Moran-Type Iterated Function Systems and Dimensions of Moran Self-Similar Sets

TL;DR

This paper introduces Moran-type iterated function systems, establishing their theoretical framework, defining attractors and measures, and exploring their dimension theory with illustrative examples.

Contribution

It develops the foundational theory of Moran-type IFS, including separation conditions and dimension analysis, which was not previously formalized.

Findings

Defined Moran-type attractors and measures

Established separation conditions for MIFS

Analyzed the dimension theory of Moran self-similar sets

Abstract

Moran-type iterated function systems (Moran-type IFS or MIFS) are defined by a sequence of iterated function systems, and their basic theoretical framework is established. We define Moran-type attractors and invariant probability measures associated with a sequence of probability weight vectors. Furthermore, separation conditions for MIFS are introduced, and the dimension theory of Moran-type self-similar sets is investigated. Appropriate examples are provided to illustrate and support the definitions and results.