The impact of alphabet size on pattern complexity of maxmin-ω cellular automata
We present an analysis of an additive cellular automaton (CA) under asynchronous dynamics. The asynchronous scheme is maxmin-ω, a deterministic system, introduced in our previous work with a binary alphabet. Extending this work, we study the impact of a larger alphabet, which also allows a meaningfu...
| Main Author: | |
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| Format: | Journal article |
| Language: | English |
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Springer
2020
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| _version_ | 1826289220256268288 |
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| author | Patel, EL |
| author_facet | Patel, EL |
| author_sort | Patel, EL |
| collection | OXFORD |
| description | We present an analysis of an additive cellular automaton (CA) under asynchronous dynamics. The asynchronous scheme is maxmin-ω, a deterministic system, introduced in our previous work with a binary alphabet. Extending this work, we study the impact of a larger alphabet, which also allows a meaningful inference of the behaviour of the resultant CA from the asymptotic behaviour of the maxmin-ω update system. Far from being a straightforward positive correlation between complexity and alphabet size, we show that there is a region of ω and alphabet size where complexity of CA is maximal. Thus, despite employing a fixed CA rule, the complexity of this CA can be controlled by ω and alphabet size. The main message is that the effect of maxmin-ω updating on the state of a network can be well understood, especially if the state alphabet is counter-intuitively large. |
| first_indexed | 2024-03-07T02:25:34Z |
| format | Journal article |
| id | oxford-uuid:a5750490-0aa6-4d59-9aa0-e4759165a542 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:25:34Z |
| publishDate | 2020 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:a5750490-0aa6-4d59-9aa0-e4759165a5422022-03-27T02:40:41ZThe impact of alphabet size on pattern complexity of maxmin-ω cellular automataJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a5750490-0aa6-4d59-9aa0-e4759165a542EnglishSymplectic ElementsSpringer2020Patel, ELWe present an analysis of an additive cellular automaton (CA) under asynchronous dynamics. The asynchronous scheme is maxmin-ω, a deterministic system, introduced in our previous work with a binary alphabet. Extending this work, we study the impact of a larger alphabet, which also allows a meaningful inference of the behaviour of the resultant CA from the asymptotic behaviour of the maxmin-ω update system. Far from being a straightforward positive correlation between complexity and alphabet size, we show that there is a region of ω and alphabet size where complexity of CA is maximal. Thus, despite employing a fixed CA rule, the complexity of this CA can be controlled by ω and alphabet size. The main message is that the effect of maxmin-ω updating on the state of a network can be well understood, especially if the state alphabet is counter-intuitively large. |
| spellingShingle | Patel, EL The impact of alphabet size on pattern complexity of maxmin-ω cellular automata |
| title | The impact of alphabet size on pattern complexity of maxmin-ω cellular automata |
| title_full | The impact of alphabet size on pattern complexity of maxmin-ω cellular automata |
| title_fullStr | The impact of alphabet size on pattern complexity of maxmin-ω cellular automata |
| title_full_unstemmed | The impact of alphabet size on pattern complexity of maxmin-ω cellular automata |
| title_short | The impact of alphabet size on pattern complexity of maxmin-ω cellular automata |
| title_sort | impact of alphabet size on pattern complexity of maxmin ω cellular automata |
| work_keys_str_mv | AT patelel theimpactofalphabetsizeonpatterncomplexityofmaxminōcellularautomata AT patelel impactofalphabetsizeonpatterncomplexityofmaxminōcellularautomata |