Theory and Applications of Three Dimensional Fractal Transformations

In this project we aim to develop mathematical theory and algorithms for fractal transformations. Fractal transformations are continuous invertible mappings (homeomorphisms) between fractals. They will be used to map complex fractals onto simpler ones. Their theory will enhance the understanding of fractals and ultimately lead to new algorithms for video compression. Outcomes include existence theorems and equivalence classes of fractals which can be mapped continuously onto each other. Fast algorithms to transform images (or functions) defined on fractals and identification of fractal transformations from data will be investigated. Theoretical results include bounds on accuracy and efficiency of the new algorithms.