THE HARMONIC PATTERN FUNCTION: A Mathematical Model Integrating Synthesis of Sound and Graphical Patterns

This dissertation substantiates the thesis that a large portion of known sound and graphical synthesis techniques can be unified through a rational function of inverse discrete Fourier transforms and that symmetry, invariance under transformation, plays an important role in understanding the patterns that it produces. The author calls this newly proposed audio/visual synthesis model the harmonic pattern function. A survey of a wide assortment of historic mechanical and electronic devices and computational systems used for generating sonic and visual patterns in art and science reveals that their underlying mathematical descriptions are special cases of this synthesis function.