Introduction

Symbolic dynamics provides a mathematical framework for representing complex systems as sequences of discrete symbols. As described by Marcus and Williams [MaWi08]:

“Symbolic Dynamics is the study of shift spaces, which consist of infinite or bi-infinite sequences defined by a shift-invariant constraint on the finite-length sub-words. Mappings between two such spaces can be regarded as codes or encodings. Shift spaces are classified, up to various kinds of invertible encodings, by combinatorial, algebraic, topological and measure-theoretic invariants. The subject is intimately related to dynamical systems, ergodic theory, automata theory and information theory.”

This formal perspective highlights the richness of symbolic sequence analysis and its connections to multiple domains. More recent overviews of symbolic dynamics can be found in [HiAm23], while [Cai23] presents a Python package focused on the theoretical foundations of the field.

ScySeq adopts a complementary approach. Rather than focusing primarily on theoretical developments, it provides a practical and modular framework for working with symbolic sequences in applied contexts. The package enables users to construct, manipulate, analyze, and visualize sequences of symbols in a consistent and extensible way.

The motivation for ScySeq arises in particular from behavioral research, where observations (e.g., movement, vocalization, interaction states) are often coded as discrete events over time. These coded observations can naturally be represented as symbolic sequences and analyzed to quantify structure, variability, complexity, and recurrence patterns.

An example of the use of ScySeq in a behavioral context is provided in [DoPN22].