Pattern regeneration in two-dimensional cellular automata models of bivalve shell symmetry

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, R, based on normalized XOR differences between perturbed and unperturbed states. In representative iterations, we observe high restoration (e.g., R≈0.98), 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 et al., 1992; Derrida, 1986; Ather and Gordon, 2026). We discuss how this behavior relates to discrete models of morphogenesis, including differentiation-wave frameworks (Gordon et al., 2020), 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.