  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.
