Fractals Beyond Hierarchy—Analyzing the Temporal Patterns of Contact Networks in a French Public Sector Organization

Fractals describe structural details at arbitrarily small scales, but are mathematically not necessarily complex, presenting a pragmatic way of describing nature. They are also common in social settings, including the organizational space. However, attention has been devoted to temporal fractal patterns in heterarchical or networked organizations. This article leverages data on face-to-face interactions collected by the SocioPatterns collaboration in a public sector organization to investigate temporal fractal patterns in interaction networks and three types of processes have been identified in this. White noise exhibits no correlation in time with rapid, chaotic changes. Brown noise entails a diffusion process with stable, structural patterns, but no quick adaptation. Pink noise exhibits an equilibrium between the two, producing dynamics that maintain stable patterns of interactions, remaining flexible to regulate interaction. The interaction network is described with metrics of social network analysis, and analyzed with detrended fluctuation analysis (DFA) to detect temporal fractal patterns within the three largest departments as well as the whole organization. Results indicate high levels of pink noise with traces of white noise in the departments as well as pink noise with traces of brown noise on the organizational level. While previous research found pink noise processes in self-organizing networks, this article extends them to structured intraorganizational networks. The low levels of brown noise question the influence of rigid organizational structures and processes on the temporal structure of interaction. Hence, the fractal temporal structure of the interactions themselves is a factor that contributes to the stability of interactions between individuals over time.