An object is said to be self-similar if it looks "roughly" the same on any scale. Fractals are a particularly interesting class
of self-similar objects. Self-similar objects with parameters and are described by a power law such as

Harris, J. W. and Stocker, H. "Scaling Invariance and Self-Similarity" and "Construction of Self-Similar Objects." §4.11.1-4.11.2
in Handbook
of Mathematics and Computational Science. New York: Springer-Verlag, p. 113,
1998.Hutchinson, J. "Fractals and Self-Similarity." Indiana
Univ. J. Math.30, 713-747, 1981.