الحياة على طرف قلم الرصاص: كيف تولد الخلايا من قواعد بسيطة سريع

الملخص الأصلي

كما كتبه المؤلفون، بالإنجليزية arXiv:2607.27402

Conway's Game of Life shows that simple rules can generate a rich diversity of emerging structures. This cellular automaton has been translated to continuous space by Rafler (2011) in a simulation called SmoothLife. The isotropic rule of this continuous Game of Life generates patterns whose beauty has attracted the attention of a growing community at the intersection of science and computer art. We study a minimal variant of this model, continuous in space and time, that generates cell-like patterns capable of self-replicating, gliding and disappearing. The phenomenology of these unit patterns is reported and related to homogeneous-state bifurcations, symmetry breaking, observed shape instabilities, finite-amplitude morphological changes, and a dilute-to-dense transition associated with cell proliferation. Its mapping onto a large reaction--diffusion system is interpreted in terms of homeostatic concentrations of morphogens, regulated by the nonlinear survival rule and generated through a cell-sourced cascade of auxiliary reactions. Introducing a global conservation law that limits resource availability causes the system to self-organize at this dilute-to-dense transition, which we call the edge of growth. A further exploration of parameter space reveals a variety of phases and the richness of life-like morphologies organized around this edge. Resemblance to biological processes such as division, motility, and death, together with a concise formulation and numerical implementation, makes the continuous Game of Life an appealing model system for investigating the emergence and self-organization of life-like patterns.