Emergence of Temporally Irreversible Hierarchical Solid Patterns through Information-Bearing Field Evolution and History-Dependent Growth Arrest
Abstract
Patterns are widespread in natural and synthetic systems. Their formation is often interpreted through diffusion-driven instabilities or static geometric constructions. While successful in many contexts, these frameworks struggle to encode the spatiotemporal growth history of independently nucleated domains and their resulting collective behavior, including temporal asymmetry and hierarchical pattern formation with progressive solidification. This study shows that the TRACE (Temporal Recording through Arrested Coupled Evolution) mathematical model can generate intricate hierarchical patterns of solidifying and growing domains from simple, local growth rules through a phase information event-driven discretization operator within continuously evolving spatial information-bearing fields. The framework reveals how competition between growing domains can transform simple initial conditions into diverse final patterns, offering a new perspective on the emergence of spatial complexity from local growth processes, as observed experimentally in hierarchical pattern formation with solidification from fixed nuclei. This model suggests that complex patterns can emerge from the interaction of local, time-evolving growth, kinetic arrest rules with irreversible solidification embedded in front propagation. Numerical simulations reveal emergent patterns from the only TRACE equation, such as cell-like domains, stripes, banded structures, and hierarchical boundaries arising from variations in spatial confinement, nucleation timing, and domain density. The TRACE model also qualitatively reproduces the reported hierarchical macroscopic pattern formation observed in a chemical system. With these results, a phenomenon for growth-based natural patterns with solidification, and the featured characteristics of resultant patterns via growth and exclusion of each local cell are proposed.
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BibTeX
@misc{lee2026emergence,
title = {{Emergence of Temporally Irreversible Hierarchical Solid Patterns through Information-Bearing Field Evolution and History-Dependent Growth Arrest}},
author = {Junhyung Lee},
howpublished = {ChemRxiv},
year = {2026},
month = oct,
doi = {10.26434/chemrxiv-2026-5sdw8/v2},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv-2026-5sdw8/v2},
note = {CC BY-NC-ND},
}
RIS
TY - UNPB
TI - Emergence of Temporally Irreversible Hierarchical Solid Patterns through Information-Bearing Field Evolution and History-Dependent Growth Arrest
AU - Junhyung Lee
PY - 2026
DA - 2026/10/12
PB - ChemRxiv
DO - 10.26434/chemrxiv-2026-5sdw8/v2
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv-2026-5sdw8/v2
AB - Patterns are widespread in natural and synthetic systems. Their formation is often interpreted through diffusion-driven instabilities or static geometric constructions. While successful in many contexts, these frameworks struggle to encode the spatiotemporal growth history of independently nucleated domains and their resulting collective behavior, including temporal asymmetry and hierarchical pattern formation with progressive solidification. This study shows that the TRACE (Temporal Recording through Arrested Coupled Evolution) mathematical model can generate intricate hierarchical patterns of solidifying and growing domains from simple, local growth rules through a phase information event-driven discretization operator within continuously evolving spatial information-bearing fields. The framework reveals how competition between growing domains can transform simple initial conditions into diverse final patterns, offering a new perspective on the emergence of spatial complexity from local growth processes, as observed experimentally in hierarchical pattern formation with solidification from fixed nuclei. This model suggests that complex patterns can emerge from the interaction of local, time-evolving growth, kinetic arrest rules with irreversible solidification embedded in front propagation. Numerical simulations reveal emergent patterns from the only TRACE equation, such as cell-like domains, stripes, banded structures, and hierarchical boundaries arising from variations in spatial confinement, nucleation timing, and domain density. The TRACE model also qualitatively reproduces the reported hierarchical macroscopic pattern formation observed in a chemical system. With these results, a phenomenon for growth-based natural patterns with solidification, and the featured characteristics of resultant patterns via growth and exclusion of each local cell are proposed.
ER -