Deterministic scale-invariant dynamics in a logistic Game-of-Life model
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866915904545095680 |
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| author | Akgun, Hakan Yan, Xianquan Taskiran, Tamer Ibrahimi, Muhamet Lee, Ching Hua Jahangirov, Seymur |
| author_facet | Akgun, Hakan Yan, Xianquan Taskiran, Tamer Ibrahimi, Muhamet Lee, Ching Hua Jahangirov, Seymur |
| contents | Scale invariance is a hallmark of criticality in complex dynamical systems. While random external inputs or tunable stochastic interactions are typically required to produce critical behavior, it remains unclear whether scale-invariant dynamics can emerge from purely deterministic interactions. Here, we address this question by studying the asymptotic dynamics of the logistic Game of Life (GOL), a deterministic-parameter extension of Conway's GOL. In this system, we identify three distinct asymptotic phases separated by two fundamentally different critical points. The first critical point, associated with an unusual form of self-organized criticality, separates a sparse-static phase from a sparse-dynamic phase. The second critical point corresponds to a deterministic percolation transition between the sparse-dynamic phase and a third, dense-dynamic phase. In addition, we observe power-law cluster size distributions with unconventional critical exponents not found in standard equilibrium systems. Overall, our work paves the way for studying emergent scale invariance in purely deterministic systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_07189 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deterministic scale-invariant dynamics in a logistic Game-of-Life model Akgun, Hakan Yan, Xianquan Taskiran, Tamer Ibrahimi, Muhamet Lee, Ching Hua Jahangirov, Seymur Statistical Mechanics Chaotic Dynamics Cellular Automata and Lattice Gases Computational Physics Data Analysis, Statistics and Probability 82B43, 82B44, 82B26, 82B27, 37B15 Scale invariance is a hallmark of criticality in complex dynamical systems. While random external inputs or tunable stochastic interactions are typically required to produce critical behavior, it remains unclear whether scale-invariant dynamics can emerge from purely deterministic interactions. Here, we address this question by studying the asymptotic dynamics of the logistic Game of Life (GOL), a deterministic-parameter extension of Conway's GOL. In this system, we identify three distinct asymptotic phases separated by two fundamentally different critical points. The first critical point, associated with an unusual form of self-organized criticality, separates a sparse-static phase from a sparse-dynamic phase. The second critical point corresponds to a deterministic percolation transition between the sparse-dynamic phase and a third, dense-dynamic phase. In addition, we observe power-law cluster size distributions with unconventional critical exponents not found in standard equilibrium systems. Overall, our work paves the way for studying emergent scale invariance in purely deterministic systems. |
| title | Deterministic scale-invariant dynamics in a logistic Game-of-Life model |
| topic | Statistical Mechanics Chaotic Dynamics Cellular Automata and Lattice Gases Computational Physics Data Analysis, Statistics and Probability 82B43, 82B44, 82B26, 82B27, 37B15 |
| url | https://arxiv.org/abs/2411.07189 |