Rep-tiling Euclidean space
This is an introduction (for non-specialists) to some aspects of self- replicating (or self-similar) tilings. The author concentrates on the connection between lattice tilings and radix systems (digit sets). In particular, he discusses whether, in a given system, every lattice point has a representation, and whether its representation is unique. But since, moreover, related topics are discussed briefly (with references) the article is also a good survey of recent progress in the subject (in a more general sense). (Remark: There is a slight inconsistency concerning Figure 1. Though all three tilings shown are called reptilings, both in the caption and in the text, only the first meets the definition as given, since the other two contain tiles which are not translates of each other).
scientific article; zbMATH DE number 794228
scientific article