Transformations Between Self-Referential Sets

[Nahee_Enterprises]

On the Mathematical Association of America's web site, the April issue of the AMERICAN MATHEMATICAL MONTHLY has an article by Michael F. Barnsley, which states in the Table-Of-Contents:

     Did you know that there are continuous transformations from a fractal fern onto a filled square?
    Also, there are functions of a similar wild character that map from a filled triangle onto itself.   We prove that
    these fractal transformations may be homeomorphisms, under simple conditions, and that they may be
    calculated readily by means of a coupled Chaos Game.   We illustrate several examples of these beautiful
    functions and show how they exemplify basic notions in topology, probability, analysis, and geometry.  Thus
    they are worthy of the attention of the mathematics community, both for aesthetic and pedagogical reasons.

You may need membership to read the full article from:
    http://www.maa.org/pubs/monthly_apr09_toc.html