Building “invertible” fractals: Introduction to Context-Dependant Iterated Function Systems

A novel formalism for the construction of fractal and fractal-like sets is proposed. A Context-Dependant Iterated Function System has the particularity to build self-similar sets having the property to be “invertible”: the hierarchical organization of their construction process can be preserved in their topology. This method offers new insights on the topological forms of simple solutions for the inverse problem of building fractals. The convergence conditions to a fractal set are discussed, together with simple examples to illustrate the process of generation of fractal-like sets, and extraction of a simple representation. Implicitly is detailed a novel method to solve the inverse problem of building fractals.