Analysing network motifs is a common way of characterising biological networks. Motifs are small subgraphs that are more abundant in the observed network than would be expected in random graphs. They may play an important role in network function, and as such may be selected by evolution. In some cases, such as neural networks, they are instantiated via a developmental process. The processes used to structure Artificial Neural Networks, whether training or evolution, do not usually result in motifs or modularity more generally. We introduce a new version of Developmental Graph Cellular Automata (DGCA) which can be used in an evolutionary and developmental (evo-devo) process to produce networks with specific motif profiles. We evolve developmental rules (the “genome”) so that networks are produced with similar motif profiles to specific biological networks. Networks produced in this way may have useful computational and/or dynamical properties when deployed as Recurrent Neural Networks (RNNs) or in Reservoir Computing (RC).

We explore a wide variety of behaviours possible with Developmental Graph Cellular Automata. We use novelty search to find more extreme types of behaviour in terms of transient length and attractor cycle length. This also serves as a proof-of-concept that the system is evolvable. We then examine in more detail some individual examples of interesting behaviour, particularly focusing on cases where the graph divides into two or more separate components.

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.