Orbits of one-dimensional cellular automata induced by symmetry transformations
Using a group-theoretic approach, a method for determining the equivalence classes (also called orbits) of the set of rules of one-dimensional cellular automata induced by the symmetry operations of reflection and permutation and their product is presented. Orbits are classified by their isomorphism...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-08-01
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| Series: | Physics Open |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666032625000481 |
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| author | Martin Schaller Karl Svozil |
| author_facet | Martin Schaller Karl Svozil |
| author_sort | Martin Schaller |
| collection | DOAJ |
| description | Using a group-theoretic approach, a method for determining the equivalence classes (also called orbits) of the set of rules of one-dimensional cellular automata induced by the symmetry operations of reflection and permutation and their product is presented. Orbits are classified by their isomorphism type. Results for the number of orbits and the number of orbits by type for state sets of size two and three are included. |
| format | Article |
| id | doaj-art-46e9d20305ff4a35a0e8b7ac99bf6676 |
| institution | Kabale University |
| issn | 2666-0326 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Physics Open |
| spelling | doaj-art-46e9d20305ff4a35a0e8b7ac99bf66762025-08-20T04:00:32ZengElsevierPhysics Open2666-03262025-08-012410029810.1016/j.physo.2025.100298Orbits of one-dimensional cellular automata induced by symmetry transformationsMartin Schaller0Karl Svozil1Vienna, AustriaInstitute for Theoretical Physics, TU Wien, Wiedner Hauptstrasse 8-10/136, 1040 Vienna, Austria; Corresponding author.Using a group-theoretic approach, a method for determining the equivalence classes (also called orbits) of the set of rules of one-dimensional cellular automata induced by the symmetry operations of reflection and permutation and their product is presented. Orbits are classified by their isomorphism type. Results for the number of orbits and the number of orbits by type for state sets of size two and three are included.http://www.sciencedirect.com/science/article/pii/S2666032625000481One-dimensional cellular automataSymmetry transformationsG-isomorphism |
| spellingShingle | Martin Schaller Karl Svozil Orbits of one-dimensional cellular automata induced by symmetry transformations Physics Open One-dimensional cellular automata Symmetry transformations G-isomorphism |
| title | Orbits of one-dimensional cellular automata induced by symmetry transformations |
| title_full | Orbits of one-dimensional cellular automata induced by symmetry transformations |
| title_fullStr | Orbits of one-dimensional cellular automata induced by symmetry transformations |
| title_full_unstemmed | Orbits of one-dimensional cellular automata induced by symmetry transformations |
| title_short | Orbits of one-dimensional cellular automata induced by symmetry transformations |
| title_sort | orbits of one dimensional cellular automata induced by symmetry transformations |
| topic | One-dimensional cellular automata Symmetry transformations G-isomorphism |
| url | http://www.sciencedirect.com/science/article/pii/S2666032625000481 |
| work_keys_str_mv | AT martinschaller orbitsofonedimensionalcellularautomatainducedbysymmetrytransformations AT karlsvozil orbitsofonedimensionalcellularautomatainducedbysymmetrytransformations |