Neural Cellular Automata (NCA) models are trainable variations of traditional Cellular Automata (CA). Emergent motion in the patterns created by NCA has been successfully applied to synthesize dynamic textures. However, the conditions required for an NCA to display dynamic patterns remain unexplored. Here, we investigate the relationship between the NCA architecture and the emergent dynamics of the trained models. Specifically, we vary the number of channels in the cell state and the number of hidden neurons in the MultiLayer Perceptron (MLP), and draw a relationship between the combination of these two variables and the motion strength between successive frames. Our analysis reveals that the disparity and proportionality between these two variables have a strong correlation with the emergent dynamics in the NCA output. We thus propose a design principle for creating dynamic NCA.

翻译：神经细胞自动机（NCA）模型是传统细胞自动机（CA）的可训练变体。NCA所生成模式中的涌现运动已成功应用于动态纹理合成。然而，NCA展现动态模式所需的条件仍未得到探索。本文研究了NCA架构与训练模型涌现动力学之间的关系。具体而言，我们改变了细胞状态中的通道数以及多层感知机（MLP）中的隐藏神经元数量，并建立了这两个变量的组合与连续帧之间运动强度之间的关系。我们的分析表明，这两个变量之间的差异性和比例性与NCA输出中的涌现动力学存在强相关性。因此，我们提出了一种用于创建动态NCA的设计原则。