Over the edge of chaos: Rethinking the relationship between chaos, complexity,
and emergent order;
Implications for novel types of computation
Martin J. Dudziak
Dept. of Physics, Virginia Commonwealth University, Richmond, VA (USA)
and Quantum Dynamics International, Inc. Melbourne, FL (USA)
A dominant trend within the study of nonlinear dynamical systems has been to associate self-organization and emergent coherent behavior with classes of phenomena that meet the criteria of deterministic chaos. Significant attention has been paid to computational models that are based upon formal encoding schema, such as rule-based cellular automata and networks, which after some time-evolution demonstrate behaviors that qualitatively resemble highly complex structures. The nature of complexity as an anticipatory and global response to regulating energy (or information) dissipation is examined in the light of work by Rosen, Kampis, Mikulecky, and others. This results in a critical re-examination of such models that derive self-organization from chaos. A mathematical framework based upon the concept of phase web networks is presented as a system for modeling complex organisms and for working toward both the theoretical and experimental foundations of a new form of computation. This form is based not upon the sequential Turing Machine paradigm but instead upon a type of parallel Co-Processing Network. A fundamental component of such a framework is considered to be in the co-generation of multiple weakly unstable soliton-like phenomena that form the basis of holographic-like structures capable of maintaining memory and correlation of prior events.