Past research has revealed that in natural social interactions, such as having a conversation or emptying a dishwasher with someone, the overall bodily activity of actors increases and decreases in a periodic fashion and that the bodily activity of the co-actors are synchronized. We have been using a recently discovered a video-based methodology for acquiring whole body time series to evaluate and model this interactional synchrony in natural but structured conversation tasks. In recent experiments, pairs of participants perform a task that requires conversation to accomplish its goal such as alphabetizing a list of words or telling knock-knock jokes to each other. Analyses of whole body activity time series revealed rhythmic activity of the participants that was significantly correlated and phase entrained at multiple timescales that correspond to the goals and sub-goals of the task and also revealed that the coupling of these multiple local dynamics has a fractal composition. Although these results suggest that synchronization occurs implicitly in everyday conversations, the traditional steady-state synchronization models we have used in our previous work on interpersonal synchronization are inappropriate to understand these results. New mathematical modeling of the dynamics of the local component dynamics as well as their coupling is necessary for understanding the multi-scale, fractal interpersonal coordination found in these structured conversation tasks.