Dimension spectrum of infinite self-affine iterated function systems

Quantization Dimension for Infinite Conformal Iterated Function Systems

The quantization dimension function for an F -conformal measure mF generated by an infinite conformal iterated function system satisfying the strong open set condition and by a summable Hölder family of functions is expressed by a simple formula involving the temperature function of the system. The temperature function is commonly used to perform a multifractal analysis, in our context of the m...

Quantization Dimension for Conformal Iterated Function Systems

On Self‐Affine and Self‐Similar Graphs of Fractal Interpolation Functions Generated from Iterated Function Systems

This chapter provides a brief and coarse discussion on the theory of fractal interpolation functions and their recent developments including some of the research made by the authors. It focuses on fractal interpolation as well as on recurrent fractal interpolation in one and two dimensions. The resulting self-affine or self-similar graphs, which usually have non-integral dimension, were generat...

Spatial Bounding of Self-Affine Iterated Function System Attractor Sets

An algorithm is presented which, given the parameters of an Iterated Function System (IFS) which uses affine maps, constructs a closed ball which completely contains the attractor set of the IFS. These bounding balls are almost always smaller than those computed by existing methods, and are sometimes much smaller. The algorithm is numerical in form, involving the optimisation of centre-point an...

Infinite Iterated Function

We examine iterated function systems consisting of a countably innnite number of contracting mappings (IIFS). We state results analogous to the well-known case of nitely many mappings (IFS). Moreover, we show that IIFS can be approximated by appropriately chosen IFS both in terms of Hausdorff distance and of Hausdorff dimension. Comparing the descriptive power of IFS and IIFS as mechanisms deen...