From Michael F. Barnsley



The attractor of an IFS may be a Sierpinski triangle, a fractal fern or simply a filled square. With the aid of the "top" of an attractor, transformations between attractors may be established. Under simple mathematical conditions these transformations are continuous. In this way, a continuous mapping from a fractal fern onto a filled square can be constructed. Some such transformations may be ubiquitous in nature.