Using chaos to generate variations on movement sequences

We describe a method for introducing variations into predefined motion sequ ences using a chaotic symbol-sequence reordering technique. A progression o f symbols representing the body positions in a dance piece, martial arts fo rm, or other motion sequence is mapped onto a chaotic trajectory, establish ing a symbolic dynamics that links the movement sequence and the attractor structure. A variation on the original piece is created by generating a tra jectory with slightly different initial conditions, inverting the mapping, and using special corpus-based graph-theoretic interpolation schemes to smo oth any abrupt transitions. Sensitive dependence guarantees that the variat ion is different from the original; the attractor structure and the symboli c dynamics guarantee that the two resemble one another in both aesthetic an d mathematical senses. (C) 1998 American Institute of Physics. [S1054-1500( 98)00603-X].