Raymarching

This is a technique which allows the rendering of 3D scenes in a 2D fragment shader.

You can learn more about this technique on Iñigo Quilez's site. The dude is awesome (except his comments on cyclists, of course).

Fractals

Fractals allow you to generate epic images with only some lines of math & code.

To get started with the math, you can start with Wikipedia: Mandelbrot fractal.

For the mandelbrot set, you just need a for loop and some complex number knowledge (You will have to google things like "how to take the exponent of a complex number", no need to actually learn anything).

Pro tip: Try using a vec2 to store the complex number, myvec.x will be the real part and myvec.y will be the imaginary part.