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Seed-Turbulence-Iteration explores the aesthetic application of chaos and fractal geometry onto the musical parameters of a work constructed for chamber orchestra. Verhulst's Logistic Map and Devaney's Gingerbreadman Map are the dynamic systems from which melodic contour and temporal duration are derived. These algorithms are used to produce heterophonic and polyphonic results that iterate for a set duration before restarting. Each new beginning involves a change in density (of individual lines, as well as points of articulation in time), orchestration, register, and the pitch reservoir. All pitches are derived from a quantized spectrum that interpolates from a state of harmonicity to inharmonicity across a series of changing fundamentals. Each stage of interpolation coincides with the reseting of algorithmic iterations. Self-similarity and self-affinity are represented vertically, in the family resemblances of the lines produced within each algorithm that occur inside of a given segment, as well as horizontally, in the reiterations that occur over time. Each algorithmic reiteration and each copy within a set of iterations has varied starting or “seed” conditions that produce differentiated results of greater or lesser degrees which are presented in non-linear, strategic arrangement. Turbulence is implemented in the form of probabilistic distortions inserted into algorithmic processes that are meant to vary to some degree the amount of unpredictability of an output parameter (pitch or duration) as well as in intuitive manipulations of algorithmically generated material.

Our investigation was to study the feasibility of piece-wise synchronization of chaotic circuits. In conventional experiments of electronic-circuit chaotic synchronization, two circuits were real-time and continuous connected together. In our research, a computer was used as the master subsystem that output chaotic signals to a slave circuit to study the performance of synchronization. The circuit was based on Cuomo¡¦s design. Several methods of piece-wise control were tested to find out the key point of chaotic synchronization. The experimental results revealed that the most important synchronized waveforms were the chaotic orbits near the region that the attractor change quadrants. A conditional piece-wise synchronization method was developed based on our discoveries. Comparing to the periodic piece-wise synchronization method, our method is more robust to sustain the circuit noise. Another advantage is that, in our method, the experimental results fit the computer simulation quite well.

Dissertation--Evangelisch-Theologische Fakultät--Tübingen--Eberhard-Karls-Universität, 2003.

Thesis (M.A.)--Harding University Graduate School of Religion, 2002. / Committee chair Professor Phillip McMillion. Includes bibliographical references (leaves 191-209).

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Thesis (Ph. D.)--University of Texas at Austin, 2003. / Vita. Includes bibliographical references. Available also from UMI Company.