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 an instability, growing out from noise. 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 emerge a typical biased reconnection between canals, and 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, respectively. This reveals the gastrovascular network as a model system to study morphogenesis of circulation networks and the morphogenetic mechanisms at play.