Space-time dynamic of normalized doxatons: automata models of pathologicalcollective mentality

The paper aims to investigate influences of norms on a space-time dynamic o f stirred (solutions) and non-stirred (lattices) collectives of very simple believing agents. A mental state of an agent is characterized by agent's b elief in some proposition and a truth value of the proposition in agents lo cal vicinity. Every agent of the collective updates its belief depending on its current belief. belief of its closest neighbours and truth value of th e proposition in neighbourhood of the neighbours. Each agent is represented by a finite automaton - a so-called doxaton [A. Adamtzky, Appl. Math. Comp ut.. in press]. The doxaton takes five doxastic states, derived from the be lief: knowledge, doubt, misbelief delusion and ignorance. In the above ment ioned reference, we defined a binary composition of doxastic states and inv estigated its algebraic structure. The composition itself is not determinis tic; however, it can be made deterministic by applying norms. The norms are expressed in a priority order on the doxastic states. Space-time evolution of the solutions and the lattices of doxatons is studied in computer exper iments to understand influences of norms and initial conditions on the beha viour of abstract collectives of simple agents. Diffusion and reaction of d oxastic states are explored as well as formation of stationary patterns of the doxastic states. (C) 2001 Elsevier Science Ltd. All rights reserved.