A body of scientific/mathematical theory arising from a description of the behavior of complex dynamical systems is explored in terms of its pertinence to and utility in musical schemes for the generation of melodic lines and textures. Such systems are known to model significant behavioral features of real-world phenomena, including turbulent or chaotic behavior. Many of the features of nonlinear dynamical systems that are intriguing from a mathematical point of view, especially the properties and nature of chaos, are likewise suggestive of musical qualities. A variety of musical behaviors may be elicited from chaotic systems, some quite novel, while others are evocative of already well-known practices. Typical is a type of continuous variation form, in which motivic materials are spun out within a constantly evolving context.

Four archetypal chaotic systems, the Hénon and Lorenz systems, the standard map, and the Hénon-Heiles system, are explored in terms of their potential for the generation of melodic lines, textures and rhythms--raw materials suitable for further musical exploration and elaboration. Approximately one hour of recorded examples accompany the dissertation.