As part of my University course we had to use the scientific MATLAB programming language, and computing environment, for several tasks in the first year. While the set tasks were as drab and dreary as you would expect from a Physics course, it taught us the basic skills and the problem solving skills key to the course.
In my spare time I ported a PHP script my friend created to MATLAB which enables the creation of beautiful fractals from the Mandlebrot set. The maximum image size you can create depends on the amount of memory available in your system and the script isn’t something I’ve spent a lot of time on so feel free to improve on it.
On my laptop, a 10,000 x 10,000 pixel image took about an hour to create, using 20 iterations. You may find this differs on other machines.
Download the MATLAB Fractal Generator Code.