Spontaneous social coordination has been extensively described in natural settings but so far no controlled methodological approaches have been employed that systematically advance investigations into the possible self-organized nature of bond formation and dissolution between humans. We hypothesized that, under certain contexts, spontaneous synchrony-a well-described phenomenon in biological and physical settings-could emerge spontaneously between humans as a result of information exchange. Here, a new way to quantify interpersonal interactions in real time is proposed. In a simple experimental paradigm, pairs of participants facing each other were required to actively produce actions, while provided (or not) with the vision of similar actions being performed by someone else. New indices of interpersonal coordination, inspired by the theoretical framework of coordination dynamics (based on relative phase and frequency overlap between movements of individuals forming a pair) were developed and used. Results revealed that spontaneous phase synchrony (i.e., unintentional in-phase coordinated behavior) between two people emerges as soon as they exchange visual information, even if they are not explicitly instructed to coordinate with each other. Using the same tools, we also quantified the degree to which the behavior of each individual remained influenced by the social encounter even after information exchange had been removed, apparently a kind of social memory.