A New Generation of Fractals: Theory, Computation and Applications Particularly to Digital Imaging

The aim of the project is to discover the mathematical and computational properties of superfractals and related structures, and to investigate their applications to digital imaging. Superfractals give hierarchies of new fractals which include both deterministic fractals and standard random fractals. Techniques of mathematical analysis, in particular geometric measure theory and stochastic processes, will be applied to provide a better understanding and characterization of superfractals and the related structures. Such understanding will be used towards the development of new methodology, and the design of efficient computational algorithms, essential for applications in computer graphics and image compression.