Fractal model of nonlinear hierarchical complexity: measuring transition dynamics as fractals of themselves

Abstract

Fractal transition theory and measurement enable fine-grained analysis of the most seemingly-chaotic of the developmental transition phases. The explication of the fractal nature of those transition dynamics informs study of learning, decision making, and complex systems in general. A hallmark of the fractal measure is the use of thesis-organized transition measures that are orthogonal to time. Using this method, unpredictable behaviors become “rational” when understood in terms of attractors within developmental processes. An implication for nonlinear science is to transform data otherwise interpreted as incoherent “white noise” into the coherent fractals of the “pink noise” dimension. By integrating Commons et al’s Model of Hierarchical Complexity ( mhc) and this nonlinear model of the fractal transitional orders of hierarchical complexity, a unified mathematical theory of behavioral development will be possible. Such a new formal theory would account for the entire span of behavioral development’s equilibrium states and phase transitions, from lowest to highest orders of complexity. The mathematical expressions for the transitional orders of hierarchical complexity must be developed and integrated with the existing mhc.