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Origin of complexity and conditional predictability in cellular automata.

Vladimir García-Morales¹

¹Institute for Advanced Study, Technische Universität München, Lichtenbergstrasse 2a, D-85748 Garching, Germany and Nonequilibrium Chemical Physics, Physics Department, Technische Universität München, James-Franck-Strasse 1, D-85748 Garching, Germany.

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Summary

This summary is machine-generated.

This study introduces conditional predictability for complex systems. A cellular automaton model shows how synchrony and incoherence coexist in oscillators, with incoherence exhibiting much longer periodicity.

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Area of Science:

Complex Systems
Computational Science
Nonlinear Dynamics

Background:

Predictable dynamics can generate complex behavior in systems like cellular automata.
Understanding emergent complexity is crucial in various scientific fields.
Characterizing systems with both synchronous and incoherent behavior is challenging.

Purpose of the Study:

To describe a simple mechanism for the emergence of complexity from predictable dynamics.
To introduce the concept of conditional predictability for systems with piecewise known trajectories.
To model discrete chimera-like states in ensembles of identical oscillators.

Main Methods:

Development of a cellular automaton model.
Analysis of system dynamics exhibiting both synchrony and incoherence.
Comparison of periodicity in synchronous and incoherent regions.

Main Results:

A mechanism for emergent complexity from simple rules is demonstrated.
Conditional predictability is defined for systems with partially known trajectories.
The cellular automaton model successfully replicates chimera-like states.
The incoherent regions display periodicity three orders of magnitude longer than synchronous oscillations.

Conclusions:

Emergent complexity can arise from simple, predictable rules.
Conditional predictability offers a new framework for analyzing complex systems.
The proposed model provides insights into the coexistence of order and chaos in oscillator ensembles.