Dimensional Cellular Automata Research Articles

Simulation of a Vibrant Membrane Using a 2-Dimensional Cellular Automaton

This paper proposes a 2-dimensional cellular automaton (CA) model and how to derive the model evolution rule to simulate a two-dimensional vibrant membrane. The resulting model is compared with the analytical solution of a two-dimensional hyperbolic partial differential equation (PDE), linear and homogeneous. This models a vibrant membrane with specific conditions, initial and boundary. The frequency spectrum is analysed as well as the error between the data produced by the CA model. Then it is compared to the data provided by the solution evaluation to the differential equation. This shows how the CA obtains a behavior similar to the PDE. Moreover, it is possible to simulate nonclassical initial conditions for which there is no exact solution using PDE. Very interesting information could be obtained from the CA model such as the fundamental frequency.

THREE-DIMENSIONAL CELLULAR AUTOMATON FOR MODELING THE HEPATITIS B VIRUS INFECTION

Hepatitis B is considered as the most common hepatic in the world and may lead to cirrhosis and liver cancer. It is caused by the hepatitis B virus, which attacks and can damage the liver. In this paper we investigate a new mathematical model to study the dynamic process of HBV infection on the liver. This model is based on a three dimensional cellular automaton, which is composed of four state variables. The model takes into account the heterogeneous feature and the spatial localization of the population studied. Furthemore, since the virus doesn’t remain only on the liver surface but penetrates into the organ, our model describes better the behavior of interactions between cells and hepatitis B virus in the liver than the previous works found in the literature, which have used only two cellular automata in their models.

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.

Grain Competitive Growth Prediction during Solidification in Single Crystal Superalloy DD6 Castings

Competitive growth and grain selection were simulated and analyzed during the directional solidification with the conditions for single crystal superalloy DD6 castings using Commercial software, ProCAST. A three dimensional cellular automaton (CA) model coupled with finite-element (FE) heat flow calculation was applied. Measurements at the grain scale were made using the EBSD method at the cross sections in the starter block and grain selector at an interval of 4 mm from the chill surface. The grain characteristics and the rules of competition growth were obtained. The validity of the simulation results were compared with those of the experiment. It concluded that the model-predicted tendency shows satisfactory agreement with the experiment. Increasing the distance from the chill decreases the number of grains, increases the radius of grains and drives the crystallization orientation of grains to principal stress orientation.

Analysis of Hexagonal Network Based on Cellular Automation

With reference to the traditional two dimensional cellular automata network model, we design a kind of hexagonal network model with reconfigurable boundary. By simulating, we have achieved a series of experiments based on the model of the network packet exchange .Then we draw that the node load under congestion phase state is with characteristics of white noise and 1/f noise by computing the power spectrum density. And the results reveal the fact that, the hexagonal one gains more efficient network transmission capacity than the square one, and it is more applicable for the behavioral modeling study on the large-scale network.

Homogeneous Systolic Pyramid Automata with n-Dimensional Layers

Cellular automata were investigated not only in the viewpoint of formal language theory, but also in the viewpoint of pattern recognition. Cellular automata can be classified into some types. A systolic pyramid automata is also one parallel model of various cellular automata. A homogeneous systolic pyramid automaton with n-dimensional layers (n-HSPA) is a pyramid stack of n-dimensional arrays of cells in which the bottom n-dimensional layer (level 0) has size an (a≥1), the next lowest (a-1)n, and so forth, the (a-1)st n-dimensional layer (level (a-1)) consisting of a single cell, called the root. Each cell means an identical finite-state machine. The input is accepted if and only if the root cell ever enters an accepting state. An n-HSPA is said to be a real-time n-HSPA if for every n-dimensional tape of size a n (a≥1) it accepts the n-dimensional tape in time a-1. Moreover, a 1- way n-dimensional cellular automaton (1-nCA) can be considered as a natural extension of the 1-way two- dimensional cellular automaton to n-dimension. The initial configuration is accepted if the last special cell reaches a final state. A 1-nCA is said to be a real- time 1-nCA if when started with n-dimensional array of cells in nonquiescent state, the special cell reaches a final state. In this paper, we propose a homogeneous systolic automaton with n-dimensional layers (n-HSPA), and investigate some properties of real-time n-HSPA. Specifically, we first investigate a relationship between the accepting powers of real-time n-HSPA’s and real-time 1-nCA’s. We next show the recognizability of n-dimensional connected tapes by real-time n-HSPA’s.

