Formal model of embodiment on abstract systems: From hierarchy to heterarchy

Abstract

An embodiment of a simple system, such as a one-dimensional map system, derived from heterarchical duality is discussed. We formalized two pairs of heterarchical layers induced by the indefiniteness of the environment and inconsistency between parts and wholeness by using category theory and applied its construction to a logistic map. From the analysis of its behavior, we universally observed 1/f spectrum for orbits and the fractal-like behavior in the dynamics of return maps. For the coupling map system, the parameter region with an on-off intermittency was clearly extended. Finally, we discuss the relationship between this model and the recent interest in morphological computations and search for a way to deal theoretically with the concept of adaptability. © Springer-Verlag Berlin Heidelberg 2007.