Dimensional Cellular Automata Research Articles

DNA Sequence Evolution through Integral Value Transformations

AbstractIn 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.

Cellular automata with limited inter-cell bandwidth

A d -dimensional cellular automaton is a d -dimensional grid of interconnected interacting finite automata. There are models with parallel and sequential input modes. In the latter case, the distinguished automaton at the origin, the communication cell, is connected to the outside world and fetches the input sequentially. Often in the literature this model is referred to as an iterative array. In this paper, d -dimensional iterative arrays and one-dimensional cellular automata are investigated which operate in real and linear time and whose inter-cell communication bandwidth is restricted to some constant number of different messages independent of the number of states. It is known that even one-dimensional two-message iterative arrays accept rather complicated languages such as { a p ∣ p prime } or { a 2 n ∣ n ∈ N } (H. Umeo, N. Kamikawa, Real-time generation of primes by a 1-bit-communication cellular automaton, Fund. Inform. 58 (2003) 421–435). Here, the computational capacity of d -dimensional iterative arrays with restricted communication is investigated and an infinite two-dimensional hierarchy with respect to dimensions and messages is shown. Furthermore, the computational capacity of the one-dimensional devices in question is compared with the power of two-way and one-way cellular automata with restricted communication. It turns out that the relations between iterative arrays and cellular automata are quite different from the relations in the unrestricted case. Additionally, an infinite strict message hierarchy for real-time two-way cellular automata is obtained as well as a very dense time hierarchy for k -message two-way cellular automata. Finally, the closure properties of one-dimensional iterative arrays with restricted communication are investigated and differences to the unrestricted case are shown as well.

Cellular automata models of tumour natural shrinkage

In this paper we present three dimensional cellular automata models for tumour growth, with a focus on the tumour’s natural shrinkage caused by the removal of the dead cells’ mortal remains. The significance of this phenomenon for the resulting volume of the in silico tumour is shown. Two algorithms are presented, one using the chain shifting approach for tumour expansion and shrinkage and another improving the performance of the chain shifting approach. Simulations are validated against the experimental results.

Quantum algorithm of evolutionary analysis of one dimensional cellular automata

Quantum algorithm of evolutionary analysis of one dimensional cellular automata

Generating PNS for Secret Key Cryptography Using Cellular Automaton

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

A Three Dimensional Cellular Automaton Model for the Prediction of Solidification Morphologies of Brass Alloy by Horizontal Continuous Casting and Its Experimental Verification

A Three Dimensional Cellular Automaton Model for the Prediction of Solidification Morphologies of Brass Alloy by Horizontal Continuous Casting and Its Experimental Verification

CAFE Modeling of Segregation and Structure in Levitated Droplets

The coupled two dimensional (2D) Cellular Automaton (CA) Finite Element (FE) model has been extended based on the recent work by Guillemot et al. [1]. Extensions concern i microsegregation at the scale of the CA cells ii macrosegregation at the scale of the FE mesh based on a remeshing technique. The model is applied to segregation taking place upon single grain nucleation and growth from the centre of a spherical domain. The simulation retrieves the prediction of Heringer et al. [2]. Application to solidification of a spherical Al-4wt%Cu droplet demonstrates its capability to deal with mass exchange by diffusion outside the grain envelope defined by the mushy zone together with back diffusion in the solid [3].

Topological Dynamics of Cellular Automata: Dimension Matters

Topological dynamics of cellular automata (CA), inherited from classical dynamical systems theory, has been essentially studied in dimension 1. This paper focuses on higher dimensional CA and aims at showing that the situation is different and more complex starting from dimension 2. The main results are the existence of non sensitive CA without equicontinuous points, the non-recursivity of sensitivity constants, the existence of CA having only non-recursive equicontinuous points and the existence of CA having only countably many equicontinuous points. They all show a difference between dimension 1 and higher dimensions. Thanks to these new constructions, we also extend undecidability results concerning topological classification previously obtained in the 1D case. Finally, we show that the set of sensitive CA is only $\varPi _{2}^{0}$ in dimension 1, but becomes $\varSigma _{3}^{0}$ -hard for dimension 3.