Salt and pepper noise filtering with fuzzy-cellular automata

A new image denoising algorithm is proposed to restore digital images corrupted by impulse noise. It is based on two dimensional cellular automata (CA) with the help of fuzzy logic theory. The algorithm describes a local fuzzy transition rule which gives a membership value to the corrupted pixel neighborhood and assigns next state value as a central pixel value. The proposed method removes the noise effectively even at noise level as high as 90%. Extensive simulations show that the proposed algorithm provides better performance than many of the existing filters in terms of noise suppression and detail preservation. Also, qualitative and quantitative measures of the image produce better results on different images compared with the other algorithms.

Foreword: cellular automata and applications

This special issue contains four papers presented during the workshop, ‘‘18th International Workshop on Cellular Automata and Discrete Complex Systems’’ (Automata 2012), held in La Marana, Corsica island (France) in the period September 19–21th, 2012. The aim of this workshop is to establish and maintain a permanent, international, multidisciplinary forum for the collaboration of researchers in the field of Cellular Automata (CA) and Discrete Complex Systems (DCS), provide a platform for presenting and discussing new ideas and results, and support the development of theory and applications of CA and DCS. Typical, but not exclusive, topics of the workshop are: dynamics aspects, algorithmic, computational and complexity issues, emergent properties, formal language processing, models of parallelism and distributed systems, phenomenological descriptions, scientific modeling and practical applications. After an additional review process, four papers were selected and included in this special issue. They are now presented in an extended and improved form with respect to the already refereed workshop version that appeared in the proceedings of Automata 2012. The paper ‘‘Computation of Functions on n Bits by Asynchronous Clocking Cellular Automata’’ by Michael Vielhaber aims at proving that different functions on binary vectors can be computed by changing the updating scheme from a fully synchronous to an asynchronous one on some fixed CA local rule. In their paper ‘‘Solving the Parity Problem in One– Dimensional Cellular Automata’’, Heather Betel, Pedro P. B. de Oliveira, and Paola Flocchini deal with the parity problem in one–dimensional cellular automata (CA): a CA local rule solves the parity problem if, starting from any initial configuration, the CA converges to the 0–configuration (resp., the 1–configuration) if and only if the initial configuration contains an even number of 1s (resp., an odd number of 1s). In particular, authors focus on the neighborhood size of CA rules solving the problem. Murillo G. Carneiro and Gina M. B. Oliveira present in the paper ‘‘Synchronous Cellular Automata-Based Scheduler initialized by Heuristic and modeled by a Pseudolinear neighborhood’’ two approaches based on CA to the task scheduling problem in multiprocessor systems. The implementation of cellular automata on processor arrays is considered by Jean-Vivien Millo and Robert de Simone in the paper ‘‘Explicit routing schemes for implementation of cellular automata on processor arrays’’. They deal with the trade-offs between the generality of the CA neighborhood and the limited expressive power provided by physical platforms. This is an extremely hot topic which will help in turning CA towards real extended applications. We would like to warmly thank the authors for their work and effort which made this special issue possible. Special thanks go to all referees for their valuable contributions both during the selection and the final review process. Finally, we also want to thank Professor Grzegorz Rozenberg for offering us the opportunity to publish this special issue in Natural Computing.

Quantitative Modeling of Fibrinogen Adsorption on Different Biomaterials

Adsorption processes of biological macromolecules on solid surfaces, e.g. on implant materials, are of scientific, medical and technological interest. The adsorption process of the blood plasma protein fibrinogen from aqueous solutions on biomaterial surfaces is simulated by solving the diffusion equation in one dimension in combination with a two dimensional cellular automaton model. The adsorption/desorption kinetics of fibrinogen on different metallic biomaterials is tracked until a dynamic equilibrium is reached. In addition to mass transfer towards the surface, adsorption of fibrinogen molecules and surface diffusion of single fibrinogen molecules and clusters the algorithm also accounts for the desorption of single molecules. By varying the desorption behavior in the simulation calculation, the equilibrium surface coverage changes in the range of 0.2–0.85, implying more flexible and higher surface coverage than previous models. The influences of surface properties of the biomaterials and of the initial concentration of fibrinogen on the adsorption process are quantified. Experimental results from the literature on fibrinogen adsorption kinetics are compared with our simulation results and illustrate good quantitative agreement that is only achievable using desorption as essential model component.

