Fractal
From AoPSWiki
A fractal is defined as a figure that does not become simpler under any level of magnification.
Mandelbrot set
Probably the most well-known example of a fractal, the Mandelbrot set is the set of all points 
in the complex plane for which the sequence 
is bounded.
File:MandelbrotSet.png
If one were to plot all points in the Mandelbrot set using the complex plane, it would look like this.
