 8]], { snapWidth: 0.2, name: 'len' });
 var k = board.create('slider', [[1, 6], [6, 6], [0, 2, 12]], { snapWidth: 1, name: 'k' });

 var c = board.create('curve', [
     (phi) => f.Value() * Math.cos(k.Value() * phi), // polar curve term
     [0, 0], // center
     0, // start phi
     () => len.Value() * Math.PI // end phi
], { curveType: 'polar', strokewidth: 2 });
<jsxgraph width="100%" aspect-ratio="1 / 1" title="Rose" 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: [-10, 10, 10, -10],
        keepaspectratio: true
    });
   
    var f = board.create('slider', [[1, 8], [6, 8], [0, 4, 8]]);
    var len = board.create('slider', [[1, 7], [6, 7], [0, 2, 8]], { snapWidth: 0.2, name: 'len' });
    var k = board.create('slider', [[1, 6], [6, 6], [0, 2, 12]], { snapWidth: 1, name: 'k' });
   
    var c = board.create('curve', [
        (phi) => f.Value() * Math.cos(k.Value() * phi), // polar curve term
        [0, 0], // center
        0, // start phi
        () => len.Value() * Math.PI // end phi
   ], { curveType: 'polar', strokewidth: 2 });
</jsxgraph>
A __rose__ or __rhodonea curve__ is a sinusoid plotted in polar coordinates. Up to similarity, these curves can all be expressed by a polar equation of the form $$r=\cos(k\phi).$$ If $k$ is an integer, the curve will be rose shaped with - $2k$ petals if $k$ is even, and - $k$ petals if $k$ is odd. When $k$ is even, the entire graph of the rose will be traced out exactly once when the value of $\phi$ runs from $0$ to $2\pi$. When $k$ is odd, this will happen on the interval between $0$ and$\pi$. (More generally, this will happen on any interval of length $2\pi$ for $k$ even, and $\pi$ for $k$ odd.) The __quadrifolium__ is a type of rose curve with $n=2$ (this is the curve shown initially). It has polar equation: $$r = \cos(2\phi)\,,$$ with corresponding algebraic equation $$(x^2+y^2)^3 = (x^2-y^2)^2.$$
// Define the id of your board in BOARDID

 var board = JXG.JSXGraph.initBoard(BOARDID, {
     axis: true,
     boundingbox: [-10, 10, 10, -10],
     keepaspectratio: true
 });

 var f = board.create('slider', [[1, 8], [6, 8], [0, 4, 8]]);
 var len = board.create('slider', [[1, 7], [6, 7], [0, 2, 8]], { snapWidth: 0.2, name: 'len' });
 var k = board.create('slider', [[1, 6], [6, 6], [0, 2, 12]], { snapWidth: 1, name: 'k' });

 var c = board.create('curve', [
     (phi) => f.Value() * Math.cos(k.Value() * phi), // polar curve term
     [0, 0], // center
     0, // start phi
     () => len.Value() * Math.PI // end phi
], { curveType: 'polar', strokewidth: 2 });

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.