2D Cellular Automata Research Articles

Audio security through compressive sampling and cellular automata

In this paper, a new approach for scrambling the compressive sensed (CS) audio data using two dimensional cellular automata is presented. In order to improve the security, linear feedback shift register (LFSR) based secure measurement matrix for compressive sensing is used. The basic idea is to select the different states of LFSR as the entries of a random matrix and orthonormalize these values to generate a Gaussian random measurement matrix. It is proposed to generate the initial state matrix of cellular automata using an LFSR based random bitstream generator. In order to improve the security and key space of the proposed cryptosystem, piecewise linear chaotic map (PWLCM) based initial seeds generation for LFSRs is used. In the proposed approach, the initial value, parameter value and the number of iterations of PWLCM are kept as secret to provide security. The proposed audio encryption method for CS audio data is validated with different compressive sensing reconstruction approaches. Experimental and analytical verification shows that the proposed encryption system gives good reconstruction performance, robustness to noise, high level of scrambling and good security against several forms of attack. Moreover, since the measurement matrix used for CS operation and the initial state matrix used for 2D cellular automata are generated using the secret key, the storage/transmission requirement of the same can be avoided.

Application of Linear and Non Linear Modified 3D Cellular Automata Rules in Cryptography for Improved Security of Transmitted Data

Internet is the prime vehicle to disseminate information from one place to another. Providing security to data is a major issue in transmitting data. One way of providing security to the data is encryption and decryption. Normal encryption is the way of changing the plaintext into cipher text using encryption and decryption algorithm and key. Literature reported different methods for encryption. An attempt is made in this paper to propose a modified encryption and decryption process performed with modified cellular automata rules. Cellular automata is idealized parallel processing machine which depends upon the cell value which is updated based on updating rule, which involves the cell and other cell values in a particular neighbourhood .Discrete references were made in the literature on the application of cellular automata rules. However lot more work remains to be done in this area. An attempt is made in this paper to provide encryption and decryption with cellular automata rules, using Data Encryption Standard (DES) and Advance Encryption Standard (AES) algorithms. They are operated at various stages, with the number of stages involved in sequential and cellular automata operating parallel. The major contribution of present work is, to develop methodology for identifying and application of 1D and 2D cellular automata rules and to fix the issues and challenges there in. A modified cellular automata set of rules are considered to develop 3D cellular automata rules for improved safety. Further a comparison is provided between existing 1, 2D automata rules versus the modified 3D cellular automata rules with respect to certain parameters. Keywords : Internet, Security, Cipher text, Plaintext, Cell value.

Two-dimensional patterns and images reconstruction with use of cellular automata

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.

Does 3D Cellular Automata Using WordNet Can Improve Text Clustering?

With the abundance of text documents available through the Web and digital libraries. Text clustering still plays an important role in information retrieval and applications like search result grouping and categorization, topic extraction and content filtering. Several clustering methods have been applied to textual documents where results depend on the application and on the representation of text. In this paper, an experiment of 3D Cellular Automata approach using WordNet for text representation is proposed and compared with some text clustering algorithms to see if this approach provides best results.

A non-qubit quantum adder as one-dimensional cellular automaton

A complete quantum addition machine is presented and compared with methods employing unitary transformations first. A quantum half-adder circuit shown earlier can be implemented into each cell of a 1D cellular automaton. An electric Aharonov–Bohm effect version of the quantum circuit is used to illustrate this implementation. Whatever a quantum Turing machine can achieve is realized in the cellular automata architecture we propose here. The coherence requirement is limited to one cell area. The magnetic flux needed is 0.1Φ0, corresponding to 0.414mT for a ring area of 1 square micron or an electric potential of 0.414mV at 1ps with an energy dissipation of 0.041eV per iteration.

