back (“fold”) into the spiral unpredictably somewhere in a mixing mechanism that has been called “displaced reinjection.” In the slow-fast oscillations of the forced van der Pol in the chaotic regime, points in the slow phase (“repolarization”) jitter around and step on each other’s heels, getting out of order while waiting on the ledge before jumping (“depolarization”) to the next slow phase (“repolarization”) at some unpredictable time, thus generating a variably irregular series of interspike intervals. Stretching and folding are also responsible for getting points get out of order in the single maximum map of the unit interval (studied for universal qualitative and quantitative properties by May and Feigenbaum and others as described above). With increases in parameter values, the parabolic hill function onto which the unit line has been stretched gets steeper, more stretched. Mapping points on the hill back onto the straight line of the unit interval results in what amounts to the line folding back on itself. This stretching and folding eventually fills the line with points, but their sequence, from end to end, gets shuffled like a deck of cards. As described more generally above, points that start as neighbors may get separated (“divergence along the attractor’) and those that start at a distance from each other may be thrown together (“compression back onto the attractor”). These expanding and folding motions that characterize the chaotic behavior on strange attractors have been likened to the actions of a taffy puller (Réssler, 1976). It is in this way that nearby points can separate without leaving the attractor. It is also the case that once indistinguishably close but then separated points may be compressed together again generating new, temporary (unstable) cycles of all possible period lengths. These unstable fixed points may be the most important feature of chaotic systems from the standpoint of new ideas about brain mechanisms (Pei and Moss, 1996; S