Cellular Automata Rules Research Articles

Topology Optimization of Periodic Structures Subject to Self-Weight Loading Using a Heuristic Method.

This paper deals with the actual and challenging process of the optimal design of topologies of periodic structures taking into account the design-dependent loads. The topology formulation used in this paper minimizes the compliance value of the structure and is subject to a total volume constraint while maintaining a periodic pattern and self-weight load. This combination represents a promising and original contribution to the field of ongoing research, although it is not yet widely recognized. This paper aims to fill this gap by presenting the first results of numerical optimization tests. The redistribution of material within a design domain is governed by the rules of Cellular Automata, a locally oriented optimization tool that can be applied to all types of structural optimization, including topology optimization. The technique has been demonstrated by numerical tests on two- and three-dimensional examples. The calculations were performed for different types of periodic schemes. The optimized structures did not show the checkerboard effect or the presence of residual gray elements in the final topologies. The strategy used in this paper ensures connectivity between periodic subdomains without imposing additional conditions on the algorithm.

Hardware Design Strategies Oriented to Edge Computing and AgriFood Electronics for Image Processing using Cellular Automata

There has been a growing interest from academia and industry in developing circuits and systems for edge computing and quality control tasks in food production lines, where image-processing is frequently required. This paper outlines the required considerations for designing a fruit classification system based on image-processing using Cellular Automata (CA) models and integrating it into reconfigurable hardware (HW) such as Field Programmable Gate Arrays (FPGAs). Parallel processing in CA requires numerous processing elements to be implemented and mapping CA models to HW generally comes with limitations. Homogeneous CA arrays are easier to design and implement in HW but can be resource-demanding. To fill this gap, this study explores different alternatives for the HW implementation of CA models, particularly trading computational-parallelism for a more optimized use of the available HW resources. We conducted experimental tests of the designed HW system using the Digilent Nexys development board, and the operation was validated against software-based benchmarks for image-processing, particularly concerning edge-detection. The presented study provides a broader range of design solutions for the HW implementation of two-dimensional CA models and a better understanding of their advantages and disadvantages. The results show that solutions focusing on instruction-parallelism add some complexity to the conception and require more design effort, compared to homogeneous CA models composed of identical cells. However, the instruction-parallel design solutions can significantly improve the HW resource utilization, especially when implementing computationally intensive CA rules in FPGAs.

Quantum Cellular Automata for Quantum Error Correction and Density Classification.

Quantum cellular automata are alternative quantum-computing paradigms to quantum Turing machines and quantum circuits. Their working mechanisms are inherently automated, therefore measurement free, and they act in a translation invariant manner on all cells or qudits of a register, generating a global rule that updates cell states locally, i.e., based solely on the states of their neighbors. Although desirable features in many applications, it is generally not clear to which extent these fully automated discrete-time local updates can generate and sustain long-range order in the (noisy) systems they act upon. In particular, whether and how quantum cellular automata can perform quantum error correction remain open questions. We close this conceptual gap by proposing quantum cellular automata with quantum-error-correction capabilities. We design and investigate two (quasi)one dimensional quantum cellular automata based on known classical cellular-automata rules with density-classification capabilities, namely the local majority voting and the two-line voting. We investigate the performances of those quantum cellular automata as quantum-memory components by simulating the number of update steps required for the logical information they act upon to be afflicted by a logical bit flip. The proposed designs pave a way to further explore the potential of new types of quantum cellular automata with built-in quantum-error-correction capabilities.

Review on Cellular Automata for Microstructure Simulation of Metallic Materials.

The cellular automata (CA) method has played an important role in the research and development of metallic materials. CA can interpret the microstructure changes of materials and obtain more abundant, accurate and intuitive information of microstructure evolution than conventional methods. CA can visually represent the process of grain formation, growth, development and change to us in a graphical way, which can assist us in analysis, thinking and solving problems. In the last five years, the application of CA in materials research has been rapidly developed, and CA has begun to occupy an increasingly important position in the simulation research of metallic materials. After introducing the advantages and limitations of CA compared to other widely used simulation methods, the purpose of this paper is to review the recent application progress on the microstructure simulation of metallic materials using CA, such as solidification, recrystallization, phase transformation and carbide precipitation occurring during forming and heat treatment. Specifically, recent research advances on microstructure simulation by CA in the fields of additive manufacturing, welding, asymmetrical rolling, corrosion prevention, etc., are also elaborated in this paper. Furthermore, this paper points out the future work direction of CA simulation in the research of metallic materials, especially in the simulation of the crystal structure, the prediction of mechanical properties, CA simulation software and rule systems, etc. These are expected to attract wide attention of researchers in the field of metallic materials and promote the development of CA in materials research.

