The essential ingredient for studying the phenomena of emergence is the ability to generate and manipulate emergent systems that span large scales. Cellular automata are the model class particularly known for their effective scalability but are also typically constrained by fixed local rules. In this paper, we propose a new model class of adaptive cellular automata that allows for the generation of scalable and expressive models. We show how to implement computation-effective adaptation by coupling the update rule of the cellular automaton with itself and the system state in a localized way. To demonstrate the applications of this approach, we implement two different emergent models: a self-organizing Ising model and two types of plastic neural networks, a rate and spiking model. With the Ising model, we show how coupling local/global temperatures to local/global measurements can tune the model to stay in the vicinity of the critical temperature. With the neural models, we reproduce a classical balanced state in large recurrent neuronal networks with excitatory and inhibitory neurons and various plasticity mechanisms. Our study opens multiple directions for studying collective behavior and emergence.

翻译：研究涌现现象的关键要素在于能够生成并操控跨越大规模尺度的涌现系统。细胞自动机是一类以有效可扩展性著称的模型，但其通常受限于固定的局部规则。本文提出了一类新的自适应细胞自动机模型，能够生成可扩展且富有表现力的模型。我们展示了如何通过将细胞自动机的更新规则与其自身及系统状态以局部方式耦合，从而实现计算高效的自适应。为演示该方法的实际应用，我们实现了两种不同的涌现模型：自组织伊辛模型以及两类塑性神经网络（速率模型与脉冲模型）。通过伊辛模型，我们展示了如何将局部/全局温度与局部/全局测量值相耦合，从而将模型调控至临界温度附近区域。通过神经模型，我们利用兴奋性与抑制性神经元以及多种可塑性机制，在大规模递归神经网络中复现了经典的平衡态。本研究为集体行为与涌现现象的研究开辟了多条新方向。