Multiplication cubes and multiplication automata
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909456059596800 |
|---|---|
| author | Kopra, Johan |
| author_facet | Kopra, Johan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_15293 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Multiplication cubes and multiplication automata Kopra, Johan Dynamical Systems 37B15 (Primary) 37B10, 37B51, 37B52 (Secondary) 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. |
| title | Multiplication cubes and multiplication automata |
| topic | Dynamical Systems 37B15 (Primary) 37B10, 37B51, 37B52 (Secondary) |
| url | https://arxiv.org/abs/2211.15293 |