Tangle machines are topologically inspired diagrammatic models. Their novel feature is their natural notion of equivalence. Equivalent tangle machines may differ locally, but globally they share the same information content. The goal of tangle machine equivalence is to provide a context-independent method to select, from among many ways to perform a task, the ‘best’ way to perform the task. The concept of equivalent tangle machines is illustrated through examples in which tangle machines represent networks for distributed information processing, networks of adiabatic quantum computations, and iterative computations.