Fractal

In mathematics, a fractal is a self-similar subset of Euclidean space whose fractal dimension strictly exceeds its topological dimension .

Fractals exhibit similar patterns at increasingly small scales called self-similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge, it is called affine self-similar. Fractal geometry lies within the mathematical branch of measure theory .

Sources:

Gouyet, Jean-François (1996). Physics and fractal structures. Paris/New York: Masson Springer. ISBN 978-0-387-94153-0.