A Physically Grounded Discrete Causal Recording Formalism Based on Spatiotemporal Isolation for Surface Propagation Pattern Reconstruction
- 1Uiwang-si, Gyeonggi-do 15847, Republic of Korea
Abstract
This study introduces a pattern-oriented mathematical framework, termed the causal recording framework, which is conceptually rooted in cellular automata and consists of a discrete state layer that encodes physical information.Unlike Laplacian-based continuous partial differential equations (PDEs), which are successfully established for domain-dependent macroscopic pattern generation, the causal recording framework generates and records each local state solely from previously registered causal states, regardless of domain size, while incorporating time irreversibility and dissipative structures.The framework is applied to deterministic geometric order on liquid surfaces and validated through direct experiments and pattern reconstruction.Numerical pattern reconstructions demonstrate that the framework can reconstruct the evolution of real water ripple patterns.This research also reports that disordered, symmetry-breaking ripples on water surfaces can evolve into highly organized symmetric water patterns.This transition is reconstructed through a single causal recording framework, suggesting that emergent regularity arises from the interaction of identical local rules without any modification of the governing equations.The results also suggest that spatial confinement and local source information are critical factors in transforming disordered asymmetric patterns into highly ordered Faraday-wave-like patterns.These findings demonstrate the validity of the causal recording formulation as an effective framework for describing natural pattern formation characterized by domain independence, dissipative structures, and time irreversibility.
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BibTeX
@misc{lee2026physically,
title = {{A Physically Grounded Discrete Causal Recording Formalism Based on Spatiotemporal Isolation for Surface Propagation Pattern Reconstruction}},
author = {Junhyung Lee},
howpublished = {ChemRxiv},
year = {2026},
month = sep,
doi = {10.26434/chemrxiv.10001715/v3},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.10001715/v3},
note = {CC BY-NC-ND},
}
RIS
TY - UNPB
TI - A Physically Grounded Discrete Causal Recording Formalism Based on Spatiotemporal Isolation for Surface Propagation Pattern Reconstruction
AU - Junhyung Lee
PY - 2026
DA - 2026/09/23
PB - ChemRxiv
DO - 10.26434/chemrxiv.10001715/v3
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.10001715/v3
AB - This study introduces a pattern-oriented mathematical framework, termed the causal recording framework, which is conceptually rooted in cellular automata and consists of a discrete state layer that encodes physical information.Unlike Laplacian-based continuous partial differential equations (PDEs), which are successfully established for domain-dependent macroscopic pattern generation, the causal recording framework generates and records each local state solely from previously registered causal states, regardless of domain size, while incorporating time irreversibility and dissipative structures.The framework is applied to deterministic geometric order on liquid surfaces and validated through direct experiments and pattern reconstruction.Numerical pattern reconstructions demonstrate that the framework can reconstruct the evolution of real water ripple patterns.This research also reports that disordered, symmetry-breaking ripples on water surfaces can evolve into highly organized symmetric water patterns.This transition is reconstructed through a single causal recording framework, suggesting that emergent regularity arises from the interaction of identical local rules without any modification of the governing equations.The results also suggest that spatial confinement and local source information are critical factors in transforming disordered asymmetric patterns into highly ordered Faraday-wave-like patterns.These findings demonstrate the validity of the causal recording formulation as an effective framework for describing natural pattern formation characterized by domain independence, dissipative structures, and time irreversibility.
ER -