The Bernoulli shift map is a well-known chaotic map in chaos theory. For a binary system, however, the output is not chaotic and converges to zero instead. One way to prevent this is by perturbing the state space of the map. In a new study, researchers explore one such perturbation method to obtain non-converging outputs with long periods and analyze these periods using modular arithmetic, obtaining a complete list of parameter values for optimal perturbations.