Automatic Sequences: Theory, Applications, Generalizations
Automatic Sequences: Theory, Applications, Generalizations
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
On the language of standard discrete planes and surfaces
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Consistency of multidimensional combinatorial substitutions
Theoretical Computer Science
| Hi-index | 5.23 |
Substitutions on words, i.e., non-erasing morphisms of the free monoid, are simple combinatorial objects which produce infinite words by iteratively replacing letters by words. This paper introduces a notion of substitution acting on multi-dimensional words, namely local rule substitutions. Roughly speaking, local rules play for multi-dimensional words the role played by the concatenation product for substitutions on words. We then particularly focus on the local rule substitutions which act on the two-dimensional words coding stepped surfaces, and we show that a wide class of them can be derived from generalized substitutions.