ON A CLASS OF FRACTAL MATRICES III: LIMIT STRUCTURES AND HIERARCHICAL ITERATED FUNCTION SYSTEMS

Abstract

Fractrices (fractal matrices, excess-matrices) were defined in an earlier paper, Part I, as a special class of integer matrices with multifractal features. In contrast with Part II where a quantitative analysis of these objects was performed from a finitist constructivist point of view, the present Part III discusses the corresponding genuine limit fractal version. First this is done by a standard limit analysis which eventually leads to a (nonstandard) hyperreal-number view on this limit. Then a related hierarchical iterated function system is constructed whose attractor is the very same limit. This limit is either a hierarchical Zeno or Cantor set, or a space filling set. Its fractal dimension function is investigated.