Mathematical Modeling of Solidification Microstructure of Pure Copper by Vacuum Continuous Casting and Its Experimental Verification

The purpose of this study is to predict the solidification microstructure of pure copper rod by vacuum continuous casting (VCC) process and verify its accuracy by experimental observation. This study was extended from previous study (using 2D-CA model). A three dimensional cellular automaton (3D-CA) model and the finite difference method were utilized to simulate the macro-temperature field, nucleation, and grain growth of a pure copper rod based on the actual casting operations. The simulated solidification microstructures obtained from the 3D-CA model were found in good agreement with the results of actual casting experiments. Both numerical simulations and experimental observations show that the microstructure of a copper rod changes with casting speed and that the S/L interface moves closer to the orifice of the mould with increasing drawing speed.

Implementation of CAVENET and Its Usage for Performance Evaluation of AODV, OLSR and DYMO Protocols in Vehicular Networks

Vehicle Ad-hoc Network (VANET) is a kind of Mobile Ad-hoc Network (MANET) that establishes wireless connection between cars. In VANETs and MANETs, the topology of the network changes very often, therefore implementation of efficient routing protocols is very important problem. In MANETs, the Random Waypoint (RW) model is used as a simulation model for generating node mobility pattern. On the other hand, in VANETs, the mobility patterns of nodes is restricted along the roads, and is affected by the movement of neighbour nodes. In this paper, we present a simulation system for VANET called CAVENET (Cellular Automaton based VEhicular NETwork). In CAVENET, the mobility patterns of nodes are generated by an 1-dimensional cellular automata. We improved CAVENET and implemented some routing protocols. We investigated the performance of the implemented routing protocols by CAVENET. The simulation results have shown that DYMO protocol has better performance than AODV and OLSR protocols.

NUMERICAL MODELING OF DENDRITIC GROWTH IN ALLOY SOLIDIFICATION WITH FORCED CONVECTION

A two dimensional (2D) cellular automaton (CA) - lattice Boltzmann (LB) model is presented to investigate the effects of forced melt convection on the solutal dendritic growth. In the model, the CA approach of simulating the dendritic growth is incorporated with the kinetic-based lattice Boltzmann method (LBM) for numerically solving the melt flow and solute transport. Two sets of distribution functions are used in the LBM to model the convective-diffusion phenomena during dendritic growth. After validating the model by comparing the numerical results with the theoretical solutions, it is applied to simulate the single and multi dendritic growth of Al - Cu alloys without and with a forced convection. The typical asymmetric growth features of convective dendrite are reproduced and the dendritic morphology is strongly influenced by melt convection. The simulated convective multi dendritic features by the present model are also compared with that by the CA-NS model. The present model is found to be more computationally efficient and numerically stable than the CA-NS model.

Modeling the topological features during grain growth by cellular automaton

A two dimensional cellular automaton model, with advanced features for continuous tracking and precise estimation of curvature of grain boundary, has been developed to simulate and study the topological and kinetic features of grain growth in polycrystalline materials. The model simulations exhibited experimentally observed topological arrangements of grains as well as validated the two independently derived grain growth kinetics models, namely, Burke and Turnbull’s parabolic law and von Neumann–Mullins law for the growth rate of individual grains. Furthermore, the model was used to study the growth kinetics in graded and columnar microstructures. The growth kinetics was found to depend on the extent of gradation and the aspect ratio of columnar grains. It was observed that both the graded and columnar microstructures evolve towards the equiaxed microstructure during the grain growth.

A simple method for simulating biochemical reaction networks

We propose a simple method of simulating chemical reaction networks by using a multiset rewriting system: abstract rewriting system on multisets (ARMS). We simulate the oregonator model, a mathematical model of the Belousov-Zhabotinskii reaction, and we obtain the same behavior when the differential equations or the Gillespie method are used. We also compose a 1- and 2-dimensional cellular automata by using ARMS, and confirm that it shows the pattern forming that is observed in the BZ reaction.

