Fractal Definition: A geometric pattern that is repeated (iterated) at ever smaller (or larger) scales to produce (self similar) irregular shapes and surfaces that cannot be represented by classical (Euclidian) geometry.
A fractal is a geometric shape that has symmetry of scale. This means that it is a shape that you could zoom in on a part of it an infinite number of times and it would still look the same. This is also called self-similarity. Computer-generated fractals are produced mathematically, and these can create detailed pictures of mountains, plants, waves, and planets. Some mathematicians, such as Benoit Mandelbrot, study nature first, looking for fractal behavior.