Recurrence relations have been of interest since ancient times. Perhaps the most famous is the Fibonacci numbers, where each additional term in the sequence is obtained as the sum of the previous two. I will show how we can use a graphical language of string diagrams?a ?graphical linear algebra??to reason about recurrence relations, and as a bonus, obtain efficient implementations. The application amounts to a compositional, string diagrammatic treatment of signal flow graphs?a model of computation originally studied by Claude Shannon in the 1940s.