The effect of on-ramp and off-ramp on the one dimensional road with open boundaries

The effect of one on-ramp (entry) and one off-ramp (exit) is investigated numerically in a one dimensional cellular automaton traffic flow model, with open boundary conditions, using parallel dynamics. Our aim in this paper is to study how the injection rates α and α0 and the extraction rates β and β0 act on the density and flux of cars in a one dimensional road. The priority of occupation at entry site i1 (removing at exit site i2) is attributed to the particle that entered (was absorbed) the chain. Phase diagrams in (β0, α0) and (β, α0) plans are established. For α = 0.1, they show three different topologies in the flow behaviour. The first one corresponds to the presence of four regions, by varying α0, namely low-density phase (LDP), intermediate-density phase (IDP), plateau current phase (PCP), and high-density phase (HDP). In the second topology, the intermediate-density phase disappears. The third topology presents only two regions, i.e., low- and high-density phases. For small values of α, the (IDP) and (PCP) disappear, respectively, by increasing β. When increasing α, the fourth topology, corresponding to one phase (HDP), appears for low values of β and β0.

Disorder effect on the traffic flow behavior

The effects of some disorders, on the traffic flow behavior, are studied numerically. Especially, the effect of mixture of vehicles of different velocities and/or lengths, the effects of different drivers reactions, the position and the extraction rate of off-ramp in the free way. Using a generalized optimal velocity model, for a mixture of fast and slow vehicles, we have investigated the effect of delay times τ f and τ s on the fundamental diagram. It is Found that the small delay times have almost no effect, while, for sufficiently large delay time τ s , the current profile displays qualitatively five different forms, depending on τ f , τ s and the fractions f f and f s of the fast and slow cars, respectively. The velocity (current) exhibits first-order transitions at low and/or high densities, from freely moving phase to the congested state, and from congested state to a jamming one, respectively. The minimal current appears in intermediate values of τ s . Furthermore there exist, a critical value of τ f above which the meta-stability and hysteresis appear. The effects of disorder due to drivers behaviors have been introduced through a random delay time τ allowing the car to reach its optimal velocity traffic flow models with open boundaries. In the absence of the variation of the delay time Δτ, it is found that the transition from unstable to meta-stable and from meta-stable to stable state occur under the effect of the injecting and the extracting rate probabilities α and β respectively. Moreover, the perturbation of the traffic flow behavior due to the off-ramp has been studied using numerical simulations in the one dimensional cellular automaton traffic flow model with open boundaries. When the off-ramp is located between two critical positions i c1 and i c2 the current remains constant (plateau) for β0c1 < β0 < β0c2, and the density undergoes two successive first order transitions: from high density to plateau current phase and from average density to the low one. In the case of two off-ramps, these transitions occur only when the distance between ramps, is smaller than a critical value.

Effect of dislocation source length on yield strength of nanostructured metallic multilayer thin films

There is great interest in metallic multilayer thin films with the layer thickness on the order of nanometers due to their high hardness and strength. The yield strength deviates from Hall–Petch and Orowan predictions with layer thickness as the controlling factor, and other factors are in need to explain this phenomenon. In this work, the effect of dislocation source length on yield strength of multilayer system in the nanoscale regime is investigated using a three dimensional cellular automaton dislocation model. Different initial dislocation source lengths are assumed in the model for the metallic multilayer thin films with different layer thicknesses. The multilayer system studied here is composed of alternating A and B components with FCC structure, cube-on-cube orientation relationship, and the same layer thickness. The results show that the initial dislocation source length can provide an explanation for the above deviations.

PARALLELIZING THREE DIMENSIONAL CELLULAR AUTOMATA WITH OpenMP

This paper describes our research on using Genetic Programming to obtain transition rules for Cellular Automata, which are one type of massively parallel computing system. Our purpose is to determine the existence of a limit of chaos for three dimensional Cellular Automata, empirically demonstrated for the two dimensional case. To do so, we must study statistical properties of 3D Cellular Automata over long simulation periods. When dealing with big three dimensional meshes, applying the transition rule to the whole structure can become a extremely slow task. In this work we decompose the Automata into pieces and use OpenMp to parallelize the process. Results show that using a decomposition procedure, and distributing the mesh between a set of processors, 3D Cellular Automata can be studied without having long execution times.

