Merging Cellular Automata for Simulating Surface Effects

International audienceThis paper describes a model of three-dimensional cellular automata allowing to simulate different phenomena in the fields of com- puter graphics and image processing, and to combine them together in order to produce complex effects such as automatic multitexturing, sur- face imperfections, or biological retina multi-layer cellular behaviours. Our cellular automaton model is defined as a network of connected cells arranged in a natural and dynamic way, which affords multi-behavior ca- pabilities. Based on cheap and widespread computing systems, real-time performance can be reached for simulations involving up to a hundred thousand cells. Our approach efficiency is illustrated through a set of CA related to computer graphics –e.g. erosion, sedimentation, or vegetal growing processes– and image analysis –e.g. pipeline retina simulation

Information gain measure for structural discrimination of cellular automata configurations

Cellular automata (CA) are known for their capability in exhibiting interesting emergent behaviour and capacity to generate complex and often aesthetically appealing patterns through the local interaction of rules. Mean information gain has been suggested as a measure of discriminating structurally different two-dimensional (2D) patterns. This paper addresses quantitative evaluation of the complexity of CA generated configurations. In particular, we examine information gain as a spatial complexity measure for discriminating multi-state 2D CA generated configurations. This information-theoretic quantity, also known as conditional entropy, takes into account conditional and joint probabilities of cell states in a 2D plane. The effectiveness of the measure is shown in a series of experiments for multi-state 2D patterns generated by CA. The results of the experiments show that the measure is capable of distinguishing the structural characteristics including symmetries and randomness of 2D CA patterns

Analysis of information gain and Kolmogorov complexity for structural evaluation of cellular automata configurations

Shannon entropy fails to discriminate structurally different patterns in two-dimensional images. We have adapted information gain measure and Kolmogorov complexity to overcome the shortcomings of entropy as a measure of image structure. The measures are customised to robustly quantify the complexity of images resulting from multi-state cellular automata (CA). Experiments with a two-dimensional multi-state cellular automaton demonstrate that these measures are able to predict some of the structural characteristics, symmetry and orientation of CA generated patterns

Aesthetic Automata: Synthesis and Simulation of Aesthetic Behaviour in Cellular Automata

This thesis addresses the computational notion of aesthetics in the framework of multistate two-dimensional cellular automata (2D CA). The measure of complexity is a core concept in computational approaches to aesthetics. Shannon's information theory provided an objective measure of complexity, which led to the emergence of various informational theories of aesthetics. However, entropy fails to take into account the spatial characteristics of 2D patterns; these characteristics are fundamental in addressing the aesthetic problem, in general, and of CA-generated patterns, in particular. This thesis proposes two empirically evaluated alternative measures of complexity, taking into account the spatial characteristics of 2D patterns and experimental studies on human aesthetic perception in the visual domain. The measures are extended to robustly quantify the complexity of multi-state 2D CA-generated patterns. The first model, spatial complexity, is based on the probabilistic spatial distribution of homogeneous/heterogeneous neighbouring cells over the lattice of a multi-state 2D cellular automaton. The second model is based on algorithmic information theory (Kolmogorov complexity) which is extended to estimate the complexity of 2D patterns. The spatial complexity measure presents performance advantage over information-theoretic models, specifically in discriminating symmetries and the orientation in CA-generated patterns, enabling more accurate measurement of complexity in relation to aesthetic evaluations of 2D patterns. A series of experimental stimuli with various structural characteristics and levels of complexity were generated by seeding 3-state 2D CA with different initial configurations for psychological experiments. The results of experimentation demonstrate the presence of correlation between spatial complexity measures and aesthetic judgements of experimental stimuli. The same results were obtained for the estimations of Kolmogorov complexity of experimental stimuli

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