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Infinite Iterated Function Systems

✍ Scribed by Henning Fernau

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
615 KB
Volume
170
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

We examine iterated function systems consisting of a countably infinite number of contracting mappings (IIFS). We state results analogous to the well‐known case of finitely 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 defining closed and bounded sets, we show that IIFS are strictly more powerful than IFS. On the other hand, there are closed and bounded non‐empty sets not describable by IIFS.

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