Chapter 1: Time and Self-Similar Structure in Behavior and Interactions: From Sequences to Symmetry and Fractals

Abstract

This chapter concerns the temporal structure of behavior and interaction amongst individuals as diverse as brain neurons and humans. It suggests a view of behavior and interaction in terms of recurrent self-similar tree structures, T-patterns, which thus have the basic characteristics of fractals and exemplify translation symmetry through the similarity of the recurrence of each, a view that is the basis for the special pattern (T-pattern) detection algorithms implemented in the THEME software especially developed for T-pattern detection. Derived concepts are defined and illustrated with special T-pattern diagrams. Some comparison is made with standard multivariate statistics methods. The analysis of Big Data and Tiny Data using this particular recurrent hierarchical and multiordinal pattern detection approach is discussed, as well as the use of T-pattern Analysis (TPA) to detect experimental effects that often remain hidden to standard statistical methods.