A distributed system's interconnection structure emerges as a pattern in the system matrices. This pattern must be preserved through system analysis and control synthesis, and much has been written on these topics. A problem which has not received any attention to date is how to identify a pattern, given the linear system model. This paper proposes a method for identifying a pattern that is mathematically encoded through a commuting relationship with a base matrix. Our method generates the commuting relationship, when it exists. When it does not exist, our method produces the closest approximation to the commuting relationship. Further, it indicates which additional subsystem interconnections would render it achievable. We provide both an exact solution and an almost sure polynomial-time solution in the probabilistic sense. Finally, we give several examples to demonstrate the utility of this method for finding patterns in distributed systems.