Summary
Arep-tiling ℐ is a self replicating, lattice tiling ofR n.Lattice tiling means a tiling by translates of a single compact tile by the points of a lattice, andself-replicating means that there is a non-singular linear mapø: R n → Rn such that, for eachT ∈ ℐ, the imageø(T) is, in turn, tiled by ℐ. This topic has recently come under investigation, not only because of its recreational appeal, but because of its application to the theory of wavelets and to computer addressing. The paper presents an exposition of some recent results on rep-tiling, including a construction of essentially all rep-tilings of Euclidean space. The construction is based on radix representation of points of a lattice. One particular radix representation, called thegeneralized balanced ternary, is singled out as an example because of its relevance to the field of computer vision.
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Vince, A. Rep-tiling Euclidean space. Aeq. Math. 50, 191–213 (1995). https://doi.org/10.1007/BF01831118
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DOI: https://doi.org/10.1007/BF01831118