For starters though, fractals are rough or fragmented geometric shapes that can be subdivided into parts. Each part is (at least approximately) a reduced-size copy of the whole. Generally speaking, fractals are self-similar and independent of scale, but of course there are exceptions that we may get into later.

The self-repeating nature of fractal art is especially apparent in these examples from a digital art fair held by the Fractal Alhambra Project.

According to Mandelbrot, who invented the word: "I coined fractal from the Latin adjective fractus. The corresponding Latin verb frangere means "to break:" to create irregular fragments. It is therefore sensible - and how appropriate for our needs! - that, in addition to "fragmented" (as in fraction or refraction), fractus should also mean "irregular," both meanings being preserved in the fragment."