location, velocity and directional tendency of every point generated by a dynamical system by an arrow on the surface of action, the manifold, of a dynamical system. This field of arrows indicating directional and strength of motional tendencies is called a vector field. A vector represents its location at the base of the arrow, its velocity by the length of the arrow (called the modulus) and the direction of the motion by the direction of the arrow. If we regard all moduli as equal to one, every vector on the surface has the same length. The resulting graphs are called direction fields. Looking at a stop-action photograph of any point on this surface, its associated vector informs about where the system would take it over the next unit of time. The whole surface can be marked by initial points, which the dynamical systems move as they generate patterns of orbits of moving arrows in time. The following two brain and behavioral experimental circumstances make this depiction and its relevance to dynamical entropy more concrete. We review in more detail the concrete and visualizable findings from experiments requiring the quantification of characteristic patterns of motion in animals and man. They can be embedded into a similar surface-like setting, which might be called a behavioral manifold. For examples, my students from the past, Martin Paulus and Mark Geyer, now Professors at the Medical School of the La Jolla branch of the University of California studied the effects of psychotropic drugs on the patterns made on the floor by rats of various genetic strains while they wandered about, in exploratory behavior in a bounded space. Monitored by a video camera placed above the ceiling less cages, the patterns made by the paths taken by the rats over time were reconstructed as vectorial orbits on a behavioral manifold. This manifold was then repeatedly partitioned, covered with, from just a few large, in graded progression, to many smaller boxes, each partition composed