AbstractTo gain a deeper understanding of the impact of spatial embedding on the dynamics of complex systems, we use a measure of interaction complexity developed within neuroscience using the tools of statistical information theory. We apply this measure to a set of simple network models embedded within Euclidean spaces of varying dimensionality to characterize the way in which the constraints imposed by low‐dimensional spatial embedding contribute to the dynamics (rather than the structure) of complex systems. We demonstrate that strong spatial constraints encourage high intrinsic complexity and discuss the implications for complex systems in general. © 2010 Wiley Periodicals, Inc. Complexity 16: 29–34, 2010