Pattern Regeneration in Two-Dimensional Cellular Automata Models of Bivalve Shell Symmetry.

Authors

Syed Hussain Ather, Richard Gordon

Published in

Bio Systems. Pages 105858. Jun 20, 2026. Epub Jun 20, 2026.

Abstract

The formation of complex biological patterns is a hallmark of morphogenesis and regeneration, yet the computational principles underlying their stability remain incompletely understood. While prior models of molluscan pigmentation have primarily focused on one-dimensional growth processes along the mantle edge of Conus shells, we introduce a two-dimensional cellular-automata-based framework to investigate pattern resilience in bilaterally symmetric bivalves (clams). Using two-dimensional totalistic cellular automata, we iterate over the emergence of clam-like textures and introduce localized stochastic perturbations ("neural scars") to quantify recovery dynamics. We define a Restoration Coefficient, , based on normalized XOR differences between perturbed and unperturbed states. In representative iterations, we observe high restoration (e.g., ), indicating that global pattern structure can be largely recovered following localized disruption. Similar qualitative recovery behavior has been observed in molluscan shell patterns following physical damage; however, the present model is intended as an abstract computational framework rather than a direct biological reconstruction. These results suggest that certain rule-based systems exhibit intrinsic robustness to perturbations, favoring recovery of underlying generative structure over exact spatial reconstruction ((Bagnoli, 1992, Derrida, 1986)). We discuss how this behavior relates to discrete models of morphogenesis, including differentiation-wave frameworks, and contrast it with gradient-based approaches such as reaction-diffusion systems. Together, these findings support the view that biological pattern formation may rely on rule-level stability mechanisms that enable recovery under noise, providing a computational perspective on morphogenetic robustness.

PMID:
42323044
Bibliographic data and abstract were imported from PubMed on 22 Jun 2026.

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