SpudLenia: Coupling Synthetic Protocell Hydrodynamics with Continuous Cellular Automata for Autonomous Morphogenesis

Achieving autonomous cytokinesis in continuous fields without active cytoskeletal machinery remains an open challenge across artificial life, biophysics, and self-organizing systems. While biological eukaryotes rely on ATP-driven actin-myosin contractile rings, recent wet-lab synthetic protocells (SpudCells) demonstrate that membrane-associated protein crowding can induce furrow constriction; however, physical prototypes remain bottlenecked by external chemical triggers and mechanical extrusion. Here, we introduce SpudLenia, an in silico differentiable continuous cellular automata framework that tests whether motor-free cytokinesis can emerge autonomously in a 2D reaction-convolution field. SpudLenia operates on multi-channel fields representing lipid bilayers, crowding proteins, and nutrient liposomes, coupled via multi-scale spatial convolution kernels and channel-specific growth activations. We hypothesize that localized steric crowding imposes an effective spatial growth penalty, and test whether this single inductive bias is sufficient for cytokinesis. By parameterizing a localized growth-braking operator that quenches lipid expansion along steep crowding gradients, SpudLenia produces midline furrow constriction with a characteristic constriction timescale consistent with experimental SpudCell velocities ($0.12\mu \text{m/s}$; Adamala et al., 2026) and culminating in complete topological membrane scission into stable secondary vesicles—demonstrating in silico the origin of the incomplete fission bottleneck observed in wet-lab prototypes. We characterize the open-system mass flux balance, identifying a stable homeostatic attractor that bounds growth against pathological bloating. Implemented as a differentiable 2D convolutional field solver running at 1.2 ms per step ($256\times 256$ lattice on consumer GPUs, e.g., Apple M1 Pro), SpudLenia achieves a 94.6% fission success rate across 500 trials perturbed over initial protocell geometry, nutrient placement, and protein noise, compared to 0% without the growth-braking operator. SpudLenia provides a principled continuous substrate for modeling decentralized morphogenesis and predicting division regimes in synthetic protocells; code and an interactive web visualizer are publicly available.