Turing machine universality of the game of life

This project proves universal computation in the Game of Life cellular automaton by using a Turing machine construction.Existing proofs of universality in the Game of Life rely on a counter machine. These machines require complex encoding and decoding of the input and output and the proof of universality for these machines by the Church Turing thesis is that they can perform the equivalent of a Turing machine. A proof based directly on a Turing machine is much more accessible.The computational power available today allows powerful algorithms such as HashLife to calculate the evolution of cellular automata patterns sufficiently fast that an efficient universal Turing machine can be demonstrated in a conveniently short period of time. Such a universal Turing machine is presented here. It is a direct simulation of a Turing machine and the input and output are easily interpreted.In order to achieve full universal behaviour an infinite storage media is required. The storage media used to represent the Turing machine tape is a pair of stacks. One stack representing the Turing tape to the left of the read/write head and one for the Turing tape to the right. Collision based construction techniques have been used to add stack cells to the ends of the stacks continuously.The continuous construction of the stacks is equivalent to the formatting of blank media. This project demonstrates that large areas of a cellular automata can be formatted in real time to perform complex functions

Design and Implementation of a Framework for the Interconnection of Cellular Automata in Software and Hardware

There has been a move recently in academia, industry, and the consumer space towards the use of unsupervised parallel computation and distributed networks (i.e., networks of computing elements working together to achieve a global outcome with only local knowledge). To fully understand the types of problems that these systems are applied to regularly, a representative member of this group of unsupervised parallel and distributed systems is needed to allow the development of generalizable results. Although not the only potential candidate, the field of cellular automata is an excellent choice for analyzing how these systems work as it is one of the simplest members of this group in terms of design specification. The current ability of the field of cellular automata to represent the realm of unsupervised parallel and distributed systems is limited to only a subset of the possible systems, which leads to the main goal of this work of finding a method of allowing cellular automata to represent a much larger range of systems. To achieve this goal, a conceptual framework has been developed that allows the definition of interconnected systems of cellular automata that can represent most, if not all, unsupervised parallel and distributed systems. The framework introduces the concept of allowing the boundary conditions of a cellular automaton to be defined by a separately specified system, which can be any system that is capable of producing the information needed, including another cellular automaton. Using this interconnection concept, two forms of computational simplification are enabled: the deconstruction of a large system into smaller, modular pieces; and the construction of a large system built from a heterogeneous set of smaller pieces. This framework is formally defined using an interconnection graph, where edges signify the flow of information from one node to the next and the nodes are the various systems involved. A library has been designed which implements the interconnection graphs defined by the framework for a subset of the possible nodes, primarily to allow an exploration of the field of cellular automata as a potential representational member of unsupervised parallel and distributed systems. This library has been developed with a number of criteria in mind that will allow it to be instantiated on both hardware and software using an open and extendable architecture to enable interaction with external systems and future expansion to take into account novel research. This extendability is discussed in terms of combining the library with genetic algorithms to find an interconnected system that will satisfy a specific computational goal. There are also a number of novel components of the library that further enhance the capabilities of potential research, including methods for automatically building interconnection graphs from sets of cellular automata and the ability to skip over static regions of a given cellular automaton in an intelligent way to reduce computation time. With a particular set of cellular automaton parameters, the use of this feature reduced the computation time by 75%. As a demonstration of the usefulness of both the library and the framework that it implements, a hardware application has been developed which makes use of many of the novel aspects that have been introduced to produce an interactive art installation named 'Aurora'. This application has a number of design requirements that are directly achieved through the use of library components and framework definitions. These design requirements included a lack of centralized control or data storage, a need for visibly dynamic behaviour in the installation, and the desire for the visitors to the installation to be able to affect the visible movement of patterns across the surface of the piece. The success of the library in this application was heavily dependent on its instantiation on a mixture of hardware and software, as well as the ability to extend the library to suit particular needs and aspects of the specific application requirements. The main goal of this thesis research, finding a method that allows cellular automata to represent a much larger range of unsupervised parallel and distributed systems, has been partially achieved in the creation of a novel framework which defines the concept of interconnection, and the design of an interconnection graph using this concept. This allows the field of cellular automata, in combination with the framework, to be an excellent representational member of an extended set of unsupervised parallel and distributed systems when compared to the field alone. A library has been developed that satisfies a broad set of design criteria that allow it to be used in any future research built on the use of cellular automata as this representational member. A hardware application was successfully created that makes use of a number of novel aspects of both the framework and the library to demonstrate their applicability in a real world situation

Genetic evolution and equivalence of some complex systems: fractals, cellular automata and lindenmayer systems

Tesis doctoral inédita leída en la Universidad Autónoma de Madrid. Escuela Politécnica Superior, Departamento de Ingeniería informática.26-04-200

Design and implementation of a compiler for cellular automata machines

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1996.Includes bibliographical references (p. 152).by Daniel R. Risacher.M.Eng

Mapping textures on 3d terrains: a hybrid cellular automata approach

It is a time consuming task to generate textures for large 3D terrain surfaces in computer games, flight simulations and computer animations. This work explores the use of cellular automata in the automatic generation of textures for large surfaces. I propose a method for generating textures for 3D terrains using various approaches - in particular, a hybrid approach that integrates the concepts of cellular automata, probabilistic distribution according to height and Wang tiles. I also look at other hybrid combinations using cellular automata to generate textures for 3D terrains. Work for this thesis includes development of a tool called "Texullar" that allows users to generate textures for 3D terrain surfaces by configuring various input parameters and choosing cellular automata rules. I evaluate the effectiveness of the approach by conducting a user survey to compare the results obtained by using different inputs and analyzing the results. The findings show that incorporating concepts of cellular automata in texture generation for terrains can lead to better results than random generation of textures. The analysis also reveals that incorporating height information along with cellular automata yields better results than using cellular automata alone. Results from the user survey indicate that a hybrid approach incorporating height information along with cellular automata and Wang tiles is better than incorporating height information along with cellular automata in the context of texture generation for 3D meshes. The survey did not yield enough evidence to suggest whether the use of Wang tiles in combination with cellular automata and probabilistic distribution according to height results in a higher mean score than the use of only cellular automata and probabilistic distribution. However, this outcome could have been influenced by the fact that the survey respondents did not have information about the parameters used to generate the final image - such as probabilistic distributions, the population configurations and rules of the cellular automata