Local Transition Rules Research Articles

Algebraic properties of linear cellular automata

Cellular automata are systems evolving on lattices according to a local transition rule. In this paper we present an algebraic formalism for dealing with cellular automata whose local transition rule satisfies an additivity property. We discuss the phenomenon of self-replication and its connection with higher-order cellular automata and the state transition graph.

Mathematical construction of an autonomous artificial life

A living system with autonomously emerging boundaries was presented in previous work. This paper gives a precise mathematical construction of this system by a classification of the flow diagrams and rigorous definition of the global inverse rules of cellular automata. Our model is based on the macroscopic and microscopic perpetual disequilibrations which were first introduced and studied by Mastuno. Because of the perpetual disequilibrations, the boundary conditions are determined a posteriori in succession. This means that our biological model contains the uncontrollability of both the macroscopic and the microscopic boundary conditions. Furthermore, in a typical case of this model, the local transition rule is perpetually changed because of the uncontrollable boundary conditions. Thus, an interaction between the dynamics and boundary conditions which plays an important role in living systems appears in this autonomous artificial life.

Artificial life with autonomously emerging boundaries

The boundary conditions of biological systems are not controllable, due to the perpetual disequilibration of force. This means that the possibilities for the future are open (i.e. one-to-many mapping). However, the future is uniquely determined a posteriori. We argue that such an idea is a basic concept for biological and evolutionary systems and implies unprogrammable systems. But it cannot be described only in a forward-time description. We propose a model in which the uncontrollable boundaries can be described in introducing a backward-time dynamics ( a posteriori description). With respect to the extent of the controllability of boundary conditions, systems are classified into constant, microscopic, macroscopic, and disequilibrium systems. In the last, the local transition rule is perpetually transformed as time progresses, due to the uncontrollable microscopic boundary conditions. Our paradigm deviates from the Newtonian paradigm (i.e. the paradigm of prediction), and its purpose is not to describe the physics of being but to describe that of becoming (evolution).

ON A POLYNOMIAL REPRESENTATION OF FINITE LINEAR CELLULAR AUTOMATA

This paper decides the behaviour of cellular automata, including the existence of fixed points and the order of configurations, using the poly nomial representation of configurations with respect to a basis derived from a series of state transition. We are mainly concerned with cellular automata with local transition rule 90 since the method described here can be used for any finite cellular automata with a little alternations [7].

EXISTENCE OF THE CHARACTERISTIC NUMBERS ASSOCIATED WITH CELLULAR AUTOMATA WITH LOCAL TRANSITION RULE 90

This paper concerns the fundamentals on a new type of finite linear cellular automata with socalled local transition rule 90. Some problems about a few characteristic numbers associated with these automata, initially introduced by S. Huzino, are extensively solved and consequently the author gives a new algebraic formulation of these types of cellular automata, which enables us to challenge further investigations on these types of cellular auto mata of higher dimensions.

Structural basis of multistationary quantum systems. II. Effective few-particle dynamics.

The mutual coupling of electronic multistationary quantum systems realized, e.g., by semiconductor quantum dots is discussed. For local charge-transfer states such coupling can approximately be described in terms of dipole-dipole interactions: the respective renormalized transition frequencies allow for optically controlled conditional switching processes. Two coupled subsystems can in this way perform all the elementary logical operations, including microscopic information transfer. The appropriate architecture for such a quasimolecular computing system is shown to be the distributed computation based on local transition rules. As a simple example a microscopic realization of a one-dimensional one-way cellular automaton with two states per cell and nearest-neighbor coupling is discussed.