2-Dimensional Reversible Hexagonal Cellular Automata with Periodic Boundary

Cellular Automata (CA) is used in pseudo-random number generators (PRNG) to produce high-rate random numbers. The randomness of such numbers directly depends upon the CA rules and the number of neighbor cells. The two-dimensional (2D) CA has several limitations such as, finding the best CA rules, boundary cell problems, etc. To address the problems existing in the 2D CA, we propose a random number generator based on 3D cellular automata. The proposed generator is based on rule numbers 43, 85, 170, and 201, and incremental boundary conditions. The rules are randomly changed after each cycle depending on a clock bit mechanism. The output bits are then passed to the Diehard and ENT test suites to test its randomness [1]. The results reveal that the bit stream generated by the proposed scheme passes all the tests present in the test suites.

The non-orthogonal multiple access-passive optical network (NOMA-PON) is facing the dual security threats of primary user interference and unauthorized third-party user eavesdropping, so efficient data security enhancement techniques are crucial. To solve these problems, we propose a fixed-point extended (FE)-logistic chaotic mapping to reduce the computational complexity while employing a two-dimensional (2D) cellular automata (CA) and Turing pattern (TP) cascading scramble (CA-TPCS) encryption algorithm to further improve the sensitivity of the NOMA-PON system. The CA-TPCS consists of 2D-CA dynamic bit encryption and Turing symbol substitution (TSS). By using FE chaos to construct 2D-CA and adopting index sort to extract the TSS matrix, dynamic diffusion of bits and scrambling of a 2D symbol matrix are achieved. To ensure the key privacy, we employ a dual key mechanism, and uplink data is introduced as the private key. To verify the feasibility of the proposed method, a simulation validation is built on a 17.6 Gb/s power division multiplexing-orthogonal frequency division multiplexing (PDM-OFDM) NOMA-PON system transmitted over 25 km standard single mode fiber (SSMF). The results show that the proposed scheme has no effect on the optimal power allocation rate (PAR) values and the values are all 3. Meanwhile, the receiver sensitivity gains of 0.2 and 0.3 dB are obtained for high-power and low-power users after encryption. The ciphertext has good diffusion and statistical properties, and the key space is flexibly controlled by the FE precision f, the length l of the transmitted bit, and the size T of the TP, with the value of 22f+l+T×T. The results show that the proposed scheme is not only very compatible with PDM technology but also can realize the dual defense of internal aggression and external aggression. It has a good application prospect in the future NOMA-PON.

Matrix algebraic formulae concerning some exceptional rules of two-dimensional cellular automata

Feature Extraction is a long active topic in image processing, and it attracts lots of attention over the last five decades due to its uses in real-life applications. Edge detection method allows users to discover the features of an image for a notable change in the gray level. This texture indicates an ending of one region and the beginning of another in the image. Likewise, over the last few decades, researchers have been exploring to exploit the simple computing model of Cellular Automata (CA) with local neighborhood structure in image processing techniques. The usage of CA in applications of medical image-processing is identified by Kendall Preston [1] in 1979. It is found that edge detection using CA has a potential advantage over traditional approaches for its lightweight nature and computational efficiency. This paper introduces a new technique for image edge detection using two-dimensional CA. The method can use specific rule sets of CA using the Von Neumann neighborhood for edge detection with null boundary conditions. The performance analysis of the scheme is done and compared with some existing standard edge detection techniques. The results obtained from the proposed technique is very promising for feature extraction.

An approach based on an application of cellular automata (CA) to the problem of two-dimensional (2D) patterns or images reconstruction from ones with only partial information available is presented in the paper. 2D CA are used to process patterns/images, and genetic algorithm (GA) is applied to discover CA rules, which will be able to reconstruct original patterns/images from, e.g. destroyed or modified ones. A number of experiments have been conducted to reconstruct patterns and human face images with use of the proposed approach. Results of experiments show that CA rules discovered by GA in the learning process allow to reconstruct images with large number of damaged pixels.

A cellular automation method is one of calculation methods, which allows for modeling of complex joint phenomena that take place in material during and after the deformation in the meso‐ and micro‐scale. The phenomena, which can be taken into consideration with high precision, are processes connected with microstructure evolution. For modeling by cellular automata (CA) are mainly used two‐dimensional ones, because of more expensive calculations by three‐dimensional CA. But three‐dimensional phenomena cannot be generally reduced to two‐dimensional solution. In the paper a description of a modified three‐dimensional CA is presented. The model of microstructure contains three parts: deformation of grains, recrystallization and grains growth after recrystallization. Recrystallization is considered as a process without division on the different kinds (dynamic, metadynamic or static). It consists of two stages: nucleation and new grains growth. Nucleation rate and grain growth rate are dependent on parameters of deformation. In the model such parameters as temperature, strain, strain rate, dislocation density, crystallographic orientation and some others are taken into account. Along with calculation of microstructure evolution, model allows for prediction of mechanical properties, for example flow stress. A flow stress calculations reckon processes of hardening and softening using model of the dislocation density development in consideration with an effect of the recrystallization. Some results of simulations based on 3D cellular automaton are presented in the paper.