Simulation of Evacuation Characteristics Using a 2-Dimensional Cellular Automata Model for Pedestrian Dynamics

In public places, the high pedestrian density is one of the direct causes leading to crowding and trample disaster, so it is very necessary to investigate the collective and evacuation characteristics for pedestrian movement. In the occupants’ evacuation process, the people-people interaction and the people-environment interaction are sufficiently considered in this paper, which have been divided into the exit attraction, the repulsion force between people, the friction between people, the repulsion force between human and barrier, and the attraction of surrounding people. Through analyzing the existing models, a new occupant evacuation cellular automata (CA) model based on the social force model is presented, which overcomes the shortage of the high density crowd simulation and combines the advantages that CA has sample rules and faster calculating speed. The simulating result shows a great applicability for evacuation under the high density crowd condition, and the segregation phenomena have also been found in the bidirectional pedestrian flow. Besides these, setting isolated belt near the exit or entrance of underpass not only remarkably decreases the density and the risk of tramper disaster but also increases the evacuation efficiency, so it provides a new idea for infrastructure design about the exits and entrances.

Two Dimensional Cellular Automaton Model of the Mixed Traffic Flow for Urban Traffic

Based on the two-dimension cellular automaton traffic flow model (BML model), a mixed traffic flow model for urban traffic considering the transit traffic is established in this paper. Under the don't block the box rules and the opening boundary conditions, the impacts of transit traffic, the central station, traffic lights cycle, the vehicles length on the mixed traffic flow is studied by computer simulation. Some important characters appearing in the new model are also elucidated. It shows that traffic flow is closely related to traffic lights cycle, the geometric structure of transport network and boundary conditions. Under certain traffic light cycle time, the traffic flow has a periodical oscillation change. The comparison to practical measured data shows that our stimulation results are accordant with the changes of real traffic flow, which confirms the accuracy and rationality of our model.

Secret image sharing scheme with authentication and remedy abilities based on cellular automata and discrete wavelet transform

A meaningful secret image sharing scheme with authentication and remedy abilities is proposed in this paper. One dimensional cellular automata, discrete wavelet transform and hash function are adopted in the proposed scheme. The stego images are allowed to be verified to determine whether they are tampered or not. Once the stego images are tampered, shared bits retrieved from these tampered areas cannot be used to reconstruct the secret image. Instead, those damaged areas in the secret image can be repaired by the hidden information. Experimental results exhibit that low computation cost, high tamper detection rate and advanced remedy ability against tampering and cropping attacks are achieved by the proposed scheme.

3D CAFE simulation of a macrosegregation benchmark experiment

A macrosegregation benchmark experiment is simulated using a three dimensional (3D) Cellular Automaton (CA) - Finite Element (FE) model. It consists of a Sn - 3 wt% Pb alloy solidified in a rectangular cavity. Thanks to tabulated thermodynamic properties and solidification paths with temperature and composition, the effect of natural convection and macrosegregation on cooling curves is correctly predicted. Nucleation parameters are adjusted so that the simulated grain structure correlates with the real grain structure. Although macrosegregation is well predicted, this is not the case for freckles yet observed in the solidified sample.

Cost Optimized Design Technique for Pseudo-Random Numbers in Cellular Automata

In this research work, we have put an emphasis on the cost effective design approach for high quality pseudo-random numbers using one dimensional Cellular Automata (CA) over Maximum LengthCA. This work focuses on different complexities e.g ., space complexity, time complexity, design complexity and searching complexity for the generation of pseudo -random numbers in CA. The optimization procedure for these associated complexities is commonly referred as the cost effective generation approach for pseudorandom numbers. The mathematical approach for proposed methodology over the existing maximum length CA emphasizes on better flexibility to fault coverage. The randomness quality of the generated patterns for the proposed methodology has been ve rified using Diehard Tests which reflects that the randomness quality achieved for proposed methodology is equal to the quality of randomness of the patterns generated by the maximum length cellular automata. The cost effectiveness results a cheap hardware implementation for the concerned pseudo-random pattern generator. Short version of this paper has been published in [1].

A Novel Method for Generating Self Replicate Patterns Based on two Dimensional Cellular Automata, Twenty Five Neighborhood Model

A Novel Method for Generating Self Replicate Patterns Based on two Dimensional Cellular Automata, Twenty Five Neighborhood Model

