We present a system for growing graphs which can be thought of as an extension of the update rules used by Cellular Automata. As in Neural Cellular Automata, these rules are encoded in the real-valued weight matrix of a neural network. This should make the system easy to evolve, allowing it to be used as an evolutionary-developmental method of creating graph structures for use as recurrent neural networks or substrates in Reservoir Computing. Here we conduct a random search experiment and characterise five different classes of behaviour of the system. The most interesting of these is when the graph grows for a number of timesteps before naturally coming to a halt as it enters an attractor. This behaviour is seen more frequently than might be expected and contrasts with most developmental systems in which growth must be stopped by external intervention. There are clear parallels with biological morphogenetic processes where growth naturally comes to a halt.
@inproceedings(Waldegrave++:2023-ALife, author = "Riversdale Waldegrave and Susan Stepney and Martin Trefzer", title = "Developmental Graph Cellular Automata", pages = "386-394", doi = "10.1162/isal_a_00658", crossref = "ALife-2023" ) @proceedings(ALife-2023, title = "ALife 2023, Sapporo, Japan, July 2023", booktitle = "ALife 2023, Sapporo, Japan, July 2023", publisher = "MIT Press", year = 2023 )