Set Of Cellular Automata Rules Research Articles

Cellular automata as convolutional neural networks

Deep-learning techniques have recently demonstrated broad success in predicting complex dynamical systems ranging from turbulence to human speech, motivating broader questions about how neural networks encode and represent dynamical rules. We explore this problem in the context of cellular automata (CA), simple dynamical systems that are intrinsically discrete and thus difficult to analyze using standard tools from dynamical systems theory. We show that any CA may readily be represented using a convolutional neural network with a network-in-network architecture. This motivates the development of a general convolutional multilayer perceptron architecture, which we find can learn the dynamical rules for arbitrary CA when given videos of the CA as training data. In the limit of large network widths, we find that training dynamics are nearly identical across replicates, and that common patterns emerge in the structure of networks trained on different CA rulesets. We train ensembles of networks on randomly sampled CA, and we probe how the trained networks internally represent the CA rules using an information-theoretic technique based on distributions of layer activation patterns. We find that CA with simpler rule tables produce trained networks with hierarchical structure and layer specialization, while more complex CA produce shallower representations-illustrating how the underlying complexity of the CA's rules influences the specificity of these internal representations. Our results suggest how the entropy of a physical process can affect its representation when learned by neural networks.

Game level layout generation using evolved cellular automata

ABSTRACTDesign of level layouts typically involves the production of a set of levels which are different, yet display a consistent style based on the purpose of a particular level. In this paper, a new approach to the generation of unique level layouts, based on a target set of attributes, is presented. These attributes, which are learned automatically from an example layout, are used for the off-line evolution of a set of cellular automata rules. These rules can then be used for the real-time generation of level layouts that meet the target parameters. The approach is demonstrated on a set of maze-like level layouts. Results are presented to show the effect of various CA parameters and rule representation.

Hyperspectral image segmentation through evolved cellular automata

Segmenting multidimensional images, in particular hyperspectral images, is still an open subject. Two are the most important issues in this field. On one hand, most methods do not preserve the multidimensional character of the signals throughout the segmentation process. They usually perform an early projection of the hyperspectral information to a two dimensional representation with the consequent loss of the large amount of spectral information these images provide. On the other hand, there is usually very little and dubious ground truth available, making it very hard to train and tune appropriate segmentation and classification strategies. This paper describes an approach to the problem of segmenting and classifying regions in multidimensional images that performs a joint two-step process. The first step is based on the application of cellular automata (CA) and their emergent behavior over the hyperspectral cube in order to produce homogeneous regions. The second step employs a more traditional SVM in order to provide labels for these regions to classify them. The use of cellular automata for segmentation in hyperspectral images is not new, but most approaches to this problem involve hand designing the rules for the automata and, in general, average out the spectral information present. The main contribution of this paper is the study of the application of evolutionary methods to produce the CA rule sets that result in the best possible segmentation properties under different circumstances without resorting to any form of projection until the information is presented to the user. In addition, we show that the evolution process we propose to obtain the rules can be carried out over RGB images and then the resulting automata can be used to process multidimensional hyperspectral images successfully, thus avoiding the problem of lack of appropriately labeled ground truth images. The procedure has been tested over synthetic and real hyperspectral images and the results are very competitive.

Unsupervised Segmentation of Hyperspectral Images through Evolved Cellular Automata

The problem of segmenting multidimensional images, in particular hyperspectral images, is still an open subject. The main issue is related to preserving the multidimensional character of the signals throughout the segmentation process avoiding an early projection onto a 2D plane with the consequent loss of the wealth of information these images provide. The approach followed here is based on the use of cellular automata (CA) and their emergent behavior over the hyperspectral cube in order to achieve this objective. Using cellular automata for segmentation in hyperspectral images is not new, but most approaches to this problem involve hand designing the rules for the automata. Additionally, most references found are just extensions of one or three-dimensional methods to multidimensional images, and, as a consequence, average out the spectral information present. The main contributions of this paper is the study of the application of evolutionary methods to produce the CA rule sets that result in the best possible segmentation properties under different circumstances without resorting to any form of projection until the information is presented to the user. The procedure has been tested over synthetic and real hyperspectral images.

Generating PNS for Secret Key Cryptography Using Cellular Automaton

The paper presents new results concerning application of cellular automata (CAs) to the secret key using vernam cipher cryptography.CA are applied to generate pseudo-random numbers sequence (PNS) which is used during the encryption process. One dimensional, non-uniform CAs is considered as a generator of pseudorandom number sequences (PNSs) used in cryptography with the secret key. The quality of PNSs highly depends on a set of applied CA rules. Rules of radius r = 1 and 2 for non-uniform one dimensional CAs have been considered. The search of rules is performed with use of evolutionary technique called cellular programming. As the result of collective behavior of discovered set of CA rules very high quality PNSs are generated. The quality of PNSs outperforms the quality of known one dimensional CA-based PNS generators used in the secret key cryptography. The extended set of CA rules which was found makes the cryptography system much more resistant on breaking a cryptography key.

Emergent behavior in two complex cellular automata rule sets: Research Articles

Cellular automata systems often produce complex behavior from simple rule sets. The behaviors and results of two complex combinations of cellular automata rules are analyzed. Both two-dimensional rule sets add complexities to typical cellular automata systems by attaching attributes and rules to each cell. One of the rule sets produces gliders that reproduce upon collision, whereas the other grows into an intricate shape. Projection and entropy analysis classify the rule sets as complex for the intricate shape, but measurements indicate that the self-reproducing gliders fall between ordered and complex classification, despite their complex appearance. © 2005 Wiley Periodicals, Inc. Complexity 10: 45–55, 2005

Emergent behavior in two complex cellular automata rule sets

Cellular automata systems often produce complex behavior from simple rule sets. The behaviors and results of two complex combinations of cellular automata rules are analyzed. Both two-dimensional rule sets add complexities to typical cellular automata systems by attaching attributes and rules to each cell. One of the rule sets produces gliders that reproduce upon collision, whereas the other grows into an intricate shape. Projection and entropy analysis classify the rule sets as complex for the intricate shape, but measurements indicate that the self-reproducing gliders fall between ordered and complex classification, despite their complex appearance. © 2005 Wiley Periodicals, Inc. Complexity 10: 45–55, 2005

Cellular-automaton model for reactive systems.

A method for constructing a variety of probabilistic lattice-gas cellular automata for chemically reacting systems is described. The microscopic reactive dynamics give rise to a general fourth-order polynomial rate law for the average particle density. The reduction of the microdynamical equations to a discrete or continuous Boltzmann equation is presented. Connection between the linearized Boltzmann equations and a reaction-diffusion macroscopic equation is discussed. As an example of the general formalism a set of cellular automata rules that yield the Schl\"ogl phenomenological model is constructed. Simulation results are presented.