A Universal Semi-totalistic Cellular Automaton on Kite and Dart Penrose Tilings

In this paper we investigate certain properties of semi-totalistic cellular automata (CA) on the well known quasi-periodic kite and dart two dimensional tiling of the plane presented by Roger Penrose. We show that, despite the irregularity of the underlying grid, it is possible to devise a semi-totalistic CA capable of simulating any boolean circuit on this aperiodic tiling.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249

Evolutionary games on graphs

Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first three sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fourth section surveys the topological complications implied by non-mean-field-type social network structures in general. The last three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.Comment: Review, final version, 133 pages, 65 figure

Basic Cable: Notes Toward Digital Ontology

This thesis begins the work of constructing a fundamental ontology that employs the network automaton—a class of abstract computer program—as its model. Following a brief historical overview of the theory of network automata and its culmination in the work of Steven Wolfram, I examine how it bears on the ancient question concerning whether the continuous or the discrete has ontological primacy, consider the ontological status of materiality in consultation with Deleuzean ontology, and introduce the concept of prescience as a means of topologically mapping emergent patterns within the causal relations that compose the network. Finally, I will break the network automaton down even further into its most rudimentary functional operations, and consider preliminarily how this model might be adapted toward an atomistic theory of the subject

Fluctuation-driven computing on number-conserving cellular automata

A number-conserving cellular automaton (NCCA) is a cellular automaton in which the states of cells are denoted by integers, and the sum of all of the numbers in a configuration is conserved throughout its evolution. NCCAs have been widely used to model physical systems that are ruled by conservation laws of mass or energy. lmai et al. [13] showed that the local transition function of NCCA can be effectively translated into the sum of a binary flow function over pairs of neighboring cells. In this paper, we explore the computability of NCCAs in which the pairwise number flows are performed at fully asynchronous timings. Despite the randomness that is associated with asynchronous transitions, useful computation still can be accomplished efficiently in the cellular automata through the active exploitation of fluctuations [18]. Specifically, certain numbers may flow randomly fluctuating between forward and backward directions in the cellular space, as if they were subject to Brownian motion. Because random fluctuations promise a powerful resource for searching through a computational state space, the Brownian-like flow of the numbers allows for efficient embedding of logic circuits into our novel asynchronous NCCA

Proceedings of AUTOMATA 2010: 16th International workshop on cellular automata and discrete complex systems

International audienceThese local proceedings hold the papers of two catgeories: (a) Short, non-reviewed papers (b) Full paper

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