![Scan of the density 碌 (order parameter), with constant resource abundance r as control parameter. Standard deviation around the mean (coloured area) over independent simulations for a given volume |鈩. Edges of growth and droplet stability (dotted and dashed lines). Scale ratio 位 = 3, initial state with 2 seeds, cutoff time tmax = 5000. -- [physics.bio-ph]](https://i0.wp.com/astrobiology.com/wp-content/uploads/2026/08/Continuous-Game.png?fit=1200%2C674&ssl=1)
[physics.bio-ph] 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.
Alexandre Guillet, Frank J眉licher
Comments: Code is available at: this https URL To be published in Artificial Life 26 pages, 7 figures
Subjects: Biological Physics (physics.bio-ph); Adaptation and Self-Organizing Systems (nlin.AO); Pattern Formation and Solitons (nlin.PS)
MSC classes: 92C05, 35R09, 35B36
ACM classes: F.1.1; I.6.8; G.1.8; J.3
Cite as: arXiv:2607.27402 [physics.bio-ph] (or arXiv:2607.27402v1 [physics.bio-ph] for this version)
https://doi.org/10.48550/arXiv.2607.27402
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Submission history
From: Alexandre Guillet
[v1] Wed, 29 Jul 2026 19:15:15 UTC (9,535 KB)
https://arxiv.org/abs/2607.27402
Astrobiology,
