A fractal is a mathematical set that typically displays self-similar patterns, which means they are “the same from near as from far”.

Fractals may be exactly the same at every scale, or, they may be nearly the same at different scales. The definition of fractal goes beyond self-similarity per se to exclude trivial self-similarity and include the idea of a detailed pattern repeating itself.

As mathematical equations, fractals are usually nowhere differentiable. An infinite fractal curve can be perceived of as winding through space differently from an ordinary line, still being a 1-dimensional line yet having a fractal dimension indicating it also resembles a surface.

Pancake fractals via culinary artist Nathan Shields via The Mary Sue.
Fractal image via Weed’s Fractal Gallery.

Quoted text via Wikipedia.