A fractal is an entity that displays self-similarity.

examples of fractals

Break-out room (10 minutes) :: What kind of fractals do You know ?

arbor bronchialis

DNA fractal

arbor vitae

Fractal dimension

In mathematics, more specifically in fractal geometry, a fractal dimension is a ratio providing a statistical index of complexity comparing how detail in a pattern (strictly speaking, a fractal pattern) changes with the scale at which it is measured. It has also been characterized as a measure of the space-filling capacity of a pattern that tells how a fractal scales differently from the space it is embedded in; a fractal dimension does not have to be an integer.

https://en.wikipedia.org/wiki/Fractal_dimension

Fractal dimension of trees