It is much more about programming, than math. You can find equations that produce fractal designs easily. The trick is writing the program that graphs, colors, zooms, rotates, etc.

I would say that you do need to be a math major, and have taken calculus (I,II and III), linear algebra (a must), differential equations. But you also need to know how to program. C++ and java are probably the best languages for what you want.