In previous work I examined an information based complexity measure of networks with weighted links. The measure was compared with that obtained from by randomly shuffling the original network, forming an Erdos-Renyi random network preserving the original link weight distribution. It was found that real world networks almost invariably had higher complexity than their shuffled counterparts, whereas networks mechanically generated via preferential attachment did not. The same experiment was performed on foodwebs generated by an artificial life system, Tierra, and a couple of evolutionary ecology systems, EcoLab and WebWorld. These latter systems often exhibited the same complexity excess shown by real world networks, suggesting that the complexity surplus indicates the presence of evolutionary dynamics. In this paper, I report on a mechanical network generation system that does produce this complexity surplus. The heart of the idea is to construct the network of state transitions of a chaotic dynamical system, such as the Lorenz equation. This indicates that complexity surplus is a more fundamental trait than that of being an evolutionary system.