Dispersion of personal spaces

TL;DR

This work treats personal space as a dispersive entity, focusing on the dynamic formation of seating patterns in a rectangular auditorium and quantifying them with an entropy measure over time. It develops several stochastic seat-selection rules, including a center-of-mass–guided approach, and benchmarks their entropy evolution $e(A)$ against real time-lapse data from a $7 \times 14$ seating layout. The key finding is that a center-of-mass–based rule most closely reproduces the observed entropy trajectory, with simpler distance-based heuristics offering partial explanations, while fully random or maximum-distance rules fail to capture the dynamics. The study acknowledges limitations—single observational video and artificial questionnaire data—and proposes richer data collection, alternative distance and entropy metrics, and design implications for improve crowd comfort and space utilization via the notion of crowd social computing.

Abstract

There are many entities that disseminate in the physical space - information, gossip, mood, innovation etc. Personal spaces are also entities that disperse and interplay. In this work we study the emergence of configurations formed by participants when choosing a place to sit in a rectangular auditorium. Based on experimental questionnaire data we design several models and assess their relevancy to a real time-lapse footage of lecture hall being filled up. The main focus is to compare the evolution of entropy of occupied seat configurations in time. Even though the process of choosing a seat is complex and could depend on various properties of participants or environment, some of the developed models can capture at least basic essence of the real processes. After introducing the problem of seat selection and related results in close research areas, we introduce preliminary collected data and build models of seat selection based on them. We compare the resulting models to the real observational data and discuss areas of future research directions.

Figures (5)

• Figure 1: A tabular depiction of the real auditorium filled with participants. The black cells represent occupied seats. The white cells represent empty seats. The seats marked with X represent participants seated before the start of recording. The number in the black cell depicts the order of arrival of the corresponding participant.
• Figure 2: Four initial example configurations. The position of a speaker is marked for each hypothetical auditorium tableau.
• Figure 3: Frequency of distances to the nearest seated participant.
• Figure 4: Frequency of distances to the center of mass.
• Figure 5: Evolution of entropy in time for each of the predefined models and the real data. For each model the trajectory is averaged over 1,000 independent runs of the model.