http://gbrlgrct.com/gists/53e9405a69ad5922c3ed/mandelbrot.html

## mandelbrot.html
<body style="margin:0"></body>

<script>

var CLICKZOOM = 3;
var NUMWORKERS = 8;

var workers = (function () {
  var w = [];

  for (var i = 0; i < NUMWORKERS; ++i)
    w.push(new Worker('worker.js'));

  return w;
})();

function sendWorkerDraw(i /* args */) {
  var args = [].slice.call(arguments, 1);

  return new Promise(function (resolve) {
    var worker = workers[i];

    worker.addEventListener('message', function done(ev) {
      worker.removeEventListener('message', done);

      resolve(ev.data.buf);
    });

    worker.postMessage({
      args: args
    });
  });
}

function draw(i, ctx, drawX, drawY, screenX, screenY, screenW, screenH, scale, maxiter) {
  sendWorkerDraw(i, screenX, screenY, screenW, screenH, scale, maxiter)
    .then(function (buf) {
      var arr  = new Uint8ClampedArray(buf);
      var data = new ImageData(arr, screenW, screenH);

      ctx.putImageData(data, drawX, drawY);
    });
}

function mandelbrot(canvas, planeX, planeY, scale, maxiter) {
  var SCALE   = scale;
  var MAXITER = maxiter;

  var ISCALE = 1 / scale;

  var PLANEX = planeX;
  var PLANEY = planeY;

  var SCREENX = PLANEX * SCALE;
  var SCREENY = PLANEY * SCALE;

  var SCREENW = canvas.width;
  var SCREENH = canvas.height;

  var PLANEW = SCREENW * ISCALE;
  var PLANEH = SCREENH * ISCALE;

  var ctx = canvas.getContext('2d');

  canvas.addEventListener('click', function zoom(ev) {
    canvas.removeEventListener('click', zoom);

    var px = ev.offsetX;
    var py = ev.offsetY;

    var scale_    = CLICKZOOM * SCALE;
    var maxiters_ = 1.4 * MAXITER;

    var planeW_ = SCREENW / scale_;
    var planeH_ = SCREENH / scale_;

    var planeX_ = PLANEX + px * ISCALE - planeW_ / 2;
    var planeY_ = PLANEY + py * ISCALE - planeH_ / 2;

    planeX_ += (SCREENW / 2 - px) / scale_;
    planeY_ += (SCREENH / 2 - py) / scale_;

    var copyW = SCREENW / CLICKZOOM;
    var copyH = SCREENH / CLICKZOOM;

    var copyX = px - copyW / 2;
    var copyY = py - copyH / 2;

    copyX += (SCREENW / 2 - px) / CLICKZOOM;
    copyY += (SCREENH / 2 - py) / CLICKZOOM;

    ctx.drawImage(
      canvas,
      copyX, copyY, copyW, copyH,
      0, 0, SCREENW, SCREENH
    );

    mandelbrot(canvas, planeX_, planeY_, scale_, maxiters_);
  });

  var BLOCKY = Math.ceil(SCREENH / NUMWORKERS);

  for (var i = 0; i < NUMWORKERS; ++i) {
    draw(
      i,

      ctx,
      0,
      i * SCREENH / NUMWORKERS,

      SCREENX,
      SCREENY + i * BLOCKY,
      SCREENW,
      BLOCKY,

      SCALE,
      MAXITER
    );
  }

  return canvas;
}

window.addEventListener('load', function () {
  var SCREENW = document.body.clientWidth
  var SCREENH = document.body.clientHeight;

  var canvas = document.createElement('canvas');
  canvas.width  = SCREENW;
  canvas.height = SCREENH;
  canvas.style.background = 'black';

  document.body.appendChild(canvas);

  var DOMAINX = -2.5;
  var DOMAINY = -1.1;

  var DOMAINW = 3.5;
  var DOMAINH = 2.2;

  var scale = Math.min(
    SCREENW / DOMAINW,
    SCREENH / DOMAINH
  );

  var startX = DOMAINX - (SCREENW - DOMAINW * scale) / 2 / scale;
  var startY = DOMAINY - (SCREENH - DOMAINH * scale) / 2 / scale;

  mandelbrot(canvas, startX, startY, scale, 100);
});

</script>

## worker.js
var last = 0;

onmessage = function (ev) {
  var result = draw.apply(null, ev.data.args);

  var buf = result.buffer;

  postMessage({
    buf: buf
  }, [buf]);
};

// inspired by https://www.shadertoy.com/view/4df3Rn
function draw(screenX, screenY, screenW, screenH, scale, maxiter) {
  var SCALE   = scale;
  var MAXITER = maxiter;

  var ISCALE = 1 / scale;

  var SCREENX = screenX;
  var SCREENY = screenY;

  var SCREENW = screenW;
  var SCREENH = screenH;

  var PLANEX = screenX * ISCALE;
  var PLANEY = screenY * ISCALE;

  var PLANEW = screenW * ISCALE;
  var PLANEH = screenH * ISCALE;

  var output = new Uint8ClampedArray(4 * SCREENW * SCREENH);

  for (var py = 0; py < SCREENH; ++py) {
    for (var px = 0; px < SCREENW; ++px) {
      var x0 = PLANEX + px * ISCALE;
      var y0 = PLANEY + py * ISCALE;
      var x = 0;
      var y = 0;

      var it = 0;
      var runaway = false;
      var dot = 0;

      for (var i = 0; i < MAXITER; ++i) {
        var x2 = x * x;
        var y2 = y * y;
        dot = x2 + y2;

        if (dot > 4.0) {
          it = i;
          runaway = true;
          break;
        }

        var xtmp = x2 - y2 + x0;
        y = 2*x*y + y0;
        x = xtmp;
      }

      var ix = 4 * (py * SCREENW + px);

      if (runaway) {
        var ip = i - Math.log2(Math.log2(dot * dot)) + 4.0;

        output[ix + 0] = 255 * (0.5 + 0.5 * Math.cos(3.0 + ip*0.15 + 0.0));
        output[ix + 1] = 255 * (0.5 + 0.5 * Math.cos(3.0 + ip*0.15 + 0.6));
        output[ix + 2] = 255 * (0.5 + 0.5 * Math.cos(3.0 + ip*0.15 + 1.0));
        output[ix + 3] = 255;
      } else {
        output[ix + 0] = 0;
        output[ix + 1] = 0;
        output[ix + 2] = 0;
        output[ix + 3] = 255;
      }
    }
  }

  return output;
}