A Generic NSRTD Framework for Characterizing Cellular Automaton Rules in Constant (0/1) Boundary Conditions

A Generic NSRTD Framework for Characterizing Cellular Automaton Rules in Constant (0/1) Boundary Conditions

ReLiCADA: Reservoir Computing Using Linear Cellular Automata design algorithm

In this paper, we present a novel algorithm to optimize the design of Reservoir Computing using Cellular Automata models for time series applications. Besides selecting the models’ hyperparameters, the proposed algorithm particularly solves the open problem of Linear Cellular Automaton rule selection. The selection method pre-selects only a few promising candidate rules out of an exponentially growing rule space. When applied to relevant benchmark datasets, the selected rules achieve low errors, with the best rules being among the top 5% of the overall rule space. The algorithm was developed based on mathematical analysis of Linear Cellular Automaton properties and is backed by almost one million experiments, adding up to a computational runtime of nearly one year. Comparisons to other state-of-the-art time series models show that the proposed Reservoir Computing using Cellular Automata models have lower computational complexity and, at the same time, achieve lower errors. Hence, our approach reduces the time needed for training and hyperparameter optimization by up to several orders of magnitude.

The Effect of Noise on the Density Classification Task for Various Cellular Automata Rules.

Cellular automata (CA) are discrete dynamical systems with a prominent place in the history and study of artificial life. Here, we focus on the density classification task (DCT) in which a 1-dimensional lattice of Boolean (on/off) automata must perform a form of rudimentary quorum sensing. Typically, the ring lattice consists of 149 cells (though we consider other sizes as well) that update their state according to their own state and its six nearest neighbors in the previous time step. The goal is obtaining Boolean CA rules whose dynamics converges to the majority state of the entire lattice for a given initial configuration of the lattice. This is a nontrivial task because cells have access only to local information, and thus need to integrate and coordinate information across the lattice to converge to the correct collective state. Because initial conditions are random, they have very similar proportions of on and off states, which makes the problem very difficult. This problem has hitherto been studied with the assumption that input to each cell is perfectly stable. Since biological systems that solve similar problems (e.g. bacterial quorum sensing) must operate in noisy environments, here we study the impact of noise on DCT accuracy for the 13 highest-accuracy CA rules from the literature. We use cubewalkers, a recently released GPU-accelerated Boolean simulator to conduct large-scale random experiments. We uncover a trade-off between maximum accuracy without noise and robustness to noise among these high-performance CAs. Moreover, there is no significant difference between rules that were human-designed or evolved computationally.

Modeling the Effect of the Platoon Size of CAVs on Mixed Traffic Flow: A Cellular Automaton Method

This study proposes a cellular automaton model incorporating the platoon size of connected automated vehicles (CAVs) to examine their impact on mixed traffic flow. First, vehicles are classified into three modes, human-driven vehicles (HDVs), adaptive cruise control (ACC), and cooperative adaptive cruise control (CACC), by considering the characteristics of the car-following behavior. Second, the CACC is further subdivided into interplatoon and intraplatoon car-following modes due to the limitations of the platoon size of CAVs. Then, cellular automaton rules are developed for each of these four modes. Finally, numerical simulation experiments are conducted to analyze the influence of the penetration rate and platoon size of CAVs on mixed traffic flow. The results demonstrate that (1) the simulation results closely align with the theoretically derived outcomes, with an error rate of only 0.46% at a penetration rate of 100%; (2) when the penetration rate of CAVs reaches 100%, increasing the platoon size further enhances the traffic capacity; and (3) the optimal platoon size is determined to be seven CAVs under moderate traffic density.

