This article describes a method of digital sound synthesis and algorithmic composition based on iterated nonlinear functions. The mathematical framework of Functional Iteration Synthesis (FIS) is outlined, and the dynamics of a specific FIS model are explained. Given the model's peculiarly chaotic system dynamics, an empirical, exploratory attitude is needed in order to achieve compositionally relevant controls. The required method of this exploration is interactive computer music systems. Some examples are discussed bearing on the author's compositional experience with his Sound Fury project. The approach is described in terms of real-time interaction with a source of chaotic but structured flow of sonic information. The relevance of an “ecological” view of composing is emphasized.