Norman Margolus

Physics-like models of computation☆

Abstract Reversible Cellular Automata are computer-models that embody discrete analogues of the classical-physics notions of space, time, locality, and microscopic reversibility. They are offered as a step towards models of computation that are closer to fundamental physics.

Ininvertible cellular automata: a review

Abstract In the light of recent developments in the theory of invertible cellular automata, we attempt to give a unified presentation of the subject and discuss its relevance to computer science and mathematical physics.

Programmable matter: concepts and realization

Abstract This paper is a manifesto, a brief tutorial, and a call for experiments on programmable matter machines.

Universal cellular automata based on the collisions of soft spheres

Fredkin’s Billiard Ball Model (BBM) is a continuous classical mechanical model of computation based on the elastic collisions of identical finite-diameter hard spheres. When the BBM is initialized appropriately, the sequence of states that appear at successive integer time-steps is equivalent to a discrete digital dynamics.

Thermodynamically reversible generalization of diffusion limited aggregation.

We introduce a lattice gas model of cluster growth via the diffusive aggregation of particles in a closed system obeying a local, deterministic, microscopically reversible dynamics. This model roughly corresponds to placing the irreversible diffusion limited aggregation model (DLA) in contact with a heat bath. Particles release latent heat when aggregating, while singly connected cluster members can absorb heat and evaporate. The heat bath is initially empty, hence we observe the flow of entropy from the aggregating gas of particles into the heat bath, which is being populated by diffusing heat tokens. Before the population of the heat bath stabilizes, the cluster morphology (quantified by the fractal dimension) is similar to a standard DLA cluster. The cluster then gradually anneals, becoming more tenuous, until reaching configurational equilibrium when the cluster morphology resembles a quenched branched random polymer. As the microscopic dynamics is invertible, we can reverse the evolution, observe the inverse flow of heat and entropy, and recover the initial condition. This simple system provides an explicit example of how macroscopic dissipation and self-organization can result from an underlying microscopically reversible dynamics. We present a detailed description of the dynamics for the model, discuss the macroscopic limit, and give predictions for the equilibrium particle densities obtained in the mean field limit. Empirical results for the growth are then presented, including the observed equilibrium particle densities, the temperature of the system, the fractal dimension of the growth clusters, scaling behavior, finite size effects, and the approach to equilibrium. We pay particular attention to the temporal behavior of the growth process and show that the relaxation to the maximum entropy state is initially a rapid nonequilibrium process, then subsequently it is a quasistatic process with a well defined temperature.

Simulating three-dimensional hydrodynamics on a cellular automata machine

We demonstrate how three-dimensional fluid flow simulations can be carried out on the Cellular Automata Machine 8 (CAM-8), a special-purpose computer for cellular automata computations. The principal algorithmic innovation is the use of a lattice gas model with a 16-bit collision operator that is specially adapted to the machine architecture. It is shown how the collision rules can be optimized to obtain a low viscosity of the fluid. Predictions of the viscosity based on a Boltzmann approximation agree well with measurements of the viscosity made on CAM-8. Several test simulations of flows in simple geometries—channels, pipes, and a cubic array of spheres-are carried out. Measurements of average flux in these geometries compare well with theoretical predictions.

A Bridge Of Bits

Cellular Automata are discrete physics-like systems that can be exactly simulated by digital hardware. These systems can incorporate many realistic physical constraints and still be capable of performing digital computation. Such systems bridge the boundary between physical models and computational models, and so can play a central role in investigating the relevance of physical ideas to the theory and practice of computation, and computational ideas to the construction and use of physical models.

PROGRAMMABLE MATTER: CONCEPTS AND REALIZATION

This paper is a manifesto, a brief tutorial, and a call for experiments on programmable matter machines.

The Ideal Energy of Classical Lattice Dynamics

We define, as local quantities, the least energy and momentum allowed by quantum mechanics and special relativity for physical realizations of some classical lattice dynamics. These definitions depend on local rates of finite-state change. In two example dynamics, we see that these rates evolve like classical mechanical energy and momentum.