Creation of regions for dialect features using a cellular automaton

An issue in dialect research has been how to make generalizations from survey data about where some dialect feature might be found. Pre-computational methods included drawing isoglosses or using shadings to indicate areas where an analyst expected a feature to be found. The use of computers allowed for faster plotting of locations where any given feature had been e¬licited, and also allowed for the use of statistical techniques from technical geography to estimate regions where particular features might be found. However, using the computer did not make the analysis less subjective than isoglosses, and statistical methods from technical geography have turned out to be limited in use. We have prepared a cellular automaton (CA) for use with data collected for the Linguistic Atlas Project that can address the problems involved in this type of data visualization. The CA plots the locations where survey data was elicited, and then through the application of rules creates an estimate of the spatial distributions of selected features. The application of simple rules allows the CA to create objective and reproducible estimates based on the data it was given, without the use of statistical methods

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

Sand ripple volume generator for underwater acoustic models, a cellular automaton Monte-Carlo approach

Cellular automata have been successfully used to model the sand dynamics of aeolian dunes and ripples. The cellular automata Monte-Carlo model proposed in this paper expands the capabilities of cellular automata models to under water ripple formation introducing not a two dimensional matrix but two three dimensional volumes, being a sand volume and a water volume. The proposed model has the capability to generate optimal environmental data to input in other mathematical models in need of environmental data. The following enhancements were implemented: optional abstraction levels of the hydrodynamic behavior, morphological formation of underwater ripples under unilateral currents in any direction as well as morphological formation of underwater ripples under wave current interaction, grain size distribution of the sand in every time step in the entire volume and compaction distribution in every time step in the entire sediment volume. The proposed cellular automata model is a closed toroidal system. The toroidal approach of the model enables to build up infinite rippled surfaces by using the generated sediment volumes as tiles; this solves boundary problems in for example acoustic models. Using the fractal properties of the sand ripples, infinite surfaces containing rippled dunes can be generated

When--and how--can a cellular automaton be rewritten as a lattice gas?

Both cellular automata (CA) and lattice-gas automata (LG) provide finite algorithmic presentations for certain classes of infinite dynamical systems studied by symbolic dynamics; it is customary to use the term `cellular automaton' or `lattice gas' for the dynamic system itself as well as for its presentation. The two kinds of presentation share many traits but also display profound differences on issues ranging from decidability to modeling convenience and physical implementability. Following a conjecture by Toffoli and Margolus, it had been proved by Kari (and by Durand--Lose for more than two dimensions) that any invertible CA can be rewritten as an LG (with a possibly much more complex ``unit cell''). But until now it was not known whether this is possible in general for noninvertible CA--which comprise ``almost all'' CA and represent the bulk of examples in theory and applications. Even circumstantial evidence--whether in favor or against--was lacking. Here, for noninvertible CA, (a) we prove that an LG presentation is out of the question for the vanishingly small class of surjective ones. We then turn our attention to all the rest--noninvertible and nonsurjective--which comprise all the typical ones, including Conway's `Game of Life'. For these (b) we prove by explicit construction that all the one-dimensional ones are representable as LG, and (c) we present and motivate the conjecture that this result extends to any number of dimensions. The tradeoff between dissipation rate and structural complexity implied by the above results have compelling implications for the thermodynamics of computation at a microscopic scale.Comment: 16 page