self-similarity

A structure is said to be (strictly) self-similar if it can be broken down into arbitrarily small pieces, each of which is a small replica of the entire structure. It is important that the small pieces can in fact be obtained by a similarity transformation.


The best way to think of such a transformation is what we obtain from a photocopier with a reduction feature. For example, if we take a Koch curve and put it on a copying machine, set the reduction to 1/3 and produce four copies, then the four copies can be pasted back together to give back the Koch curve. It then follows that if we copy each of the four reduced copies...With an ideal copier, this process could be repeated infinitely often.

see phyllotaxis for self-similar forms in nature.

(Peitgen, Jürgens, Saupe, pp 202-203)