Index Making Pictures

Iterated Function Systems

This simple example shows three functions, differing only in translation, being used to give a pattern which is self-similar at all scales. Each function is a scale to half the size of the whole picture. One function covers the lower left quarter, one the lower right and one the central top. The detail within each is generated automatically because each function has to be a half-size image of the whole picture.

Here we have added a small rotation, only to the lower right function. Notice how all its sub-areas are also rotated, by successively greater amounts overall. Note too how the areas of the other two functions are also affected, because each is a copy of the whole picture.