Mandelbrot set using a HTML5 canvas and a JavaScript object

Mandelbrot data

r min:

r max:

i min:

i max:

Zoom increment:

Max iterations:

Colour options





Click the left-hand mouse button on the graphic to zoom in. Hold down either shift, ctrl or alt when clicking to zoom out. You can also zoom out by setting the zoom value to less than 1.0.

Move first two sliders to change the amount of zoom per click and also the maximum number of iterations carried out for each pixel. A larger number of iterations may be required as you zoom in to the fractal.

The next three sliders control the overall colour of the fractal. Moving these will immediately change the colour of the fractal.


The Mandelbrot set is an example of a fractal. It is calculated by taking a complex number, c, and iterating it using the expression zn+1 = zn2 + c, where z0 is zero. For each possible value of c the result of the iteration either remains small no matter how many iterations are carried out, or becomes large. The result is considered large if the magnitude of z exceeds a value of 4.

Each pixel in the image represents a particular complex number. The colour of each pixel is determined by how many iterations it has undergone. Only the pixels with a magnitude below 4 continue to be iterated. Here the fractal is redrawn after each iteration, and the JavaScript has been written by defining a Mandelbrot object with associated properties and methods. It seems that this is faster than the functional or procedural methods I used to begin with.

Code snippets

I found it a bit tricky to work out how to update the canvas after each iteration. To begin with I put the iteration and draw commands inside a for loop, but this only updated the canvas at the end of the loop. The solution was to use the setInterval command. The function specified by this command is repeatidly run until the clearInterval command is called. The canvas can be successfully updated within the function that is called. The setInterval command is used on line 4 in the startCalculating function below.

In this case it is the function progress (line 7) that is called by the setInterval command. The progress function iterates the fractal and draws it on the canvas until the maximum number of iterations has been reached. At this point the progress function runs the clearInterval command to cancel the calling of progress (line 11).

	function startCalculating() {
	   calculating = setInterval(progress, 0);

	function progress() {
	   if (mandelbrot.numIterations <= mandelbrot.maxIterations) {
	   } else clearInterval(calculating);