Cellular Automata on Graphs: Topological Properties of ER Graphs Evolved towards Low-Entropy Dynamics
Cellular automata (CA) are a remarkably efficient tool for exploring general properties of complex systems and spatiotemporal patterns arising from local rules. Totalistic cellular automata, where the update rules depend only on the density of neighboring states, are at the same time a versatile...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2012-06-01
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| Series: | Entropy |
| Subjects: | |
| Online Access: | http://www.mdpi.com/1099-4300/14/6/993 |
| _version_ | 1828120107742658560 |
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| author | Marc-Thorsten Hütt Carsten Marr |
| author_facet | Marc-Thorsten Hütt Carsten Marr |
| author_sort | Marc-Thorsten Hütt |
| collection | DOAJ |
| description | Cellular automata (CA) are a remarkably efficient tool for exploring general properties of complex systems and spatiotemporal patterns arising from local rules. Totalistic cellular automata, where the update rules depend only on the density of neighboring states, are at the same time a versatile tool for exploring dynamical processes on graphs. Here we briefly review our previous results on cellular automata on graphs, emphasizing some systematic relationships between network architecture and dynamics identified in this way. We then extend the investigation towards graphs obtained in a simulated-evolution procedure, starting from Erdő s–Rényi (ER) graphs and selecting for low entropies of the CA dynamics. Our key result is a strong association of low Shannon entropies with a broadening of the graph’s degree distribution. |
| first_indexed | 2024-04-11T13:59:53Z |
| format | Article |
| id | doaj.art-01ef68e4c2894ed08303676deb3116c6 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T13:59:53Z |
| publishDate | 2012-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-01ef68e4c2894ed08303676deb3116c62022-12-22T04:20:09ZengMDPI AGEntropy1099-43002012-06-01146993101010.3390/e14060993Cellular Automata on Graphs: Topological Properties of ER Graphs Evolved towards Low-Entropy DynamicsMarc-Thorsten HüttCarsten MarrCellular automata (CA) are a remarkably efficient tool for exploring general properties of complex systems and spatiotemporal patterns arising from local rules. Totalistic cellular automata, where the update rules depend only on the density of neighboring states, are at the same time a versatile tool for exploring dynamical processes on graphs. Here we briefly review our previous results on cellular automata on graphs, emphasizing some systematic relationships between network architecture and dynamics identified in this way. We then extend the investigation towards graphs obtained in a simulated-evolution procedure, starting from Erdő s–Rényi (ER) graphs and selecting for low entropies of the CA dynamics. Our key result is a strong association of low Shannon entropies with a broadening of the graph’s degree distribution.http://www.mdpi.com/1099-4300/14/6/993network dynamicssimulated evolutioncellular automata on graphsdynamic probes |
| spellingShingle | Marc-Thorsten Hütt Carsten Marr Cellular Automata on Graphs: Topological Properties of ER Graphs Evolved towards Low-Entropy Dynamics Entropy network dynamics simulated evolution cellular automata on graphs dynamic probes |
| title | Cellular Automata on Graphs: Topological Properties of ER Graphs Evolved towards Low-Entropy Dynamics |
| title_full | Cellular Automata on Graphs: Topological Properties of ER Graphs Evolved towards Low-Entropy Dynamics |
| title_fullStr | Cellular Automata on Graphs: Topological Properties of ER Graphs Evolved towards Low-Entropy Dynamics |
| title_full_unstemmed | Cellular Automata on Graphs: Topological Properties of ER Graphs Evolved towards Low-Entropy Dynamics |
| title_short | Cellular Automata on Graphs: Topological Properties of ER Graphs Evolved towards Low-Entropy Dynamics |
| title_sort | cellular automata on graphs topological properties of er graphs evolved towards low entropy dynamics |
| topic | network dynamics simulated evolution cellular automata on graphs dynamic probes |
| url | http://www.mdpi.com/1099-4300/14/6/993 |
| work_keys_str_mv | AT marcthorstenhutt cellularautomataongraphstopologicalpropertiesofergraphsevolvedtowardslowentropydynamics AT carstenmarr cellularautomataongraphstopologicalpropertiesofergraphsevolvedtowardslowentropydynamics |