Implementation of Logical Functions in the Game of Life

The Game of Life cellular automaton is a classical example of a massively parallel collision-based computing device. The automaton exhibits mobile patterns, gliders, and generators of the mobile patterns, glider guns, in its evolution. We show how to construct basic logical perations, AND, OR, NOT in space-time configurations of the cellular automaton. Also decomposition of complicated Boolean functions is discussed. Advantages of our technique are demonstrated on an example of binary adder, realized via collision of glider streams

On learning and the stability of cycles

We study a general equilibrium model where the multiplicity of stationary periodic perfect foresight equilibria is pervasive. We investigate the extent of which agents can learn to coordinate on stationary perfect foresight cycles. The example economy, taken from Grandmont (1985), is an endowment overlapping generations model with fiat money, where consumption in the first and second periods of life are not necessarily gross substitutes. Depending on the value of a preference parameter, the limiting backward (direction of time reversed) perfect foresight dynamics are characterized by steady state, periodic, or chaotic trajectories for real money balances. We relax the perfect foresight assumption and examine how a population of artificial, heterogeneous adaptive agents might learn in such an environment. These artificial agents optimize given their forecasts of future prices, and they use forecast rules that are consistent with steady state or periodic trajectories for prices. The agents' forecast rules are updated by a genetic algorithm. We find that the population of artificial adaptive agents is able to eventually coordinate on steady state and low-order cycles, but not on the higher-order periodic equilibria that exist under the perfect foresight assumption.Business cycles

Evolving Globally Synchronized Cellular Automata

How does an evolutionary process interact with a decentralized, distributed system in order to produce globally coordinated behavior? Using a genetic algorithm (GA) to evolve cellular automata (CAs), we show that the evolution of spontaneous synchronization, one type of emergent coordination, takes advantage of the underlying medium\u27s potential to form embedded particles. The particles, typically phase defects between synchronous regions, are designed by the evolutionary process to resolve frustrations in the global phase. We describe in detail one typical solution discovered by the GA, delineating the discovered synchronization algorithm in terms of embedded particles and their interactions. We also use the particle-level description to analyze the evolutionary sequence by which this solution was discovered. Our results have implications both for understanding emergent collective behavior in natural systems and for the automatic programming of decentralized spatially extended multiprocessor systems

Introduction

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