He could solve algebra problems by thinking about how the problems looked, rather than the algebraic method of solving those problems. A fractal is not a Euclidean geometrical shape. A better definition of a fractal, is something that lets you see infinity- for example, you get an idea of infinity when you stand between two mirrors. Fractals are everywhere in nature, if you look for them. They are found in earthquakes, hurricanes, and fluid dynamics.
Clouds are the same on different scales, and even blood vessels branch out fractally.
The Koch Snowflake is an example of a fractal. It is a triangle, with triangles connected to each side of that triangle, triangles attached to each side of that one, ad infinitum. The Mandelbrot set, considered by Mandelbrot himself to be even more fractal than fractals, is probably one of the most complicated mathematical problems in existence. The image that is produced when this is graphed is extremely complicated, and is similar, but not quite the same, on every scale. Lev D. Landau had a theory about fluid dynamics, that when energy is introduced into a system, each frequency is incompatible with the last and the system gets more and more complicated.