Microstructure evolution during dynamic discontinuous recrystallization in particle-containing Cu

Control of the grain size in a material is vital in many engineering applications. Evolving through recrystallization, the grain size is strongly influenced by the presence of impurity particles. These particles exert drag forces on migrating grain boundaries and prevent grain boundary motion by pinning of the boundaries. Taking copper as example material, the present work establishes a novel simulation model where dynamic discontinuous recrystallization is influenced by particle drag. The recrystallization kinetics are established on a microlevel and the simulations are performed using a 3D cellular automaton algorithm with probabilistic cell state switches. By this approach, computational efficiency is combined with high temporal and spatial resolution of the microstructure evolution. The simulated microstructure changes are in good agreement with experimental findings and the recrystallization kinetics are shown to comply with classical Kolmogorov–Johnson–Mehl–Avrami (KJMA) theory. In addition, through homogenization, the macroscopic flow stress behavior is studied and is also shown to exhibit the expected transition from single-peak stable flow into serrated multiple-peak flow as the processing temperature is increased. Influence of changed initial grain sizes is studied and, in compliance with experimental data, an increased initial grain size stabilizes the flow stress behavior whereas the opposite trend is found for reduced initial grain sizes. Introducing impurity particles in the simulations, the progression of recrystallization is retarded and optimum values of the particle dispersion level are identified at different temperatures, allowing minimization of the recrystallized grain size during thermomechanical processing of the material.

2D Cellular Automata with an Image Processing Application

This paper investigates the theoretical aspects of two-dimensional linear cellular automata with image applications. We consider geometrical and visual aspects of patterns generated by cellular automata evolution. The present work focuses on the theory of two-dimensional linear cellular automata with respect to uniform periodic and adiabatic boundary cellular automata conditions. Multiple copies of any arbitrary image corresponding to cellular automata nd so many applications in real life situation e.g. textile design, DNA genetics research, etc.

Modeling of Ferrite-Austenite Phase Transformation Using a Cellular Automaton Model

A two-dimensional (2D) cellular automaton (CA) model is proposed to simulate the ferrite-austenite transformation in binary low-carbon steels. In the model, the preferential nucleation sites of austenite, the driving force of phase transformation coupled with thermodynamic parameters, solute partition at the ferrite/austenite interface, and carbon diffusion in both the ferrite and austenite phases are taken into consideration. The proposed model is applied to simulate the ferrite-to-austenite transformation during isothermal heating at 760°C that is in the ferrite and austenite two-phase range, the austenite-to-ferrite transformation during continuous cooling, and carbon diffusion during tempering at different temperatures for an Fe-0.2969 mol.% C alloy. The results show that during the isothermal heating, austenite nucleates and grows. The austenite grains are mostly located at the boundaries of ferrite grains. The carbon concentration in austenite is higher than that in ferrite. The simulated microstructure agrees reasonably well with the experimental observation. During the continuous cooling process, the austenite-to-ferrite transformation occurs accompanied with carbon diffusion. After cooling from the heating temperature of 760°C to room temperature with a cooling rate of 2°C/s, the carbon concentration field is nearly uniform, while a higher cooling rate of 5°C/s results in a non-uniform carbon concentration field. After tempering at different temperatures for 20 min, the uniformity of carbon distribution increases with increasing tempering temperature. The simulation results are used to understand the mechanisms of the observed experimental phenomena that a cold-rolled low-carbon enameling steel presents different yield strengths after different heat treatment processes.

Coupled Cellular Automaton (CA) – Finite Element (FE) Modeling of Directional Solidification of Al-3.5 wt% Ni Alloy: A Comparison with X-ray Synchrotron Observations

