连续生命游戏：生长边缘的细胞涌现与自组织
Continuous Game of Life: cell emergence and self-organization at the edge of growth
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中文总结 AI 辅助
本文研究连续生命游戏的最小变体，其可生成自复制、滑行的类细胞图案，引入资源守恒定律后系统在稀-密转变处（生长边缘）自组织，为研究类生命模式涌现提供了理想模型。
中文摘要 AI 辅助
康威生命游戏表明，简单规则可生成丰富多样的涌现结构。该元胞自动机已被Rafler（2011）转化为名为SmoothLife的连续空间模拟。这种连续生命游戏的各向同性规则生成的图案之美，吸引了科学与计算机艺术交叉领域日益壮大的群体关注。我们研究该模型的一个最小变体，其在空间和时间上均连续，可生成具有自复制、滑行和消失能力的类细胞图案。我们报告了这些单元图案的现象学，并将其与均匀态分岔、对称性破缺、观测到的形状不稳定性、有限振幅形态变化以及与细胞增殖相关的稀-密转变联系起来。我们将其映射到大型反应-扩散系统，依据形态发生素的稳态浓度进行解释，该浓度由非线性存活规则调控，并通过细胞源辅助反应级联产生。引入限制资源可用性的全局守恒定律，使系统在该稀-密转变处自组织，我们将此转变称为生长边缘。对参数空间的进一步探索揭示了围绕该生长边缘组织的多种相和丰富的类生命形态。其与分裂、运动和死亡等生物过程的相似性，加上简洁的公式和数值实现，使连续生命游戏成为研究类生命模式涌现与自组织的理想模型系统。
英文摘要
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.
发表机构
- Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）
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