CanvasFractalsMath
You've almost certainly seen the Mandelbrot set; it is one of the most famous fractals. Like many fractals it is generated from a fairly simple rule yet yields infinitely complex results.
The basic goal of this project is to write code that generates the Mandelbrot set using the Canvas API. There are lots of bells and whistles you can add after you get the basics down. Play with the colors. See if you can figure out how to pan and zoom so you can explore different parts of the set. If you really want to get fancy, figure out how to render an infinite zoom on a particular point of interest.
There's a bit of math involved in this but I can help you with that when you get started.