Neural Cellular Automata (NCAs) are a promising new approach to model self-organizing processes, with potential applications in life science. However, their deterministic nature limits their ability to capture the stochasticity of real-world biological and physical systems. We propose the Mixture of Neural Cellular Automata (MNCA), a novel framework incorporating the idea of mixture models into the NCA paradigm. By combining probabilistic rule assignments with intrinsic noise, MNCAs can model diverse local behaviors and reproduce the stochastic dynamics observed in biological processes. We evaluate the effectiveness of MNCAs in three key domains: (1) synthetic simulations of tissue growth and differentiation, (2) image morphogenesis robustness, and (3) microscopy image segmentation. Results show that MNCAs achieve superior robustness to perturbations, better recapitulate real biological growth patterns, and provide interpretable rule segmentation. These findings position MNCAs as a promising tool for modeling stochastic dynamical systems and studying self-growth processes.

翻译：神经细胞自动机（NCAs）是一种模拟自组织过程的新兴方法，在生命科学领域具有潜在应用前景。然而，其确定性本质限制了其捕捉现实世界生物与物理系统随机性的能力。我们提出神经细胞自动机混合模型（MNCA），这是一个将混合模型思想融入NCA范式的新型框架。通过将概率规则分配与内在噪声相结合，MNCAs能够模拟多样化的局部行为，并复现生物过程中观察到的随机动力学特征。我们在三个关键领域评估了MNCAs的有效性：（1）组织生长与分化的合成模拟，（2）图像形态发生的鲁棒性，（3）显微图像分割。结果表明，MNCAs对扰动具有更强的鲁棒性，能更好地再现真实生物生长模式，并提供可解释的规则分割。这些发现确立了MNCAs作为模拟随机动力系统和研究自生长过程的有力工具。