Lissajous

<!DOCTYPE html>
<head>
  <meta charset="utf-8">
  <script src="https://d3js.org/d3.v4.min.js"></script>
  <style>
    body { margin:0;position:fixed;top:0;right:0;bottom:0;left:0; }
    
    path {
      stroke: black;
      fill: none;
    }
  </style>
</head>

<label>R</label>
  <input type="text" placeholder="R" id="R">
  <svg width="960" height="500"></svg>
  <script>
    var svg = d3.select('svg'),
        width = +svg.attr('width'),
        height = +svg.attr('height');
    
    // x = Asin(at + δ), y = Bsin(bt)
    
    var inputs = {
      A: 1,
      B: 1,
      c: 1,
      d: 1,
      δ: Math.PI / 2,
      
      R: Math.min(width, height) / 8,
    };
    Object.keys(inputs).forEach(function (input) {
			d3.select('input#' + input).node().placeholder = inputs[input];
    });
    var PRECISION = 360 * 2;
    
    var lissajous = function (A, B, a, b, δ) {
      return function (t) {
        return [A * Math.sin(a*t + δ), B * Math.sin(b*t)];
      };
    };
    
    var path = function () {
      var f = lissajous(inputs.A, inputs.B, inputs.c, inputs.d, inputs.δ),
          g = function (t) {
            var [x, y] = f(t);
            return [inputs.R * x, inputs.R * y];
          };
      
      var pts = d3.range(0, Math.PI * 2, Math.PI * 2 / PRECISION).map(g);
      
      return 'M' + pts.join('L');
    };
    
    var tgt = svg.append('g')
      .attr('transform', 'translate(' + (width / 2) + ',' + (height / 2) + ')')
    	.append('path');
    
    d3.timer(function () {
    	Object.keys(inputs).forEach(function (input) {
        var ud = d3.select('input#' + input).node().value;
        
        inputs[input] = ud !== '' ? +ud : inputs[input];
      });
      
      inputs.δ += 0.01;
      if (inputs.δ > Math.PI) { inputs.δ -= Math.PI * 2; }
      d3.select('input#δ').node().placeholder = inputs.δ;
      tgt.attr('d', path());
    });

</script>
</body>

https://d3js.org/d3.v4.min.js