Barnsley fern

Inspired by a Youtube video: Chaos Game - Numberphile

Learn more about how this works at Wikipedia: https://en.wikipedia.org/wiki/Barnsley_fern

<!DOCTYPE html>
<head>
  <meta charset="utf-8">
  <style>
    body { margin:0;position:fixed;top:0;right:0;bottom:0;left:0; }
  </style>
</head>

<body>
  <canvas id="mycanvas" width="960" height="500"></canvas>
  <script>
    var canvas = document.getElementById('mycanvas'),
      ctx      = canvas.getContext('2d'),
      i        = 0,
      dot      = {
        x:         0,
        y:         0,
        hue:       0.001,
        lightness: 0.35
      };

// https://en.wikipedia.org/wiki/Barnsley_fern#Construction
    var barnsley = [
      {a:  0.00, b:  0.00, c:  0.00, d: 0.16, e:  0.00, f:  0.00, p: 0.01},
      {a:  0.85, b:  0.04, c: -0.04, d: 0.85, e:  0.00, f:  1.60, p: 0.01 + 0.85},
      {a:  0.20, b: -0.26, c:  0.23, d: 0.22, e:  0.00, f:  1.60, p: 0.01 + 0.85 + 0.07},
      {a: -0.15, b:  0.28, c:  0.26, d: 0.24, e:  0.00, f:  0.44, p: 0.01 + 0.85 + 0.07 + 0.07}
    ];

// Keep track of how many frames we draw.
    var frames = 0;
    function step() {
      // Stop drawing frames after some limit.
      if (frames++ > 1e3) {
        return;
      }
      // Draw a variable number of points each frame.
      for (var k = 0; k < frames; k++) {
        draw_circle(
          ctx,
          dot.x * 105 + canvas.width / 2,
          dot.y * -49 + canvas.height,
          0.09, // radius
          dot.hue, // hue
          dot.lightness // lightness
        );
        dot = fern_step(dot);
      }
      // Draw another frame.
      window.requestAnimationFrame(step);
    }
    // Draw a frame.
    window.requestAnimationFrame(step);

function draw_circle(ctx, x, y, radius, hue, lightness) {
      ctx.fillRect(x, y, 1, 1);
      var rgb = hslToRgb(hue, 0.75, lightness);
      ctx.fillStyle = 'rgba(' +
        rgb[0] + ',' + rgb[1] + ',' + rgb[2] + ',' + 0.5 +
      ')';
      ctx.fill();
    }

/**
     * https://stackoverflow.com/a/9493060/330558
     *
     * Converts an HSL color value to RGB. Conversion formula
     * adapted from https://en.wikipedia.org/wiki/HSL_color_space.
     * Assumes h, s, and l are contained in the set [0, 1] and
     * returns r, g, and b in the set [0, 255].
     *
     * @param   {number}  h   The hue
     * @param   {number}  s   The saturation
     * @param   {number}  l   The lightness
     * @return  {Array}       The RGB representation
     */
    function hslToRgb(h, s, l){
      var r, g, b;
      if (s == 0) {
        r = g = b = l; // achromatic
      } else {
        var hue2rgb = function hue2rgb(p, q, t) {
          if (t < 0) t += 1;
          if (t > 1) t -= 1;
          if (t < 1/6) return p + (q - p) * 6 * t;
          if (t < 1/2) return q;
          if (t < 2/3) return p + (q - p) * (2/3 - t) * 6;
          return p;
        }
        var q = l < 0.5 ? l * (1 + s) : l + s - l * s;
        var p = 2 * l - q;
        r = hue2rgb(p, q, h + 1/3);
        g = hue2rgb(p, q, h);
        b = hue2rgb(p, q, h - 1/3);
      }
      return [Math.round(r * 255), Math.round(g * 255), Math.round(b * 255)];
    }
  </script>
</body>