Fitness landscape of the cellular automata majority problem: View from the Olympus

In this paper we study cellular automata (CAs) that perform the computational Majority task. This task is a good example of what the phenomenon of emergence in complex systems is. We take an interest in the reasons that make this particular fitness landscape a difficult one. The first goal is to study the landscape as such, and thus it is ideally independent from the actual heuristics used to search the space. However, a second goal is to understand the features a good search technique for this particular problem space should possess. We statistically quantify in various ways the degree of difficulty of searching this landscape. Due to neutrality, investigations based on sampling techniques on the whole landscape are difficult to conduct. So, we go exploring the landscape from the top. Although it has been proved that no CA can perform the task perfectly, several efficient CAs for this task have been found. Exploiting similarities between these CAs and symmetries in the landscape, we define the Olympus landscape which is regarded as the ''heavenly home'' of the best local optima known (blok). Then we measure several properties of this subspace. Although it is easier to find relevant CAs in this subspace than in the overall landscape, there are structural reasons that prevent a searcher from finding overfitted CAs in the Olympus. Finally, we study dynamics and performance of genetic algorithms on the Olympus in order to confirm our analysis and to find efficient CAs for the Majority problem with low computational cost

Defect Particle Kinematics in One-Dimensional Cellular Automata

Let A^Z be the Cantor space of bi-infinite sequences in a finite alphabet A, and let sigma be the shift map on A^Z. A `cellular automaton' is a continuous, sigma-commuting self-map Phi of A^Z, and a `Phi-invariant subshift' is a closed, (Phi,sigma)-invariant subset X of A^Z. Suppose x is a sequence in A^Z which is X-admissible everywhere except for some small region we call a `defect'. It has been empirically observed that such defects persist under iteration of Phi, and often propagate like `particles'. We characterize the motion of these particles, and show that it falls into several regimes, ranging from simple deterministic motion, to generalized random walks, to complex motion emulating Turing machines or pushdown automata. One consequence is that some questions about defect behaviour are formally undecidable.Comment: 37 pages, 9 figures, 3 table

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

An artificial development model for cell pattern generation

La formation de structures cellulaires a un rôle crucial dans le développement tant artificiel que naturel. Cette thèse présente un modèle de développement artificiel pour la génération de structures cellulaires basé sur le paradigme des automates cellulaires (AC). La croissance cellulaire est contrôlée par un génome comportant un réseau de régulation artificiel (RRA) et une série de gènes structurels. Ce génome a subi une évolution par algorithme génétique (AG) afin de produire des structures cellulaires en 2D grâce à l'activation et inhibition sélective des gènes. De plus des gradients morphogénétiques ont été utilisés pour fournir aux cellules une information de position permettant de contraindre leur reproduction. Après évolution d'un génome par algorithme génétique, une cellule unique est placée au milieu de la grille de l’AC où sa reproduction, contrôlée par le RRA, produit une structure cellulaire cible. Le modèle a été appliqué avec succès au problème classique de génération de la structure d’un drapeau français (French flag problem).Cell pattern formation has a crucial role in both artificial and natural development. This thesis presents an artificial development model for cell pattern generation based on the cellular automata (CA) paradigm. Cellular growth is controlled by a genome consisting of an artificial regulatory network (ARN) and a series of structural genes. The genome was evolved by a genetic algorithm (GA) in order to produce 2D cell patterns through the selective activation and inhibition of genes. Morphogenetic gradients were used to provide cells with positional information that constrained cellular replication. After a genome was evolved, a single cell in the middle of the CA lattice was allowed to reproduce controlled by the ARN until a cell pattern was formed. The model was applied to the canonical problem of growing a French flag pattern.

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