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Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
445
Deterministic phase transitions and self-organization in logistic cellular automata.
M Ibrahimi1, O Gulseren1,2, S Jahangirov2,3
1Department of Physics, Bilkent University, Ankara 06800, Turkey.
Physical Review. E
|November 28, 2019
Summary
A new cellular automata (CA) extension uses a single parameter to expand state space into a Cantor set, enabling tunable emergent phenomena like phase transitions and pattern formation.
Area of Science:
- Complex Systems
- Computational Science
- Theoretical Physics
Background:
- Cellular automata (CA) exhibit complex emergent behaviors from simple rules.
- Investigating parameter effects on CA dynamics is crucial for understanding self-organization and pattern formation.
Purpose of the Study:
- To introduce a novel CA extension with a tunable parameter that expands the discrete state space into a Cantor set.
- To explore the emergent phenomena, including phase transitions and pattern formation, facilitated by this extension.
- To analyze the adaptive survival of complex propagators and deterministic transitions between CA classes.
Main Methods:
- Extending CA by mapping discrete states to a Cantor set via a single tuning parameter.
- Applying the extension to Conway's Game of Life and Rule 90 (a 1D CA).
- Analyzing asymptotic dynamics, emergent propagators, and autocatalytic local interactions.
Main Results:
- The extension enables control over CA dynamics, leading to sudden changes and complex propagator emergence in Conway's Game of Life.
- Autocatalytic local interactions explain the adaptive survival of propagators within specific parameter ranges.
- Deterministic transitions between CA classes were observed in Rule 90 by continuously tuning the parameter.
Conclusions:
- The proposed CA extension provides a powerful framework for studying emergent phenomena by continuously tuning system dynamics.
- The Cantor set state space expansion offers a novel mechanism for controlling and understanding complex behaviors in CA.
- This approach facilitates deterministic transitions between different classes of cellular automata, offering new avenues for computational modeling.
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