Cellular Automata as a Model of Physical Systems

Cellular Automata (CA), as they are presented in the literature, are abstract mathematical models of computation. In this pa- per we present an alternate approach: using the CA as a model or theory of physical systems and devices. While this approach abstracts away all details of the underlying physical system, it remains faithful to the fact that there is an underlying physical reality which it describes. This imposes certain restrictions on the types of computations a CA can physically carry out, and the resources it needs to do so. In this paper we explore these and other consequences of our reformalization.Comment: To appear in the Proceedings of AUTOMATA 200

Lattice-Gas Cellular Automata In Modeling Biological Pattern Formation

There are several phenomena present in the physical world which can be defined or predicted by specific models. Cellular automata are basic mathematical models for characterization of natural systems by generating simple components and their local interactions. These models are specified on simple updating rules yet demonstrate complex behavior of physical phenomena. Besides this, lattice-gas cellular automata models go one step further and differ from cellular automata by having split updating rule into two parts as collision and propagation. In this study, the goal is to analyze hexagonal lattice-gas cellular automata with single cell type by using agent-based modeling and simulate the model with NetLogo to observe pattern formation. The model examination is focused on the two parameters for stability analysis. The results show that if there is a pattern formation in the model, the system is unstable, and if the patches are smaller and lighter patches, it is stable. Furthermore, the analysis for the choice of particle density and adhesion coefficient displayed that they are the main decision-mechanisms for general structure

Modelling Global Climate Variables with Cellular Automata Networks

Cellular automata are discrete models that can be used to simulate many physical systems. Cellular automata have been used to model gas diffusion, different types of chemical reactions, population growth, and land use change over time. Recent research into cellular automata networks has shown that if sparse long range connections are added to a cellular automata, then it will exhibit properties of complex networks. Furthermore, research into modeling climate systems has shown that modeling the global climate as a complex network can be used to predict individual climate variables. In this work we attempt to connect these ideas by simulating global climate variables, from the National Center for Environmental Prediction / National Center for Atmospheric Research Reanalysis 1 Dataset, as a cellular automata model and as a cellular automata network model. In our experiments we use neural networks as the cellular automata transition functions, using both single and multi-variable data. The results of our work suggest that cellular automata networks are better at modeling climate variables than standard cellular automata and that cellular automata based modeling is a viable approach to modeling climate data

A general representation of dynamical systems for reservoir computing

Dynamical systems are capable of performing computation in a reservoir computing paradigm. This paper presents a general representation of these systems as an artificial neural network (ANN). Initially, we implement the simplest dynamical system, a cellular automaton. The mathematical fundamentals behind an ANN are maintained, but the weights of the connections and the activation function are adjusted to work as an update rule in the context of cellular automata. The advantages of such implementation are its usage on specialized and optimized deep learning libraries, the capabilities to generalize it to other types of networks and the possibility to evolve cellular automata and other dynamical systems in terms of connectivity, update and learning rules. Our implementation of cellular automata constitutes an initial step towards a general framework for dynamical systems. It aims to evolve such systems to optimize their usage in reservoir computing and to model physical computing substrates.Comment: 5 pages, 3 figures, accepted workshop paper at Workshop on Novel Substrates and Models for the Emergence of Developmental, Learning and Cognitive Capabilities at IEEE ICDL-EPIROB 201

SIMULATION OF CALCIUM PHOSPHATE DEPOSITION ON STAINLESS STEEL SURFACES: A NEW APPROACH BASED ON CELLULAR AUTOMATA

Fouling caused by calcium phosphate upon heating is basically a crystallization/precipitation process, which starts with the formation of stable clusters of ions or molecules in a process called nucleation that occurs either in the bulk liquid or at the surface. The cellular automata are useful tools to model complex systems of the universe. They could be considered as a good alternative to differential equations and have been used to model many physical/biological systems. In this preliminary work, a two dimensional space was considered where the cellular automata lattice was represented as a grid of squares, with each square representing a single automaton cell. Several situations were simulated, representing the growth of the deposit on stainless steel materials for different surface energies. The results of the simulations were compared with experimental data obtained in the laboratory

