Patterns in biology can be considered as predetermined or arising from a self-organizing instability. Variability in the pattern can, thus, be interpreted as a trace of instability, growing out from noise. Studying this variability can, thus, hint toward an underlying morphogenetic mechanism. Here, we present the variability of the gastrovascular system of the jellyfish Aurelia. In this variability emerges a typical biased reconnection between canals and time-correlated reconnections. Both phenomena can be interpreted as traces of mechanistic effects, the swimming contractions on the tissue surrounding the gastrovascular canals, and the mean fluid pressure inside them. This reveals the gastrovascular network as a model system to study the morphogenesis of circulation networks and the morphogenetic mechanisms at play.

Many ramified, network-like patterns in nature, such as river networks or blood vessels, form as a result of unstable growth of moving boundaries in an external diffusive field. Here, we pose the inverse problem for the network growth—can the growth dynamics be inferred from the analysis of the final pattern? We show that by evolving the network backward in time one can not only reconstruct the growth rules but also get an insight into the conditions under which branch splitting occurs. Determining the growth rules from a single snapshot in time is particularly important for growth processes so slow that they cannot be directly observed, such as growth of river networks and deltas or cave passages. We apply this approach to analyze the growth of a real river network in Vermont, USA. We determine its growth rule and argue that branch splitting events are triggered by an increase in the tip growth velocity.