DNA sequence evolution through Integral Value Transformations

In deciphering the DNA structures, evolutions and functions, Cellular Automata (CA) plays a significant role. DNA can be thought as a one-dimensional multi-state CA, more precisely four states of CA namely A, T, C, and G which can be taken as numerals 0, 1, 2 and 3. Earlier, Sirakoulis et al. (2003) reported the DNA structure, evolution and function through quaternary logic one dimensional CA and the authors have found the simulation results of the DNA evolutions with the help of only four linear CA rules. The DNA sequences which are produced through the CA evolutions, however, are seen by us not to exist in the established databases of various genomes although the initial seed (initial global state of CA) was taken from the database. This problem motivated us to study the DNA evolutions from more fundamental point of view. Parallel to CA paradigm we have devised an enriched set of discrete transformations which have been named as Integral Value Transformations (IVT). Interestingly, on applying the IVT systematically, we have been able to show that each of the DNA sequence at various discrete time instances in IVT evolutions can be directly mapped to a specific DNA sequence existing in the database. This has been possible through our efforts of getting quantitative mathematical parameters of the DNA sequences involving fractals. Thus we have at our disposal some transformational mechanism between one DNA to another.

Digital Image Scrambling Based on Two Dimensional Cellular Automata

The basic idea of scrambling is to change the image pixel positions through matrix transform to achieve the visual effect of disorder. Cellular automata can be successfully applied for this purpose. This paper presents digital image scrambling based on two dimensional cellular automata. The proposed scheme is shown high quality of confusion in a few evolution steps. When the original image is compared with the descrambled image by human visual system, it is not recognizable which one is descrambled image and which one is the original image. The paper is organised as follows: first the concept of cellular automata is introduced, and then accordingly the game of life rules and the proposed model followed by the experimental results with discussions.

Autonomously Implemented Versatile Path Planning for Mobile Robots Based on Cellular Automata and Ant Colony

Abstract A path planning method for mobile robots based on two dimensional cellular automata is proposed. The method can be applied for environments with both concave and convex obstacles. It is also appropriate for multi-robot problems as well as dynamic environments. In order to develop the planning method, environment of the robot is decomposed to a rectangular grid and the automata is defined with four states including Robot cell, Free cell, Goal cell and Obstacle cell. Evolution rules of automata are proposed in order to direct the robot toward its goal. CA based path planner method is afterwards modified by a colony technique to be applicable for concave obstacles. Then a layered architecture is proposed to autonomously implement the planning algorithm. The architecture employs an abstraction approach which makes the complexity manageable. An important feature of the architecture is internal artifacts that have some beliefs about the world. Most actions of the robot are planned and performed with re...

A THREE-DIMENSIONAL CELLULAR AUTOMATON SIMULATION FOR DENDRITIC GROWTH

Perhaps dendrite is the most observed solidification microstructure of many metal- lic materials. The dendritic morphologies show a dominating effect on the performance of casting products. A lot of work has been carried out to investigate the formation mechanism of dendritic microstructure. It is found that the development of dendritic microstructures is a complicated process controlled by the interplay of many factors such as thermal and solute transfer, capillary etc. Cellular automaton (CA) can simulate the solidification process with a high computational efficiency, thus, attracts great attentions. In recent years, progress has been made on the two dimensional CA models for the solidification microstructure formation. But up to date researches on three dimensional CA model are very limited. A combined cellular automaton-finite difference (CA-FD) model for the three dimensional simulation of dendritic growth was developed in this paper. Simulations were performed to investigate the dendritic growth in an undercooled Al-Cu alloy as well as in a directionally solidified Al-Cu alloy. The numerical results showed clearly the development of the free dendrite in the under- cooled melt and the microstructure evolution in the directionally solidified alloy and agreed well with the theoretical predictions and the experimental results.

DNA Sequence Evolution through Integral Value Transformations

In deciphering the DNA structures, evolutions and functions, Cellular Automata (CA) do have a significant role. DNA can be thought of as a one-dimensional multi-state CA, more precisely four states of CA namely A, T, C, and G which can be taken as numerals 0, 1, 2 and 3. Earlier, G.Ch. Sirakoulis et al reported the DNA structure, evolution and function through quaternary logic one dimensional CA and the authors have found the simulation results of DNA evolutions with the help of only four linear CA rules. The DNA sequences which are produced through the CA evolutions, however, are seen by our research team not to exist in the established databases of various genomes although the initial seed (initial global state of CA) was taken from the database. This problem motivated us to study the DNA evolutions from a more fundamental point of view. Parallel to the CA paradigm we have devised an enriched set of discrete transformations which have been named as Integral Value Transformations (IVT). Interestingly, on applying the IVT systematically, we have been able to show that each of the DNA sequences at various discrete time instances in IVT evolutions can be directly mapped to a specific DNA sequence existing in the database. This has been possible through our efforts of getting quantitative mathematical parameters of the DNA sequences involving Fractals. Thus we have at our disposal some transformational mechanism between one DNA to another.