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.

A novel agent based, artificial life model, for the evolution of mimicry is presented. This model is a predator-prey co-evolution scenario where pattern representation phenotype is simulated with Cellular Automata, while behaviors of pattern recognition is configured with Hopfield Network. A visual three dimensional toroidal cube is used to construct a universe in which agents have complete freedom of mobility, genetic representation of behavior and reproduction capability to evolve new behaviors in successive generations. These agents are classified into categories of predator and prey species. Genome of prey species control their mobility and palatability, while 2D Cellular Automata (CA) is used to represent a pattern, where the rule to generate the CA is also genetically represented. Through evolution, successive generations of prey species develop new patterns to represent them both visually and to the predators. Predators are agents with the primary purpose of providing selection pressure for the evolution of mimicry. They are equipped with Hopfield Network memory to recognize new CA pattern and make intelligent decisions to consume the prey based on their level of palatability. Using the above construction of ideas, successful emulation of the natural process of mimicry is achieved. Also complex behavior pattern of Batesian and Mullerian mimicry is simulated and studied.

This paper explores the concept of isomorphism in cellular automata (CAs), focusing on identifying and understanding isomorphic relationships between distinct CAs. A cellular automaton (CA) is said to be isomorphic to another CA if the configuration transition diagrams of the two CAs are identical. To illustrate how isomorphism entails the preservation of structural properties while allowing for variations in state representations, we exhaustively explore the isomorphic reversible rules in the first degree CAs (FDCAs), that is, the simple three-neighborhood CAs represented by eight parameters. The experimental study includes reversible FDCAs for states two to 10 with cell lengths of four to seven under the null boundary condition and states two to seven with cell lengths of four to seven under the periodic boundary condition. Given a CA, we also provide two synthesis methods for identifying the set of CAs that are isomorphic to it. The first method operates by permuting the states of a group of CA cell locations, whereas the second method involves exchanging cells at various points. We demonstrate that, depending on the range of exchanged cell positions, the isomorphic CAs produced in this way may have a bigger neighborhood than the input CA. Finally, we provide an exhaustive classification of the elementary CAs (ECAs) using the first synthesis method and compare it with existing results.

Characterization of two-dimensional cellular automata over ternary fields

Three-state von Neumann cellular automata and pattern generation

A cellular automaton finite volume method for microstructure evolution during additive manufacturing

Production of silicon for solar cells in photovoltaic systems is mainly based on directional casting processes. Twin nucleation is favoured during silicon growth due to the low-level twin energy of formation. As a consequence, in all solidification process, a large amount of grain boundaries (GB) are in twin relationship. A 3D cellular automaton (CA) model has been recently developed for the growth of multi-crystalline silicon including facet formation and nucleation of new grains in twin relationship. Activation of facets is based on an undercooling parameter assigned to each grain and for each of the <111> crystal directions. The model also considers nucleation and growth of grains on <111> facets corresponding to Σ3 twin relationships between twin grains. This model is first applied to comparison with experimental observations. It is found that impingement of growing grains that nucleated in Σ3 twin relationships meet during growth and form Σ3, Σ9 and Σ27 GB, in good agreement with experimental observations. Finally, the model is applied at a larger scale to generate grain structures representative of industrial practice. While quantitative experimental data is missing for comparison at such scale, the model is promising and its implementation in heat and mass transfer models should be considered for assistance to production of silicon for solar cells dedicated to photovoltaic systems.

A Hybrid discrete-continuum Cellular Automata (HCA) approach based on coupling classical thermomechanics and logics of CA-switching to simulate new phase generation and grain growth is proposed. On the basis of the HCA, numerical experiments on thermal-activated recrystallization of pure titanium in the vicinity of crack edges are performed. The 3D cellular automaton is aimed at simulating the behavior of a V-notched specimen region that imitates the crack tip vicinity. Numerical experiments provide calculating heat expansion in the material under study through taking into account thermal stress accumulation and microrotation initiation. The latter gives rise to the generation of new defects and increases local entropy.

Counters are among the fundamental digital circuits in every computing system. For this reason, counter design is of great interest in the design of computers and embedded systems, in terms of area requirements, power dissipation and performance. Many techniques have been proposed in the past specifically to increase the counter's speed without increasing design complexity. Traditionally, it is of great concern to make a fast counter suitable for many applications, without adding to the critical path and keeping speed independent of its size. In this work, a binary counter is proposed, based on 1D Cellular Automata (CA), which is used as a prescaler in a systolic structure, that offers constant delay for counters of various bit-widths.