A term used to describe an image where small portions of the image resemble the entire image. A good example is Sierpinski's triangle, where small groups of triangles resemble the entire triangle. Another example is the fractal, where a mathematical function generates an image that one can zoom into infinitely (theoretically) without losing detail. Newton's method is a mathematical function that generates Julia set fractals.

A poetic interlude on the existence of self-similarity in nature, from a poem by Jonathan Swift:

So, the naturalists observe, a flea
Hath smaller fleas that on him prey
And these have smaller still to bite 'em
And so proceed ad infinitum.