I don't think programming fractals will teach you anything in particular. Depending on the fractal, I suppose it might teach you a bit about math or fractals in general.
However, I do think fractals are fun as an introduction to programming, and beginners/students are often fascinated by the result, be it more graphic fractals like mandelbrot or julia sets, or more easy to understand L-systems.
Of course, if you're new to programming, it'll also hopefully teach you a lot about programming in general. If nothing else, fractals are interesting to look at.
