In recent years, researchers in social cognition have found the `perceptual crossing paradigm' to be both a theoretical and practical advance towards meeting particular challenges. This paradigm has been used to analyze the type of interactive processes that emerge in minimal interactions and it has allowed progress towards understanding of the principles of social cognition processes. In this paper, we analyze whether some critical aspects of these interactions could not have been observed by previous studies. We consider alternative indicators that could complete, or even lead us to rethink, the current interpretation of the results obtained from both experimental and simulated modelling in the fields of social interactions and minimal perceptual crossing.In particular, we discuss the possibility that previous experiments have been analytically constrained to a short-term dynamic type of player response. Additionally, we propose the possibility of considering these experiments from a more suitable framework based on the use and analysis of long-range correlations and fractal dynamics. We will also reveal evidence supporting the idea that social interactions are deployed along many scales of activity. Specifically, we propose that the fractal structure of the interactions could be a more adequate framework to understand the type of social interaction patterns generated in a social engagement
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