Development of dendritic grain structure and mesa-segregation leading to localized intergranular eutectic is simulated during directional solidification of an Al - 3.5 wt% Ni alloy with two pulling velocities (4 mu m s(-1) and 8 mu m s(-1)) using a two-dimensional (2D) Cellular Automaton Finite Element (CAFE) model. 2D CAFE simulations are compared with in situ and real-time experiments characterized by means of X-ray radiography at the European Synchrotron Radiation Facility (Grenoble, France). Two nucleation models are used. The first model is established by listing all measured positions and orientations of experimentally-observed nucleation events. The undetermined value of the nucleation undercooling is then set to 0 degrees C for all nucleation sites. The other model considers a stochastic model with a Gaussian distribution of the nucleation site as a function of the undercooling. It is derived from series of experiments. The influences of the nucleation models and liquid convection on the grain structure characteristics are numerically investigated. A good agreement with experimental observations is achieved concerning the evolutions of both the dendritic and the eutectic growth fronts (i.e., the size of the mushy zone). The predicted grain size and elongation are compared with measurements for the two nucleation laws. Simulations using the list of nucleation events reach better agreement with the longitudinal profiles of the grain equivalent diameter and elongation factor compared to the stochastic nucleation model. Direct tracking of the eutectic growth front as well as three-dimensional analyses are found to be required for improvement of the predictions.

Cellular Automaton Modeling of Microporosity Formation during Solidification of Aluminum Alloys

A two-dimensional (2D) cellular automaton (CA)-finite difference method (FDM) model is proposed to simulate the dendrite growth and microporosity formation during solidification of aluminum alloys. The model involves a three-phase system of liquid, gas, and solid. The growth of both dendrite and gas pore is simulated using a CA approach. The diffusion of solute and hydrogen is calculated using the FDM. The model is applied to simulate the formation and interactions of dendrites and micropores in an Al-7wt.%Si alloy. The effects of initial hydrogen concentration and cooling rate on microporosity formation are investigated. It is found that the porosity nuclei with larger size grow preferentially, while the growth of the small porosity nuclei is restrained. The competitive growth between porosities and dendrites is also observed. With the increase of initial hydrogen concentration, the incubation time of porosity nucleation and growth decreases, and the percentage of porosity increases, while porosity density does not increase apparently. With the decrease of cooling rate, porosity nucleates and starts to grow at higher temperatures, and the percentage of porosity increases, but the porosity density displays a decreasing trend. In addition, at a slower cooling rate, the competitive growth between porosities and dendrites becomes more evident, leading to a more non-uniform distribution of porosity size, and an increased maximum porosity size. The simulation results agree reasonably with the experimental data in the literature.

Self-Replicating Patterns in 2D Linear Cellular Automata

This paper studies the theoretical aspects of two-dimensional cellular automata (CAs), it classifies this family into subfamilies with respect to their visual behavior and presents an application to pseudo random number generation by hybridization of these subfamilies. Even though the basic construction of a cellular automaton is a discrete model, its macroscopic behavior at large evolution times and on large spatial scales can be a close approximation to a continuous system. Beyond some statistical properties, we consider geometrical and visual aspects of patterns generated by CA evolution. The present work focuses on the theory of two-dimensional CA with respect to uniform periodic, adiabatic and reflexive boundary CA (2D PB, AB and RB) conditions. In total, there are 512 linear rules over the binary field ℤ2for each boundary condition and the effects of these CA are studied on applications of image processing for self-replicating patterns. After establishing the representation matrices of 2D CA, these linear CA rules are classified into groups of nine and eight types according to their boundary conditions and the number of neighboring cells influencing the cells under consideration. All linear rules have been found to be rendering multiple self-replicating copies of a given image depending on these types. Multiple copies of any arbitrary image corresponding to CA find innumerable applications in real life situation, e.g. textile design, DNA genetics research, statistical physics, molecular self-assembly and artificial life, etc. We conclude by presenting a successful application for generating pseudo numbers to be used in cryptography by hybridization of these 2D CA subfamilies.

The 3-dimensional cellular automata for HIV infection

The HIV infection dynamics is discussed in detail with a 3-dimensional cellular automata model in this paper. The model can reproduce the three-phase development, i.e., the acute period, the asymptotic period and the AIDS period, observed in the HIV-infected patients in a clinic. We show that the 3D HIV model performs a better robustness on the model parameters than the 2D cellular automata. Furthermore, we reveal that the occurrence of a perpetual source to successively generate infectious waves to spread to the whole system drives the model from the asymptotic state to the AIDS state.