Common metrics for cellular automata models of complex systems

The creation and use of models is critical not only to the scientific process, but also to life in general. Selected features of a system are abstracted into a model that can then be used to gain knowledge of the workings of the observed system and even anticipate its future behaviour. A key feature of the modelling process is the identification of commonality. This allows previous experience of one model to be used in a new or unfamiliar situation. This recognition of commonality between models allows standards to be formed, especially in areas such as measurement. How everyday physical objects are measured is built on an ingrained acceptance of their underlying commonality. Complex systems, often with their layers of interwoven interactions, are harder to model and, therefore, to measure and predict. Indeed, the inability to compute and model a complex system, except at a localised and temporal level, can be seen as one of its defining attributes. The establishing of commonality between complex systems provides the opportunity to find common metrics. This work looks at two dimensional cellular automata, which are widely used as a simple modelling tool for a variety of systems. This has led to a very diverse range of systems using a common modelling environment based on a lattice of cells. This provides a possible common link between systems using cellular automata that could be exploited to find a common metric that provided information on a diverse range of systems. An enhancement of a categorisation of cellular automata model types used for biological studies is proposed and expanded to include other disciplines. The thesis outlines a new metric, the C-Value, created by the author. This metric, based on the connectedness of the active elements on the cellular automata grid, is then tested with three models built to represent three of the four categories of cellular automata model types. The results show that the new C-Value provides a good indicator of the gathering of active cells on a grid into a single, compact cluster and of indicating, when correlated with the mean density of active cells on the lattice, that their distribution is random. This provides a range to define the disordered and ordered state of a grid. The use of the C-Value in a localised context shows potential for identifying patterns of clusters on the grid

Decidability and Universality in Symbolic Dynamical Systems

Many different definitions of computational universality for various types of dynamical systems have flourished since Turing's work. We propose a general definition of universality that applies to arbitrary discrete time symbolic dynamical systems. Universality of a system is defined as undecidability of a model-checking problem. For Turing machines, counter machines and tag systems, our definition coincides with the classical one. It yields, however, a new definition for cellular automata and subshifts. Our definition is robust with respect to initial condition, which is a desirable feature for physical realizability. We derive necessary conditions for undecidability and universality. For instance, a universal system must have a sensitive point and a proper subsystem. We conjecture that universal systems have infinite number of subsystems. We also discuss the thesis according to which computation should occur at the `edge of chaos' and we exhibit a universal chaotic system.Comment: 23 pages; a shorter version is submitted to conference MCU 2004 v2: minor orthographic changes v3: section 5.2 (collatz functions) mathematically improved v4: orthographic corrections, one reference added v5:27 pages. Important modifications. The formalism is strengthened: temporal logic replaced by finite automata. New results. Submitte

Making Classical Ground State Spin Computing Fault-Tolerant

We examine a model of classical deterministic computing in which the ground state of the classical system is a spatial history of the computation. This model is relevant to quantum dot cellular automata as well as to recent universal adiabatic quantum computing constructions. In its most primitive form, systems constructed in this model cannot compute in an error free manner when working at non-zero temperature. However, by exploiting a mapping between the partition function for this model and probabilistic classical circuits we are able to show that it is possible to make this model effectively error free. We achieve this by using techniques in fault-tolerant classical computing and the result is that the system can compute effectively error free if the temperature is below a critical temperature. We further link this model to computational complexity and show that a certain problem concerning finite temperature classical spin systems is complete for the complexity class Merlin-Arthur. This provides an interesting connection between the physical behavior of certain many-body spin systems and computational complexity.Comment: 24 pages, 1 figur

Causal Fermions in Discrete Spacetime

In this paper, we consider fermionic systems in discrete spacetime evolving with a strict notion of causality, meaning they evolve unitarily and with a bounded propagation speed. First, we show that the evolution of these systems has a natural decomposition into a product of local unitaries, which also holds if we include bosons. Next, we show that causal evolution of fermions in discrete spacetime can also be viewed as the causal evolution of a lattice of qubits, meaning these systems can be viewed as quantum cellular automata. Following this, we discuss some examples of causal fermionic models in discrete spacetime that become interesting physical systems in the continuum limit: Dirac fermions in one and three spatial dimensions, Dirac fields and briefly the Thirring model. Finally, we show that the dynamics of causal fermions in discrete spacetime can be efficiently simulated on a quantum computer.Comment: 16 pages, 1 figur

Sculplexity: Sculptures of Complexity using 3D printing

We show how to convert models of complex systems such as 2D cellular automata into a 3D printed object. Our method takes into account the limitations inherent to 3D printing processes and materials. Our approach automates the greater part of this task, bypassing the use of CAD software and the need for manual design. As a proof of concept, a physical object representing a modified forest fire model was successfully printed. Automated conversion methods similar to the ones developed here can be used to create objects for research, for demonstration and teaching, for outreach, or simply for aesthetic pleasure. As our outputs can be touched, they may be particularly useful for those with visual disabilities.Comment: Free access to article on European Physics Letter