Abstract: In previous work I examined an information based complexity measureof networks with weighted links. The measure was compared with thatobtained from by randomly shuffling the original network, forming anErd\"os-R\'enyi random network preserving the original link weightdistribution. It was found that real world networks almost invariablyhad higher complexity than their shuffled counterparts, whereasnetworks mechanically generated via preferential attachment didnot. The same experiment was performed on foodwebs generated by anartificial life system, Tierra, and a couple of evolutionary ecologysystems, \EcoLab{} and WebWorld. These latter systems often exhibitedthe same complexity excess shown by real world networks, suggestingthat the {\em complexity surplus} indicates the presence ofevolutionary dynamics.In this paper, I report on a mechanical network generation systemthat does produce this complexity surplus. The heart of the idea isconstruct the network of state transitions of a chaotic dynamicalsystem, such as the Lorenz equation. This indicates that complexitysurplus is a more fundamental trait than that of being an evolutionary system.