Parallel molecular computation on digital data stored in DNA

DNA is an incredibly dense storage medium for digital data. However, computing on the stored information is expensive and slow, requiring rounds of sequencing, in silico computation, and DNA synthesis. Prior work on accessing and modifying data using DNA hybridization or enzymatic reactions had limited computation capabilities. Inspired by the computational power of "DNA strand displacement," we augment DNA storage with "in-memory" molecular computation using strand displacement reactions to algorithmically modify data in a parallel manner. We show programs for binary counting and Turing universal cellular automaton Rule 110, the latter of which is, in principle, capable of implementing any computer algorithm. Information is stored in the nicks of DNA, and a secondary sequence-level encoding allows high-throughput sequencing-based readout. We conducted multiple rounds of computation on 4-bit data registers, as well as random access of data (selective access and erasure). We demonstrate that large strand displacement cascades with 244 distinct strand exchanges (sequential and in parallel) can use naturally occurring DNA sequence from M13 bacteriophage without stringent sequence design, which has the potential to improve the scale of computation and decrease cost. Our work merges DNA storage and DNA computing, setting the foundation of entirely molecular algorithms for parallel manipulation of digital information preserved in DNA.

A classification of S-boxes generated by orthogonal cellular automata

Most of the approaches published in the literature to construct S-boxes via Cellular Automata (CA) work by either iterating a finite CA for several time steps, or by a one-shot application of the global rule. The main characteristic that brings together these works is that they employ a single CA rule to define the vectorial Boolean function of the S-box. In this work, we explore a different direction for the design of S-boxes that leverages on Orthogonal CA (OCA), i.e. pairs of CA rules giving rise to orthogonal Latin squares. The motivation stands on the facts that an OCA pair already defines a bijective transformation, and moreover the orthogonality property of the resulting Latin squares ensures a minimum amount of diffusion. We exhaustively enumerate all S-boxes generated by OCA pairs of diameter 4≤d≤6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4 \\le d \\le 6$$\\end{document}, and measure their nonlinearity. Interestingly, we observe that for d=4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d=4$$\\end{document} and d=5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d=5$$\\end{document} all S-boxes are linear, despite the underlying CA local rules being nonlinear. The smallest nonlinear S-boxes emerges for d=6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d=6$$\\end{document}, but their nonlinearity is still too low to be used in practice. Nonetheless, we unearth an interesting structure of linear OCA S-boxes, proving that their Linear Components Space is itself the image of a linear CA, or equivalently a polynomial code. We finally classify all linear OCA S-boxes in terms of their generator polynomials.

Generating Loop Patterns with a Genetic Algorithm and a Probabilistic Cellular Automata Rule

The objective is to find a Cellular Automata (CA) rule that can generate “loop patterns”. A loop pattern is given by ones on a zero background showing loops. In order to find out how loop patterns can be locally defined, tentative loop patterns are generated by a genetic algorithm in a preliminary stage. A set of local matching tiles is designed and checked whether they can produce the aimed loop patterns by the genetic algorithm. After having approved a certain set of tiles, a probabilistic CA rule is designed in a methodical way. Templates are derived from the tiles, which then are used in the CA rule for matching. In order to drive the evolution to the desired patterns, noise is injected if the templates do not match or other constraints are not fulfilled. Simulations illustrate that loops and connected loops can be evolved by the CA rule.

Deep Cellular Automata-Based Feature Extraction for Classification of the Breast Cancer Image

Feature extraction is an important step in classification. It directly results in an improvement of classification performance. Recent successes of convolutional neural networks (CNN) have revolutionized image classification in computer vision. The outstanding convolution layer of CNN performs feature extraction to obtain promising features from images. However, it faces the overfitting problem and computational complexity due to the complicated structure of the convolution layer and deep computation. Therefore, this research problem is challenging. This paper proposes a novel deep feature extraction method based on a cellular automata (CA) model for image classification. It is established on the basis of a deep learning approach and multilayer CA with two main processes. Firstly, in the feature extraction process, multilayer CA with rules are built as the deep feature extraction model based on CA theory. The model aims at extracting multilayer features, called feature matrices, from images. Then, these feature matrices are used to generate score matrices for the deep feature model trained by the CA rules. Secondly, in the decision process, the score matrices are flattened and fed into the fully connected layer of an artificial neural network (ANN) for classification. For performance evaluation, the proposed method is empirically tested on BreaKHis, a popular public breast cancer image dataset used in several promising and popular studies, in comparison with the state-of-the-art methods. The experimental results show that the proposed method achieves the better results up to 7.95% improvement on average when compared with the state-of-the-art methods.

