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Predictability is dynamically constructed by topological collective modes in deterministic systems.

Lars Koopmans1,2, Elinor M Kay1,3,4, Hyun Youk1,3,4

  • 1Department of Physics, University of Illinois Urbana-Champaign, Urbana IL, USA.

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|May 8, 2026
PubMed
Summary
This summary is machine-generated.

Predictability in deterministic systems emerges dynamically, not from initial states. Complex patterns arise from simple rules, with key signatures appearing late in the system's evolution.

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Last Updated: May 9, 2026

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Area of Science:

  • Complex Systems
  • Non-equilibrium Physics
  • Theoretical Biology

Background:

  • Deterministic many-body systems often exhibit self-organization into macroscopic patterns.
  • Predictability of long-term behavior is typically assumed to be encoded within the initial configuration.

Purpose of the Study:

  • To investigate whether predictability in self-organizing systems can be dynamically constructed rather than solely relying on initial conditions.
  • To analyze the emergent behaviors and topological features in a generalized cellular automaton model.

Main Methods:

  • Studied a generalized cellular automaton model with 'secrete-and-sense' cells.
  • Treated cell states as a discrete phase field to uncover emergent topological modes.
  • Tracked the dynamics of charged vortices and their connecting strings (non-contractible loops).

Main Results:

  • The system self-organizes into static configurations, rectilinear waves, or spiral waves from disorder.
  • Emergent topological modes, specifically charged vortices connected by strings, were identified.
  • Predictive signatures of macroscopic fate appeared late in the trajectory, with vortex annihilation becoming readable via loop loss, while vortex persistence remained unreadable until spiral waves formed abruptly.

Conclusions:

  • Predictability in deterministic non-equilibrium systems can be dynamically constructed, not solely determined by the initial state.
  • Topological features, such as vortex dynamics and loop formation/loss, provide late-stage indicators of system fate.
  • This challenges the traditional view of predictability being entirely encoded in initial configurations for self-organizing systems.