Recurrence analysis of uniform binary substitutions

Abstract: Recurrence rate, determinism, average line length, and entropy of line lengths are measures of complexity in recurrence quantification analysis, that help to understand the structure, predictability and complexity of dynamical systems. In this paper, we provide explicit formulas for these characteristics for all binary substitutions of constant length. Moreover, we show that the determinism of such substitutions converges to one, which shows that these systems are highly predictable.