Viewing Algorithms as Iterative Systems and Plotting Their Dynamic Behaviour

We revive an old but little explored idea about how to think about algorithms and problem solving. Algorithms are discrete dynamical systems, also called iterative systems. Pursuing this point of view pays rich dividends. Important concepts like state space, next-state function, termination, fixed points, invariants, traces etc., can be mapped from dynamical systems to elements of algorithm design. Many of these concepts can be visualised through plots that trace the dynamic behaviour of the algorithm.