The Ghost in the Machine: Basin of Attraction Fields of Disordered Cellular Automata Networks

The “basin of attraction fields” of local 1-D cellular automata (CA) were presented in “The Global Dynamics of Cellular Automata” [1]. This paper extends the investigation to “disordered CA networks” (randomly wired/mixed rule), a very general class of discrete dynamical systems in which local CA form a special subset. A “general” direct reverse algorithm is presented for generating the “pre-images” of any global state for disordered CA networks. Computation is many orders of magnitude faster than exhaustive testing. This allows the construction of “transient trees” or “branches, basins of attraction,” or the entire “basin of attraction field,” which represents the system's global dynamics and hierarchical categorisation of state space. Contrasting the behavior of local and disordered CA suggests that local wiring is a necessary condition for “virtual automata” to emerge in the CA's “space-time pattern,” the basis of CA models of artificial life. On the other hand, disordered CA networks, with their vast behavior space, may serve as models of the activity of semi-autonomous groups of inter-connected neurons in the brain. Different wiring/rule schemes result in different field structure, suggesting a paradigm for emergent “brain-like” computation based on the categorization of input; the basin of attraction field (“the ghost in the machine”) categorizes input hierarchically at many levels, and may serve as a dynamical mide model for understanding cognitive processes such as memory and learning. A learning algorithm is outlined which enables the network to learn any number of new pre-images to any given global state (and to forget old ones) by small adjustments to the networks wiring/rule scheme. This opens up the possibility of “sculpting” a basin of attraction field to achieve any desired structure. Disordered CA networks may thus offer a new approach to neural network models for brain-like computation.