Entropy-Based Classification of Elementary Cellular Automata under Asynchronous Updating: An Experimental Study
Classification of asynchronous elementary cellular automata (AECAs) was explored in the first place by Fates et al. (Complex Systems, 2004) who employed the asymptotic density of cells as a key metric to measure their robustness to stochastic transitions. Unfortunately, the asymptotic density seems...
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| Format: | Article |
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MDPI AG
2021-02-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/2/209 |
| _version_ | 1827601824412073984 |
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| author | Qin Lei Jia Lee Xin Huang Shuji Kawasaki |
| author_facet | Qin Lei Jia Lee Xin Huang Shuji Kawasaki |
| author_sort | Qin Lei |
| collection | DOAJ |
| description | Classification of asynchronous elementary cellular automata (AECAs) was explored in the first place by Fates et al. (Complex Systems, 2004) who employed the asymptotic density of cells as a key metric to measure their robustness to stochastic transitions. Unfortunately, the asymptotic density seems unable to distinguish the robustnesses of all AECAs. In this paper, we put forward a method that goes one step further via adopting a metric entropy (Martin, Complex Systems, 2000), with the aim of measuring the asymptotic mean entropy of local pattern distribution in the cell space of any AECA. Numerical experiments demonstrate that such an entropy-based measure can actually facilitate a complete classification of the robustnesses of all AECA models, even when all local patterns are restricted to length 1. To gain more insights into the complexity concerning the forward evolution of all AECAs, we consider another entropy defined in the form of Kolmogorov–Sinai entropy and conduct preliminary experiments on classifying their uncertainties measured in terms of the proposed entropy. The results reveal that AECAs with low uncertainty tend to converge remarkably faster than models with high uncertainty. |
| first_indexed | 2024-03-09T05:04:57Z |
| format | Article |
| id | doaj.art-4b1d465901f44df989dd3c8315b6a169 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T05:04:57Z |
| publishDate | 2021-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-4b1d465901f44df989dd3c8315b6a1692023-12-03T12:55:29ZengMDPI AGEntropy1099-43002021-02-0123220910.3390/e23020209Entropy-Based Classification of Elementary Cellular Automata under Asynchronous Updating: An Experimental StudyQin Lei0Jia Lee1Xin Huang2Shuji Kawasaki3College of Computer Science, Chongqing University, Chongqing 400044, ChinaCollege of Computer Science, Chongqing University, Chongqing 400044, ChinaCollege of Computer Science, Chongqing University, Chongqing 400044, ChinaFaculty of Science and Engineering, Iwate University, Morioka, Iwate 020-8550, JapanClassification of asynchronous elementary cellular automata (AECAs) was explored in the first place by Fates et al. (Complex Systems, 2004) who employed the asymptotic density of cells as a key metric to measure their robustness to stochastic transitions. Unfortunately, the asymptotic density seems unable to distinguish the robustnesses of all AECAs. In this paper, we put forward a method that goes one step further via adopting a metric entropy (Martin, Complex Systems, 2000), with the aim of measuring the asymptotic mean entropy of local pattern distribution in the cell space of any AECA. Numerical experiments demonstrate that such an entropy-based measure can actually facilitate a complete classification of the robustnesses of all AECA models, even when all local patterns are restricted to length 1. To gain more insights into the complexity concerning the forward evolution of all AECAs, we consider another entropy defined in the form of Kolmogorov–Sinai entropy and conduct preliminary experiments on classifying their uncertainties measured in terms of the proposed entropy. The results reveal that AECAs with low uncertainty tend to converge remarkably faster than models with high uncertainty.https://www.mdpi.com/1099-4300/23/2/209asynchronous cellular automataclassificationelementary cellular automatarobustnessuncertaintyentropy |
| spellingShingle | Qin Lei Jia Lee Xin Huang Shuji Kawasaki Entropy-Based Classification of Elementary Cellular Automata under Asynchronous Updating: An Experimental Study Entropy asynchronous cellular automata classification elementary cellular automata robustness uncertainty entropy |
| title | Entropy-Based Classification of Elementary Cellular Automata under Asynchronous Updating: An Experimental Study |
| title_full | Entropy-Based Classification of Elementary Cellular Automata under Asynchronous Updating: An Experimental Study |
| title_fullStr | Entropy-Based Classification of Elementary Cellular Automata under Asynchronous Updating: An Experimental Study |
| title_full_unstemmed | Entropy-Based Classification of Elementary Cellular Automata under Asynchronous Updating: An Experimental Study |
| title_short | Entropy-Based Classification of Elementary Cellular Automata under Asynchronous Updating: An Experimental Study |
| title_sort | entropy based classification of elementary cellular automata under asynchronous updating an experimental study |
| topic | asynchronous cellular automata classification elementary cellular automata robustness uncertainty entropy |
| url | https://www.mdpi.com/1099-4300/23/2/209 |
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