Another thing I find fascinating is fractals, particularly those that occur naturally in the world. For those that don't know much about fractals, let me save you the effort of typing it into Google.
While mostly associated with the Mandelbrot set, they're actually found all over the world in nature. From river networks to crystal formations to trees to snowflakes, fractals are all around us. Also technically coastlines are fractals as well. Here are some cool pics from http://paulbourke.net/fractals/googleearth/ and Google