Definition of Fractal: a curve or geometric figure, each part of which has the same statistical character as the whole. Fractals are useful in modeling structures (such as eroded coastlines or snowflakes) in which similar patterns recur at progressively smaller scales, and in describing partly random or chaotic phenomena such as crystal growth, fluid turbulence, and galaxy formation.

Mathematical fractals are created when a complex equation is continuously reiterated (the solution divided or multiplied back into itself -- ie: 4 x 2 = 8 x 2 = 16 x 2 = 32 -- only with much larger numbers). Then a color gradient gets applied to the numbers, turning it into a work of art.