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Fractal geometry of Bedford-McMullen carpets

Research paper by Jonathan M. Fraser

Indexed on: 25 Aug '20Published on: 24 Aug '20Published in: arXiv - Mathematics - Dynamical Systems



Abstract

In 1984 Bedford and McMullen independently introduced a family of self-affine sets now known as \emph{Bedford-McMullen carpets}. Their work stimulated a lot of research in the areas of fractal geometry and non-conformal dynamics. In this survey article we discuss some aspects of Bedford-McMullen carpets, focusing mostly on dimension theory.