A1 Refereed original research article in a scientific journal
Multiplication cubes and multiplication automata
Authors: Kopra, Johan
Publisher: Cambridge University Press (CUP)
Publishing place: CAMBRIDGE
Publication year: 2024
Journal:: Ergodic Theory and Dynamical Systems
Journal name in source: Ergodic Theory and Dynamical Systems
Journal acronym: ERGOD THEOR DYN SYST
First page : 1
Last page: 40
Number of pages: 40
ISSN: 0143-3857
eISSN: 1469-4417
DOI: https://doi.org/10.1017/etds.2024.44
Web address : http://dx.doi.org/10.1017/etds.2024.44
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/458237850
We extend previously known two-dimensional multiplication tiling systems that simulate multiplication by two natural numbers p and q in base pq to higher dimensional multiplication tessellation systems. We develop the theory of these systems and link different multiplication tessellation systems with each other via macrotile operations that glue cubes in one tessellation system into larger cubes of another tessellation system. The macrotile operations yield topological conjugacies and factor maps between cellular automata performing multiplication by positive numbers in various bases.
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Funding information in the publication:
The work was supported by the Finnish Cultural Foundation (grant number 00220510).