Cellular automata imbedded memristor-based recirculated logic in-memory computing

Memristor-based circuits offer low hardware costs and in-memory computing, but full-memristive circuit integration for different algorithm remains limited. Cellular automata (CA) has been noticed for its well-known parallel, bio-inspired, computational characteristics. Running CA on conventional chips suffers from low parallelism and high hardware costs. Establishing dedicated hardware for CA remains elusive. We propose a recirculated logic operation scheme (RLOS) using memristive hardware and 2D transistors for CA evolution, significantly reducing hardware complexity. RLOS’s versatility supports multiple CA algorithms on a single circuit, including elementary CA rules and more complex majority classification and edge detection algorithms. Results demonstrate up to a 79-fold reduction in hardware costs compared to FPGA-based approaches. RLOS-based reservoir computing is proposed for edge computing development, boasting the lowest hardware cost (6 components/per cell) among existing implementations. This work advances efficient, low-cost CA hardware and encourages edge computing hardware exploration.

Cellular automaton modelling of the effects of buildings on aeolian bedform dynamics

• Sediment dynamics around buildings are included in a cellular automaton model. • Simulated deposition and erosion patterns show good agreement with field experiments. • Building effects interact with local bedform dynamics, and can affect dune shape, growth and migration. Buildings affect aeolian sediment transport and bedform development in sandy environments. Cellular automaton (CA) models have, however, only been used to simulate natural bedform dynamics. This study extends a well-known aeolian CA model to include sediment dynamics around buildings, and uses this model to explore the interaction of building-induced deposition and erosion with natural bedform dynamics. New CA rules are introduced to represent acceleration, deceleration and sideward transport of sediment around obstacles. The simulated deposition and erosion patterns show good agreement with field experiments. The model reproduces the shape and location of the morphological pattern around a single building, and effects of building spacing on this pattern for building groups. Model results further demonstrate that building-induced effects interact with local bedform dynamics and can alter the shape, growth and migration of sand dunes.

Visual Cryptography Using Neighborhood Based Encryption Techniques in The Framework of Cellular Automata

Security of digital data during data communication, data exchange, data authentication is very important. Many authentication techniques are used to secure data. Visual cryptography is one of the methods which creates signatures by applying nonlinearity into the data. The signatures consist of cipher and the key. At the receiving end if the key and the cipher match then the authentication is done. Through this visual cryptography technique, the users hide information securely based on key authentication. This paper discusses another approach to visual cryptography using neighborhood-based encryption techniques in the framework of cellular automata. A cellular automaton has a grid of cells. This cell has either value 0 or 1. These values are changed to next state level in a discrete way with respect to time using some fixed rule. A ‘Cellular Automaton’ (CA) is a 2-dimensional finite array of lattice points called cells together with an updating rule that involves values of a cell and of some predetermined neighborhood cells. Cellular automaton rules for visual cryptography are defined. These rules consist of Neighborhood generation phase and signature generation phase. A sample array is considered. Using cellular automaton rules encryption and decryption is done on sample array.

Computer modeling and simulation to predict COVID-19 propagation patterns via factual cellular automata

Computer modelling and simulation methods are very important and play a critical role in the mitigation and response to the ongoing COVID-19 pandemic. In this study, we propose a computational modeling technique based on Cellular Automata (CA) with realistic proposed rules. The rules are designed to simulate the propagation of COVID-19 disease through a bounded area. Our proposed CA rules are novel in many respects. For on, the classification of neighbors to nearest neighbors and range of neighbors based on cellular layers is explained. Moreover, the concepts of time generation and access time are deployed for the first time to model the propagation of the disease over time in this work. Further details of the proposed model including the topology of the defined area, the initial states of the cells and four-layer transfer mechanism are explained as well. This work may be considered a criterion of spreading for COVID-19 from point source in a defined population area. The results of the proposed algorithm represent the percentage of the population whose infectious status is described by different cellular state objects after a defined generation time. The results are compared under different circumstances and analyzed equanimity.