A simple 2-dimensional model of cardiac tissue conduction

Objectives: The purpose of this study is to simulate cardiac tissue conduction using a 2-dimensional cellular automata (CA) model. Methods: Using a 2-dimensional CA model, we represented ventricular myocytes by cells arranged in a 33-by-33 grid to simulate a single ventricle. The neighborhood of each cell is a von Neumann neighborhood composed of 4 directly adjoining cells. The grid was composed in the shape of a torus to permit cells across the opposite face of the grid to interact. The design allows simulations of sustainable waves of electrical activity. The NetLogo 4.01 Beta software platform (Northwestern Illinois) was used to implement the CA model. Each tick of the simulation clock is equivalent to 1 millisecond. The simulations were run over millions of iterations. The pacemaker was set at 60 beats per minute. Results: Given normal physiologic parameters of heart rate, length of Na/Ca channel opening times, and QTc, the CA model simulates the normal conduction of the heart. The waves of depolarization and repolarization spread through the cardiac tissue without formation of pathologic dysrhythmias over hundreds of thousands of heartbeats. The virtual rhythm strip created by a virtual electrocardiogram lead shows a narrow complex rhythm at the rate set by the user-defined pacemaker parameter (Fig. 1A). Given the 2-dimensional nature of the model, the T wave is in the opposite direction to the QRS because there is no epicardium or endocardium. The plot of the electric potential at a time t + 1 vs time t shows a stable system that occupies a stable orbit (Fig. 1B). Once the system is perturbed by increasing the QTc, the CA model enters into an unstable tachycardia. The rate of ventricle depolarization ranges from 120 to 180 beats per minute depending on the exact setting of the QTc. The resultant rhythm strip (Fig. 1C) shows the tachyarrhythmia with a pacemaker spike occurring at regular intervals that is independent of the ventricular rhythm (ie, AV dissociation). The tachycardia is narrow complex because of the small number of cells in the virtual cardiac tissue. The state diagram shows the system trapped in a tachyarrhythmia from which it is unable to escape (Fig. 1D). Conclusions: The initial results of this article indicate that the cardiac conduction system can be readily simulated using CA. Cellular automata simulations offer a major advantage in their ability to monitor the electric potential of each myocyte as depolarization and repolarization proceeds. This implies that the effect of a large number of factors that influence conduction, for example, electrolyte concentrations, congenital and acquired alterations in voltage-gated channels, and ischemia-induced changes in conduction, can be readily simulated. These CA simulations are expected to provide information on the overall progress of both normal and abnormal electric activity as well as on individual myocyte function over time. Thus, CA modeling of cardiac tissue affords the novel possibility of creating simulations of the effect of antiarrhythmic medications and ischemia at the cardiac myocyte and tissue level.

Kaleidoscope of life: A 24-neighbourhood outer-totalistic cellular automaton

One of the challenges of cellular automaton research is finding models with a low complexity and at the same time a rich dynamics. A measure of low complexity is the number of states in the model and the number of transition rules to switch between those states. In this paper, we propose a 2-dimensional 2-state cellular automaton that–though governed by a single simple transition rule–has a sufficiently rich dynamics to be computationally universal. According to the transition rule, a cell’s state is determined by the sum of the states of the cells at orthogonal or diagonal distances one or two from the cell (distance-2 Moore neighbourhood), but not by the previous state of the cell itself. Notwithstanding its simplicity, this model is able to generate a great variety of patterns, including several types of stable configurations, oscillators and patterns that move over cellular space (gliders). We prove the computational universality of the model by constructing a universal set of logic gates (NOT and AND) from these patterns. A key element in this proof is the shifting of phases and positions of signals such that they meet the input requirements of the logic gates. Similarities of the model with classical spin systems are also discussed.

Symmetry pattern transition in cellular automata with complex behavior

A transition from asymmetric to symmetric patterns in time-dependent extended systems is described. It is shown that one dimensional cellular automata, started from fully random initial conditions, can be forced to evolve into complex symmetrical patterns by stochastically coupling a proportion p of pairs of sites located at equal distance from the center of the lattice. A nontrivial critical value of p must be surpassed in order to obtain symmetrical patterns during the evolution. This strategy is able to classify the cellular automata rules – with complex behavior – between those that support time-dependent symmetric patterns and those which do not support such kind of patterns.