Optimized parallel computing for cellular automaton–finite element modeling of solidification grain structures

A numerical implementation of a three-dimensional (3D) cellular automaton (CA)–finite element (FE) model has been developed for the prediction of solidification grain structures. For the first time, it relies on optimized parallel computation to solve industrial-scale problems (centimeter to meter long) while using a sufficiently small CA grid size to predict representative structures. Several algorithm modifications and strategies to maximize parallel efficiency are introduced. Improvements on a real case simulation are measured and discussed. The CA–FE implementation here is demonstrated using 32 computing units to predict grain structure in a 2.08 m × 0.382 m × 0.382 m ingot involving 4.9 billion cells and 1.6 million grains. These numerical improvements permit tracking of local changes in texture and grain size over real-cast parts while integrating interactions with macrosegregation, heat flow and fluid flow. Full 3D is essential in all these analyses, and can be dealt with successfully using the implementation presented here.

Can Non-lytic CD8+ T Cells Drive HIV-1 Escape?

The CD8+ T cell effector mechanisms that mediate control of HIV-1 and SIV infections remain poorly understood. Recent work suggests that the mechanism may be primarily non-lytic. This is in apparent conflict with the observation that SIV and HIV-1 variants that escape CD8+ T cell surveillance are frequently selected. Whilst it is clear that a variant that has escaped a lytic response can have a fitness advantage compared to the wild-type, it is less obvious that this holds in the face of non-lytic control where both wild-type and variant infected cells would be affected by soluble factors. In particular, the high motility of T cells in lymphoid tissue would be expected to rapidly destroy local effects making selection of escape variants by non-lytic responses unlikely. The observation of frequent HIV-1 and SIV escape poses a number of questions. Most importantly, is the consistent observation of viral escape proof that HIV-1- and SIV-specific CD8+ T cells lyse infected cells or can this also be the result of non-lytic control? Additionally, the rate at which a variant strain escapes a lytic CD8+ T cell response is related to the strength of the response. Is the same relationship true for a non-lytic response? Finally, the potential anti-viral control mediated by non-lytic mechanisms compared to lytic mechanisms is unknown. These questions cannot be addressed with current experimental techniques nor with the standard mathematical models. Instead we have developed a 3D cellular automaton model of HIV-1 which captures spatial and temporal dynamics. The model reproduces in vivo HIV-1 dynamics at the cellular and population level. Using this model we demonstrate that non-lytic effector mechanisms can select for escape variants but that outgrowth of the variant is slower and less frequent than from a lytic response so that non-lytic responses can potentially offer more durable control.

Multidimensional cellular automata: closing property, quasi-expansivity, and (un)decidability issues

In this paper we study the dynamics of D-dimensional cellular automata (CA) by considering them as one-dimensional (1D) CA along some direction (slicing constructions). These constructions allow to give the D-dimensional version of important notions as 1D closing property and lift well-known one-dimensional results to the D-dimensional settings. Indeed, like in one-dimensional case, closing D-dimensional CA have jointly dense periodic orbits and biclosing D-dimensional CA are open. By the slicing constructions, we further prove that for the class of closing D-dimensional CA, surjectivity implies surjectivity on spatially periodic configurations (old standing open problem). We also deal with the decidability problem of the D-dimensional closing. By extending the Kariʼs construction from [31] based on tilings, we prove that the two-dimensional, and then D-dimensional, closing property is undecidable. In such a way, we add one further item to the class of dimension sensitive properties, i.e., properties that are decidable in dimension 1 and are undecidable in higher dimensions. It is well-known that there are not positively expansive CA in dimension 2 and higher. As a meaningful replacement, we introduce the notion of quasi-expansivity for D-dimensional CA which shares many global properties (in the D-dimensional settings) with the 1D positive expansivity. We also prove that for quasi-expansive D-dimensional CA the topological entropy (which is an uncomputable property for general CA) has infinite value. In a similar way as quasi-expansivity, the notions of quasi-sensitivity and quasi-almost equicontinuity are introduced and studied.

