A fractal is an image generated using mathematics. The term fractal describes a shape or object that looks like itself, even when divided into pieces. In nature, clouds, mountains, trees and coastlines are examples of fractals. Their structure is the same, or nearly the same, independent of the scale at which they are being viewed
A fractal is "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole," a property called self-similarity.
Roots of the idea of fractals go back to the 17th century, while mathematically rigorous treatment of fractals can be traced back to functions studied by Karl Weierstrass, Georg Cantor and Felix Hausdorff a century later in studying functions that were continuous but not differentiable; however, the term fractal was coined by Benoit Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured."
A mathematical fractal is based on an equation that undergoes iteration, a form of feedback based on recursion.