A Survey of Cellular Automata: Types, Dynamics, Non-uniformity and Applications

Cellular automata (CAs) are dynamical systems which exhibit complex global behavior from simple local interaction and computation. Since the inception of cellular automaton (CA) by von Neumann in 1950s, it has attracted the attention of several researchers over various backgrounds and fields for modelling different physical, natural as well as real-life phenomena. Classically, CAs are uniform. However, non-uniformity has also been introduced in update pattern, lattice structure, neighborhood dependency and local rule. In this survey, we tour to the various types of CAs introduced till date, the different characterization tools, the global behaviors of CAs, like universality, reversibility, dynamics etc. Special attention is given to non-uniformity in CAs and especially to non-uniform elementary CAs, which have been very useful in solving several real-life problems.Comment: 43 pages; Under review in Natural Computin

Proceedings of AUTOMATA 2010: 16th International workshop on cellular automata and discrete complex systems

International audienceThese local proceedings hold the papers of two catgeories: (a) Short, non-reviewed papers (b) Full paper

Proceedings of AUTOMATA 2011 : 17th International Workshop on Cellular Automata and Discrete Complex Systems

International audienceThe proceedings contain full (reviewed) papers and short (non reviewed) papers that were presented at the workshop

Robust network computation

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.Includes bibliographical references (p. 91-98).In this thesis, we present various models of distributed computation and algorithms for these models. The underlying theme is to come up with fast algorithms that can tolerate faults in the underlying network. We begin with the classical message-passing model of computation, surveying many known results. We give a new, universally optimal, edge-biconnectivity algorithm for the classical model. We also give a near-optimal sub-linear algorithm for identifying bridges, when all nodes are activated simultaneously. After discussing some ways in which the classical model is unrealistic, we survey known techniques for adapting the classical model to the real world. We describe a new balancing model of computation. The intent is that algorithms in this model should be automatically fault-tolerant. Existing algorithms that can be expressed in this model are discussed, including ones for clustering, maximum flow, and synchronization. We discuss the use of agents in our model, and give new agent-based algorithms for census and biconnectivity. Inspired by the balancing model, we look at two problems in more depth.(cont.) First, we give matching upper and lower bounds on the time complexity of the census algorithm, and we show how the census algorithm can be used to name nodes uniquely in a faulty network. Second, we consider using discrete harmonic functions as a computational tool. These functions are a natural exemplar of the balancing model. We prove new results concerning the stability and convergence of discrete harmonic functions, and describe a method which we call Eulerization for speeding up convergence.by David Pritchard.M.Eng

Macroscopic order from reversible and stochastic lattice growth models

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Physics, 1999.Includes bibliographical references (p. 197-209).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.This thesis advances the understanding of how autonomous microscopic physical processes give rise to macroscopic structure. A unifying theme is the use of physically motivated microscopic models of discrete systems which incorporate the constraints of locality, uniformity, and exact conservation laws. The features studied include: stochastic nonequilibrium fluctuations; use of pseudo-randomness in dynamical simulations; the thermodynamics of pattern formation; recurrence times of finite discrete systems; and computation in physical models. I focus primarily on pattern formation: transitions from a disordered to an ordered macroscopic state. Using an irreversible stochastic model of pattern formation in an open system driven by an external source of noise, I study thin film growth. I focus on the regimes of growth and the average properties of the resulting rough surfaces. I also show that this model couples sensitively to the imperfections of various pseudorandom number generators, resulting in non-stochastic exploration of the accessible state space. Using microscopically reversible models, I explicitly model how macroscopic dissipation can arise. In discrete systems with invertible dynamics entropy cannot decrease, and most such systems approach fully ergodic. Therefore these systems are natural candidates for models of thermodynamic behavior. I construct reversible models of pattern formation by dividing the system in two: the part of primary interest, and a "heat bath". We can observe the exchange of heat, energy, and entropy between the two subsystems, and gain insight into the thermodynamics of self-assembly. I introduce a local, deterministic, microscopically reversible model of cluster growth via aggregation in a closed two-dimensional system. The model has a realistic thermodynamics. When started from a state with low coarse grained entropy the model exhibits an initial regime of rapid nonequilibrium growth followed by a quasistatic regime with a well defined temperature. The growth clusters generated display a rich variety of morphologies. I also show how sequences of conditional aggregation events can be used to implement reusable logic gates and how to simulate any digital logic circuit with this model.by Raissa Michelle D'Souza.Ph.D