Computers, chaos, and choreography
Chaos and machine learning can be used to generate variations on predefined dance sequences. A sequence of dance moves is encoded and then mapped onto a chaotic trajectory, establishing a symbolic dynamics that links the dance sequence and the attractor structure. A choreographic variation is created by generating a trajectory from a different initial condition and then inverting the mapping. Sensitive dependence guarantees that the variation is different from the original; the attractor structure and the symbolic dynamics guarantee that it resembles the original in some sense. A similar approach has been used to generate musical variations (Dabby, in _Chaos_); the issues that arise in chaotic choreography, however, are somewhat different. In particular, while instruments may play arbitrary pitch sequences, kinesiology and style impose a variety of constraints on dance sequences. To solve this problem, we have developed an intelligent interpolation scheme that "smooth" any physically impossible or abrupt transitions that may be introduced by the re- mapping procedure. This corpus-based technique captures the dynamics ("style") of an individual dance genre using inter-move probability transition matrices and grammars; it then uses that information to insert postures that are consistent with the dance genre into nonsmooth portions of the chaotic variation.