Graph approach for Gibson’s ecological optics with dynamics of network motifs

Dynamic visual perception in complex environments is central to understanding the interaction between organisms and their surroundings. Ecological optics depicts that the visual system gains optical information from ambient light, which is structured by relative movements between organism and environment. Recent advances have developed theoretical models of optical information, commonly formalized as optical flows, that account for the perception–action link. However, these frameworks have had limited capacity to inform environmental design, due to a gap between the micro-scale, formalized models of optical information and meso-scale, semantic analyses of observer experience. To address this gap, building on basic principles of ecological optics, we develop a framework that characterizes observers’ perception–action patterns by integrating graph-theoretic concepts and measures. Our framework discretizes spatial and temporal trajectories of ambient light experienced by an observer, in the form of a weighted directed graph. This graph approach directly reveals dynamics of perception–action patterns via network motifs—recurring subgraph patterns within a larger graph. Information entropy, as a temporal measure of information content, indicates the distinct modes of the dynamics. As a demonstration, a state analysis shows that several transient states in the motif-based dynamics exhibit good correlations with observers’ inclination toward places from survey data, validating its potential for spatial analysis. Overall, the proposed framework paves the way towards real-world applications in optimizing dynamic interactions between observer and environment.