RecurrenceMicrostatesAnalysis.jl: A Julia library for analyzing dynamical systems with recurrence microstates

Recurrence Quantification Analysis (RQA) has become a standard tool for extracting nonlinear characteristics from time series. It relies on specific recurrence structures within Recurrence Plots, such as diagonal lines that are typically associated with deterministic dynamics. However, its scope is often constrained by the use of predefined patterns. To overcome this limitation, we have recently proposed Recurrence Microstates Analysis (RMA)-an advanced approach that generalizes the analysis of recurrence structures by capturing the statistical properties of generic recurrence motifs. In this paper, we introduce an efficient Julia package for RMA, which supports a wide range of motif shapes, flexible sampling strategies, and comprehensive distribution computation capabilities. Our implementation also features an optimized pipeline for estimating standard RQA quantifiers with significantly reduced memory and computational requirements, making it particularly well-suited for large-scale data sets and, thereby, supporting sustainable and green computing practices. RMA, thus, offers a robust, scalable, memory-efficient, and more versatile alternative to traditional RQA, with promising applications in machine learning and the study of dynamical systems.