"So Nat'ralists observe, a Flea hath smaller Fleas that on him prey, and these have smaller fleas to bit 'em, and so proceed ad infinitum." a fractal, to offer something in the way of a definition to those who've been craving one, is a mathematical representation of an infinite pattern, useful in describing partly random or chaotic phenomena. it is a curve or geometric figure, each part of which has the same statistical character as the whole. similar patterns recur at progressively smaller (and larger) scales (recursive self similarity is the sexy term for this). that's the dictionary definition. but look around: we live on a "fractal" and we are "fractals" ourselves. it's all very beautiful.