- tags
- Cellular automata, Graphs

This concept was mentioned in (O’Sullivan 2001), although it may not be the first ever mention of it.

The idea is also similar to graph convolutional networks and other graph neural networks, where the goal is to construct an update function for a node that doesn’t depend on the number of neighboring nodes. This enables running cellular automata on non-grid structures.

This idea was recently published at NeurIPS 2021 (Grattarola et al. 2021). In that work, the graphs are fixed and the CA are explicitly modeled as message-passing graph networks. The graph CA are trained with supervision similarly to (Mordvintsev et al. 2020) and the following papers by Mordvinstev et al.

## Bibliography

- David O'Sullivan. . "Graph-cellular Automata: A Generalised Discrete Urban and Regional Model".
*Environment and Planning B: Planning and Design*28 (5):687–705. DOI. - Daniele Grattarola, Lorenzo Livi, Cesare Alippi. . "Learning Graph Cellular Automata".
*Arxiv:2110.14237 [cs]*. http://arxiv.org/abs/2110.14237. -
Alexander Mordvintsev, Ettore Randazzo, Eyvind Niklasson, Michael Levin. . "Growing Neural Cellular Automata".
*Distill*5 (2):e23. DOI. See notes