Figure 1.

Degeneracy and the geometrical description of behavior. (A) Human dyad engaged in the virtual room clearing task (B) Behavioral degeneracy: Two qualitatively different entry patterns: Leader cross-over (left) and leader button-hook (right). Leader (green) and follower (blue). Both entry patterns are valid forms of task execution. (C) Illustration of the degeneracy of the entry pattern in a 2-D state space comprised of the horizontal locations of the leader and follower, respectively. In the cross-over entry the leader's horizontal location (x-axis) increases while the follower's horizontal location (y-axis) first increases and then decreases (red curve). The converse is the case for the button-hook entry (blue curve) (D) Geometrical description of a behavior as a trajectory in a high-dimensional state space visualized as 3-dimensional space. (E) Degeneracy leads to an ensemble of potential behavioral trajectories which together form a manifold. The 3D manifold (colored surface) and three sample trajectories (red tracks) illustrate the concept. Note that in most cases the behavioral state space has a dimension greater than three and therefore the behavioral manifold cannot be easily visualized. In our case the behavioral state-space of the avatars is 4-dimensional (2-D coordinates of the two avatars) or 6-dimensional, if the respective pieing angles of the two avatars are taken into account as well.