How to Transform and Filter Images using Iterated Function Systems
  We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves fractal geometry, chaotic dynamics, and an interplay between discrete and continuous representations. The underlying mathematics is established and applications to digital imaging are described and exemplified. 
Michael F. Barnsley, Brendan Harding, Konstantin Igudesman
math.GT math.MG