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.

New CA based Key Generation for a Robust RGB Color Image Encryption Scheme

In the past few years, study of securing the digital images has increased tremendously and several encryption algorithms based on Cellular Automata have been proposed to protect the digital images against different cryptographic attacks. This paper proposes a novel pixel based encryption scheme based on Cellular Automata and Galois Field. Here the random key image has been generated using 1D Cellular Automata and for the encryption purpose GF (2 8 ) is used. The encryption is done on pixel values of the RGB components separately. Since this cryptosystem uses only logic operations for both key generation and GF (2 8 ) operations, it requires minimized computational resources and the execution speed is also high. Experimental results exhibit the confusion and diffusion properties of the proposed system. The correlation analysis shows that the proposed scheme has zero correlation amongst adjacent pixels (horizontal, vertical, diagonal).

COLOR IMAGE ENCRYPTION BASED ON TWO-DIMENSIONAL CELLULAR AUTOMATA

Cellular automaton (CA) has a lot of inherent features, such as simple regular structure, local interaction, random-like behavior and massive parallelism, which make it a good candidate to design cryptosystems. Therefore, a number of CA-based image encryption systems have been proposed, though the drawbacks of small key space and weak security in one-dimensional (1D) CA cryptosystems are obvious. In this paper, a novel image encryption scheme is presented using a two-dimensional (2D) CA with nonlinear balanced rules. During the whole process of encryption, the confusion operation is performed by the nonlinear rule of CA, while the diffusion operation is achieved by the local interactions among cells. So confusion and diffusion are well integrated in our proposed scheme. The corresponding simulations and analyses illustrate that the scheme has quite prominent cryptographic properties as well as high security.

Explicit routing schemes for implementation of cellular automata on processor arrays

Massively parallel processor array (MPPA) architectures are becoming widely available computing platforms. Because of formal similarities, they are good candidates for implementing cellular automata (CA). An essential difference still remains regarding the freedom in communications. In MPPA there is a fixed on-chip network interconnection topology but every CA has its own definition of neighbourhood. While a cell in a CA can be considered as directly connected to its neighbours, these connections correspond to paths in the network of the MPPA. The communications need to be routed and scheduled to reach their proper destination. In previous work we introduced a formal data-flow process network model named KRG (for K-periodically Routed Graph). Its main feature is to allow regular switching directives. In the present paper we will use it to represent the proper local sequences of routing directives that will efficiently propagate values from cells to cells so as to implement the required CA neighbourhood. We present the neighbourhood broadcasting algorithm that computes these routing directives. One should note here that the problem is made more complex as data traffic between distinct source and target cells must be merged, while multicast may save a tremendous amount of communications when values are required in multiple locations. We demonstrate the expressive power of our formalism on the case of a 2D CA where the neighbourhood consists of all cells at Moore distance at most n. Further potential applications of our framework are hinted.

Grid anisotropy reduction for simulation of growth processes with cellular automaton

Growth processes simulated on a regular cellular automaton grid with simple capture rules are considerably influenced by the structure of the grid. Some of the growth directions are favored over others leading to highly anisotropic or, at least, orientation-dependent growth pattern. A new method is proposed for significant reduction of artificial grid anisotropy in 2D and 3D cellular automata with continuous state variable. The method employs additional diffusion process controlling the growth rate and allows for isotropic or anisotropic growth where the anisotropy is decoupled from the grid structure. Verification of the method is provided in the case of isotropic circular growth, isotropic growth of various shapes in uniform and spatially varying fields, and anisotropic growth with respect to orientation and symmetry of the pattern. Finally, the reduction of grid anisotropy is demonstrated in 2D simulation of dendritic grain growth in pure metal. The shape of the grain is shown to be virtually independent of the orientation. An example growth of a grain with six-fold symmetry is also included.