This project is to continue the development of tools based on Fractal Geometry for the description, generation and encoding (compression) of images, using automata-theoretic techniques. A design system will be developed based on Mutual Recursive Function Systems which should be specifically suitable for concise description (design) and efficient generation of images with a hierarchial structure and which are characterized by a mixture of order and chaos. Images of natural objects typically have both of these properties. The main goal is to improve the algorithm for image encoding (data compression) based on weighted finite automata (WFA). WFA can simulate wavelet transforms which constitute one of the best known methods for image compression. This fact will be used to design an encoder combining the advantages of both the fractal approach and the wavelet transforms. The theoretical properties of WFA as computers of real function will also be investigated. This is a new application of finite automata with much potential, for example, the possibility of mechanical integration: an automaton computing a function of one variable can be converted to one computing the integral function of f.
