Two-dimensional iterated morphisms and discrete planes
Theoretical Computer Science - Combinatorics of the discrete plane and tilings
Functional stepped surfaces, flips, and generalized substitutions
Theoretical Computer Science
Local rule substitutions and stepped surfaces
Theoretical Computer Science
Infinite snake tiling problems
DLT'02 Proceedings of the 6th international conference on Developments in language theory
On the language of standard discrete planes and surfaces
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
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Multidimensional combinatorial substitutions are rules that replace symbols by finite patterns of symbols in Z^d. We focus on the case where the patterns are not necessarily rectangular, which requires a specific description of the way they are glued together in the image by a substitution. Two problems can arise when defining a substitution in such a way: it can fail to be consistent, and the patterns in an image by the substitution might overlap. We prove that it is undecidable whether a two-dimensional substitution is consistent or overlapping, and we provide practical algorithms to decide these properties in some particular cases.