If you're studying HTML5, the next thing to try is to execute the Mandelbrot iterations on the GPU with WebGL - GPUs are very well suited for fractal rendering; with a beefy GPU you should find you can render at 60fps
This is a project I created in my spare time to practice implementing various HTML5 features such as canvas element, web workers, touch events, etc. I also use the experimental asm.js for performance enhancement, which works best in Firefox, for now.
This draws beautiful fractals, such as the Mandelbrot fractal.
You aren't the only one who thought that. Dr. Michael Barnsley (http://en.wikipedia.org/wiki/Michael_Barnsley) was an early fractal researcher and started a company called "Iterated Systems" to commercialize the use of fractal compress tech. They were somewhat successful, but I think they were a bit before their time as finding the IFS to "compress" an image was computationally extremely heavyweight and the tech had to catch up with the theory. Disclaimer: I worked in Dr. Barnsley's lab at Georgia Tech in the mid-80s but was never involved with Iterated Systems.
If you're studying HTML5, the next thing to try is to execute the Mandelbrot iterations on the GPU with WebGL - GPUs are very well suited for fractal rendering; with a beefy GPU you should find you can render at 60fps
https://www.shadertoy.com/view/4df3Rn
(if it's a little slow, on line 5 set 'AA' to 1)