This paper reports results of a network theory approach to the study of the United States patent system. We model the patent citation network as a discrete time, discrete space stochastic dynamic system. From patent data we extract an attractiveness function, A(k, l), which determines the likelihood that a patent will be cited. A(k, l) shows power law aging and perferential attachment, the exponent of the latter is increasing since 1993, suggesting that patent citations are increasingly concentrated on a relatively small number of patents. In particular, our results appear consistent with an increasing patent “thicket”, in which more and more patents are issued on minor technical advances.