Systems with high steady-state multiplicity and rich dynamic behavior are difficult to investigate using conventional reductionist methods. A network of more than five reactors hosting cubic autocatalytic reactions may potentially have more than 101 steady states and many distinct dynamic regimes, all for the same parameter set. This paper discusses how the static complexity of such systems can be measured to give a holistic picture. To achieve this, stochastic simulations were performed to statistically determine the bifurcation structure of the system, and the gathered information is summarized using a measure akin to fractal dimension. With this measure, the growth of static complexity is investigated as a function of the network size.