Mandelbrot set

You are encouraged to solve this task according to the task description, using any language you may know.


Task

Generate and draw the Mandelbrot set.



Note that there are many algorithms to draw Mandelbrot set and there are many functions which generate it .




function mandelIter(cx, cy, maxIter) {
  var x = 0.0;
  var y = 0.0;
  var xx = 0;
  var yy = 0;
  var xy = 0;
 
  var i = maxIter;
  while (i-- && xx + yy <= 4) {
    xy = x * y;
    xx = x * x;
    yy = y * y;
    x = xx - yy + cx;
    y = xy + xy + cy;
  }
  return maxIter - i;
}
 
function mandelbrot(canvas, xmin, xmax, ymin, ymax, iterations) {
  var width = canvas.width;
  var height = canvas.height;
 
  var ctx = canvas.getContext('2d');
  var img = ctx.getImageData(0, 0, width, height);
  var pix = img.data;
 
  for (var ix = 0; ix < width; ++ix) {
    for (var iy = 0; iy < height; ++iy) {
      var x = xmin + (xmax - xmin) * ix / (width - 1);
      var y = ymin + (ymax - ymin) * iy / (height - 1);
      var i = mandelIter(x, y, iterations);
      var ppos = 4 * (width * iy + ix);
 
      if (i > iterations) {
        pix[ppos] = 0;
        pix[ppos + 1] = 0;
        pix[ppos + 2] = 0;
      } else {
        var c = 3 * Math.log(i) / Math.log(iterations - 1.0);
 
        if (c < 1) {
          pix[ppos] = 255 * c;
          pix[ppos + 1] = 0;
          pix[ppos + 2] = 0;
        }
        else if ( c < 2 ) {
          pix[ppos] = 255;
          pix[ppos + 1] = 255 * (c - 1);
          pix[ppos + 2] = 0;
        } else {
          pix[ppos] = 255;
          pix[ppos + 1] = 255;
          pix[ppos + 2] = 255 * (c - 2);
        }
      }
      pix[ppos + 3] = 255;
    }
  }
 
  ctx.putImageData(img, 0, 0);
}
 
var canvas = document.createElement('canvas');
canvas.width = 900;
canvas.height = 600;
 
document.body.insertBefore(canvas, document.body.childNodes[0]);
 
mandelbrot(canvas, -2, 1, -1, 1, 1000);