An Evolutionary Approach to the Design of Controllable Cellular Automata Structure for Random Number Generation

Cellular Automata (CA) has been used in pseudorandom number generation over a decade. Recent studies show that two-dimensional (2-d) CA Pseudorandom Number Generators (PRNGs) may generate better random sequences than conventional one-dimensional (1-d) CA PRNGs, but they are more complex to implement in hardware than 1-d CA PRNGs. In this paper, we propose a new class of 1-d CA Controllable Cellular Automata (CCA) without much deviation from the structure simplicity of conventional 1-d CA. We give a general definition of CCA first and then introduce two types of CCA – CCA0 and CCA2. Our initial study on them shows that these two CCA PRNGs have better randomness quality than conventional 1-d CA PRNGs but their randomness is affected by their structures. To find good CCA0/CCA2 structures for pseudorandom number generation, we evolve them using the Evolutionary Multi-Objective Optimization (EMOO) techniques. Three different algorithms are presented in this paper. One makes use of an aggregation function; the other two are based on the Vector Evaluated Genetic Algorithm (VEGA). Evolution results show that these three algorithms all perform well. Applying a set of randomness tests on the evolved CCA PRNGs, we demonstrate that their randomness is better than that of 1-d CA PRNGs and can be comparable to that of two-dimensional CA PRNGs

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

Upper Bound on the Products of Particle Interactions in Cellular Automata

Particle-like objects are observed to propagate and interact in many spatially extended dynamical systems. For one of the simplest classes of such systems, one-dimensional cellular automata, we establish a rigorous upper bound on the number of distinct products that these interactions can generate. The upper bound is controlled by the structural complexity of the interacting particles---a quantity which is defined here and which measures the amount of spatio-temporal information that a particle stores. Along the way we establish a number of properties of domains and particles that follow from the computational mechanics analysis of cellular automata; thereby elucidating why that approach is of general utility. The upper bound is tested against several relatively complex domain-particle cellular automata and found to be tight.Comment: 17 pages, 12 figures, 3 tables, http://www.santafe.edu/projects/CompMech/papers/ub.html V2: References and accompanying text modified, to comply with legal demands arising from on-going intellectual property litigation among third parties. V3: Accepted for publication in Physica D. References added and other small changes made per referee suggestion

SOUND SYNTHESIS WITH CELLULAR AUTOMATA

This thesis reports on new music technology research which investigates the use of cellular automata (CA) for the digital synthesis of dynamic sounds. The research addresses the problem of the sound design limitations of synthesis techniques based on CA. These limitations fundamentally stem from the unpredictable and autonomous nature of these computational models. Therefore, the aim of this thesis is to develop a sound synthesis technique based on CA capable of allowing a sound design process. A critical analysis of previous research in this area will be presented in order to justify that this problem has not been previously solved. Also, it will be discussed why this problem is worthwhile to solve. In order to achieve such aim, a novel approach is proposed which considers the output of CA as digital signals and uses DSP procedures to analyse them. This approach opens a large variety of possibilities for better understanding the self-organization process of CA with a view to identifying not only mapping possibilities for making the synthesis of sounds possible, but also control possibilities which enable a sound design process. As a result of this approach, this thesis presents a technique called Histogram Mapping Synthesis (HMS), which is based on the statistical analysis of CA evolutions by histogram measurements. HMS will be studied with four different automatons, and a considerable number of control mechanisms will be presented. These will show that HMS enables a reasonable sound design process. With these control mechanisms it is possible to design and produce in a predictable and controllable manner a variety of timbres. Some of these timbres are imitations of sounds produced by acoustic means and others are novel. All the sounds obtained present dynamic features and many of them, including some of those that are novel, retain important characteristics of sounds produced by acoustic means

Transmission of packets on a hierarchical network: Avalanches, statistics and explosive percolation

We discuss transport on load bearing branching hierarchical networks which can model diverse systems which can serve as models of river networks, computer networks, respiratory networks and granular media. We study avalanche transmissions and directed percolation on these networks, and on the V lattice, i.e., the strongest realization of the lattice. We find that typical realizations of the lattice show multimodal distributions for the avalanche transmissions, and a second order transition for directed percolation. On the other hand, the V lattice shows power - law behavior for avalanche transmissions, and a first order (explosive) transition to percolation. The V lattice is thus the critical case of hierarchical networks. We note that small perturbations to the V lattice destroy the power-law behavior of the distributions, and the first order nature of the percolation. We discuss the implications of our results.Comment: 10 Pages, 11 Figures, Published in (Chapter 17) International Conference on Theory and Application in Nonlinear Dynamics (ICAND 2012), Understanding Complex System

Boolean Dynamics with Random Couplings

This paper reviews a class of generic dissipative dynamical systems called N-K models. In these models, the dynamics of N elements, defined as Boolean variables, develop step by step, clocked by a discrete time variable. Each of the N Boolean elements at a given time is given a value which depends upon K elements in the previous time step. We review the work of many authors on the behavior of the models, looking particularly at the structure and lengths of their cycles, the sizes of their basins of attraction, and the flow of information through the systems. In the limit of infinite N, there is a phase transition between a chaotic and an ordered phase, with a critical phase in between. We argue that the behavior of this system depends significantly on the topology of the network connections. If the elements are placed upon a lattice with dimension d, the system shows correlations related to the standard percolation or directed percolation phase transition on such a lattice. On the other hand, a very different behavior is seen in the Kauffman net in which all spins are equally likely to be coupled to a given spin. In this situation, coupling loops are mostly suppressed, and the behavior of the system is much more like that of a mean field theory. We also describe possible applications of the models to, for example, genetic networks, cell differentiation, evolution, democracy in social systems and neural networks.Comment: 69 pages, 16 figures, Submitted to Springer Applied Mathematical Sciences Serie