Synchronous solution of the parity problem on cyclic configurations, with elementary cellular automaton rule 150, over a family of directed, non-circulant, regular graphs

The parity problem is one of the classical benchmarks for probing the computational ability of cellular automata. It refers to conceiving a rule to allow deciding whether the number of 1s in an arbitrary binary sequence is an odd or even number, without resorting to globally accessing the sequence. In its most traditional formulation, it refers to cyclic configurations of odd length, which, under the action of a cellular automaton, should converge to a fixed point of all cells in the 0-state, if the configuration initially has an even number of 1s, or to a fixed point of all cells in the 1-state, otherwise. It has been shown that the problem can be solved in this formulation, in particular by a rule alone. Here, we provide a synchronous solution to the problem, by relying upon elementary cellular automaton rule 150, the elementary local parity rule, over a connection pattern among the cells defined by a family of directed, non-circulant, regular graphs. This represents the simplest synchronous solution currently known for cyclic configurations and, quite interestingly, being an instance of the solution of a non-trivial global problem by means of its local counterpart.

Simulating and Predicting Offshore Oil Spills by Using Cellular Automata

In recent years, offshore oil spill accidents have caused substantial damage to both marine organisms and marine ecology. Accurate simulation and prediction of oil spills could provide a scientific basis for assessing losses due to oil spills and provide support for emergency decisions regarding oil spills. We analyzed the advantages and disadvantages of existing oil spill models and constructed an offshore oil spill model based on cellular automata (CA). By considering both the flow field and wind field, we formulated new CA rules for the diffusion and drift of a pollution zone, and in our model, the cellular state in eight-neighborhood mode is updated in accordance with these rules, which makes the model suitable for dynamic simulation of offshore oil spills. We also constructed a model on the basis of fuzzy comprehensive evaluation for evaluating the oil spill grade. Finally, we developed a software system, the Ocean Oil Spill Information System (OOSIS), which includes all necessary functions such as basic operations, data management, information query, oil spill analysis, and oil spill assessment. OOSIS is used to verify the constructed oil spill model, and the sea breeze and current data from the National Oceanic and Atmospheric Administration were used to realize the dynamic simulation and prediction, grade evaluation, and cleanup plan generation for offshore oil spill.

Hardware implementation of a robust image cryptosystem using reversible cellular-automata rules and 3-D chaotic systems

In this contribution, a robust image cryptosystem built over a diffusion-confusion architecture is established. The design of a hardware pseudorandom number generator is achieved using two different chaotic systems: Lorenz chaotic system and Rössler chaotic system, exploited to build a single generic architecture. The proposed PRNG is designed using the Xilinx system Generator (XSG) tool and implemented onto an FPGA Zynq ZC 020. It showed high statistical properties as it passes all NIST statistical tests and possesses the best hardware performance. The generated key sequences from the PRNG were used in diffusion processes using XOR operation. Moreover, two extra generated bits were used in the permutation process that precedes the confusion. To further increase the complexity and the randomness of the proposed scheme the confusion process is established over reversible cellular automata. The hardware design of the suggested approach is set forth using XSG tool and implemented on FPGA Zynq ZC 020 working at high-level frequency of 184 MHz and a 23 552 mbps throughput value. Then, the hardware cryptosystem is tested over different plain images. To demonstrate the efficiency of this hardware cryptosystem, security analyses such as key sensitivity analysis and statistical analysis among others were performed to validate the security of proposed hardware-cryptosystem showing an entropy value of 7.9998. A comparative study with some recently suggested cryptosystems is established. Experimental results state that the suggested hardware cryptosystem performs better in terms of security and hardware efficiency such as power consumption, resources utilization and throughput.

Cellular automata rules solving the wireless sensor network coverage problem

The problem of an optimal coverage of a wireless sensor network area is considered. To solve this problem, a Cellular Automata (CA) approach is proposed. More specifically, the objective is to find CA rules which are able to cover the 2D space by a minimum number of so–called “Sensor Tiles”. A sensor tile consists of a von Neumann neighborhood of range 2 centered at sensor “point” and surrounded by 12 sensing “pixels”. Two probabilistic CA rules were designed that can perform this task. Results of an experimental study show that the first rule evolves very fast stable sub-optimal coverings, starting from a random configuration. The second rule finds optimal coverings, however it needs much more time for their evolution. The results are supported by a theoretical study on von Neumann neighborhoods and borrowing either from heuristics or from the spectral theory of circulant graphs.