Creative processes exhibit a new, thus far unrecognized, form of dynamical behavior distinct from the known classes of mechanical and chaotic dynamics. We present quantitative methods of time series analysis that distinguish creative processes from random and chaotic systems. Creative processes exhibit diversification, indicating an expanding phase space volume, which contrasts with processes that converge to equilibrium, or to periodic or chaotic attractors. Creative processes exhibit novelty, that is, they produce less recurrence than obtains from random series. Creative processes exhibit arrangement, a measure of patterned recurrences that indicates nonrandom complexity. These three measures, diversification, novelty, and arrangement, reliably identify creative dynamics and distinguish creativity from chaos and from randomness.