In this research, along with **cellular** **automata**, a genetic algorithm is used which, by factoring in the slowness of the algorithm, Finding the shortest path possible, is considered as an optimality criterion; the purpose of this research is to identify the paths that are reliable. In other words, the goal is to provide the robot with a high precision, low-impact, and least cost barrier.

Abstract—The identification of probabilistic **cellular** **automata** (PCA) is studied using a new two stage neighborhood detection al- gorithm. It is shown that a binary probabilistic **cellular** automaton (BPCA) can be described by an integer-parameterized polynomial corrupted by noise. Searching for the correct neighborhood of a BPCA is then equivalent to selecting the correct terms, which con- stitute the polynomial model of the BPCA, from a large initial term set. It is proved that the contribution values for the correct terms can be calculated independently of the contribution values for the noise terms. This allows the neighborhood detection technique de- veloped for deterministic rules in [14] to be applied with a larger cutoff value to discard the majority of spurious terms and to pro- duce an initial presearch for the BPCA neighborhood. A multiob- jective genetic algorithm (GA) search with integer constraints is then evolved to refine the reduced neighborhood and to identify the polynomial rule which is equivalent to the probabilistic rule with the largest probability. A probability table representing the BPCA can then be determined based on the identified neighborhood and the deterministic rule. The new algorithm is tested over a large set of one-dimensional (1-**D**), two-dimensional (2-**D**), and three-dimen- sional (**3**-**D**) BPCA rules. Simulation results demonstrate the effi- ciency of the new method.

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Although **cellular** **automata** have been widely studied as a class of the spatio temporal systems, very few investigators have studied how to identify the **CA** rules given observations of the patterns. A solution using a polynomial realization to describe the **CA** rule is reviewed in the present study based on the application of an orthogonal least squares algorithm. Three new neighbourhood detection methods are then reviewed as important preliminary analysis procedures to reduce the com- plexity of the estimation. The identification of excitable media is discussed using simulation examples and real data sets and a new method for the identification of hybrid **CA** is introduced.

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This paper performs the utilization of **cellular** **automata** computational analysis as the dynamic model of spatial epidemiology. Here, explored elementary aspects of **cellular** **automata** and its application in analyzing contagious disease, in this case avian influenza disease in Indonesia. Computational model is built and map-based simulation is performed using several simplified data of such transportation through sea in Indonesia, and its accordance with poultries in Indonesia, with initial condition of notified avian influenza infected area in Indonesia. The initial places are Pekalongan, West Java, East Java, and several regions in Sumatera. The result of simulation is showing the spreading-rate of influenza and in simple way and describing possible preventive action through isolation of infected areas as a major step of preventing pandemic.

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Wireless Multimedia Sensor Network (WMSN) is an advancement of Wireless Sensor Network (WSN) that encapsulates WSN with multimedia information like image and video. The primary factors considered in the design and deployment of WSN are low power consumption, high speed and memory requirements. Security is indeed a major concern, in any communication system. Consequently, design of compact and high speed WMSN with cryptography algorithm for security, without compromising on sensor node performance is a challenge and this paper proposes a new lightweight symmetric key encryption algorithm based on 1 **D** **cellular** **automata** theory. Simula- tions are performed using MatLab and synthesized using Xilinx ISE. The proposed approach sup- ports both software and hardware implementation and provides better performance compared to other existing algorithms in terms of number of slices, throughput and other hardware utilization.

The box-ball system [33, 32] well-known as soliton **cellular** **automata** is a dynamical sys- tem of balls in a one dimensional array of boxes. The discrete KdV equation through a limiting procedure called ultradiscretization [36] was used to show the solitonic charac- ter like the KdV solitons. The rules for soliton interactions and factorization property of scattering matrices (Yang-Baxter equation) are justiﬁed by means of inverse ultra- discretization [35]. In [35] it is shown that the dynamical systems of soliton **cellular** automaton is described by an ultra-discrete equation obtained from extended Toda molecule equation. Later it was studied by [**3**] that the scattering of two solitons in- cluding the phase shift is described by isomorphism from the tensor product of two aﬃne crystals for the quantum enveloping algebra 𝑈 𝑞 (𝐴

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The two-dimensional **cellular** automaton [7] does not have accuracy in the shape of the output obtained. Further the rate of spread is high, which decreases the efficiency [8]. Hence the hexagonal **cellular** **automata** are used, in which the spread is not linear, the rate of spread is low and the shape of the output is very similar to that obtained in real tsunamis. Let us focus for simplicity on a single **CA** cell (individuated as the “central” cell) of the two-dimensional space: it is considered limited to the universe of its neighbourhood, which consists of m cells (the central cell and its adjacent cells). Indexes are utilised to individuate the central cell (0) and the adjacent ones (1, 2 . . . m − 1), respectively. Two- dimensional **cellular** **automata** (**CA**) are discrete dynamical systems formed by a finite number of identical objects called cells, which are arranged uniformly in a two dimensional space [9]. They are endowed with a state that changes at every discrete step of time according to a deterministic rule. More precisely,

With the current work a smart surface based on small vibrating motors and controlled by **Cellular** **Automata** (**CA**) was presented. By using gliders, a phenomenologically non- dissolving **CA** pattern, we showed that an object can be transported towards a predefined target. Also, by including a cornering **CA** pattern the object can corner at 90 ◦ angles. We selected as objects toothbrush heads based on there geometry that provides a good energy manipulation behaviour. The **CA** control algorithm was described and experimental data was given. The system performed according to predictions with small variations from the intended operation, giving sound evidence of the universality of glider based transportation

The most significant application of medical image processing is brain tumor detection. Most of the methods studied till now do not take into consideration poor image quality that means the image containing noise and with low brightness. The research work processed aims to present an efficient technique for brain tumor detection that is the combination of Hybrid Roundness Metric, Region growing and **Cellular** **Automata** Edge detection. To enhance the tumor detection rate further we have integrated the proposed Hybrid roundness metric, Region Growing and **Cellular** **Automata** Edge Detection based tumor detection with the decision based median filter.

ABSTRACT: Pseudo-random number generators (PRNGs) are a key component of stream ciphers used for encryption purposes. While Non linear Feedback Shift Registers (NFSRs) combined with **cellular** **automata** has been utilized for PRNGs, the use of **cellular** **automata** (**CA**) is another viable option. This paper explores the combination of NFSRs and **CA** as the key components of an efficient stream cipher design for implementation on Field Programmable Gate Arrays (FPGAs). The proposed stream cipher design builds upon a recent published design known as A2U2, which uses the principles of stream cipher and approaches from block cipher design. Comparisons with the A2U2 design indicate that the use of **CA** have the potential to improve the quality of the random numbers generated and hence increase the security of the cipher .

This paper conducted to present a new method for edge detection based on a hybrid model of **cellular** learning **automata** (CLA) and fuzzy **cellular** **automata** (FCA). In the first part of algorithm, standard deviation is applied to obtain the initial edges. Although in the second step an optimum function with the constant power is used to improve the edges quality, this power is constant for all the pixels and causes those non edge pixels to blur. To solve this problem, a hybrid model of SCA and CLA is used. The main advantage of the proposed method is us- ing SCA and CLA for adjusting optimum function to reinforce edge pixels and castrate those non edge pixels. The numerical experiments and comparisons with the well-known existing methods justify the superior perfor- mance and efficiency of our proposed method.

**Cellular** **Automata** (**CA**) based UGMs are widely used in the prediction of ur- ban growth. **CA** models have the ability to handle spatio-temporal dataset and they model the urban growth effectively. A typical **CA** model consists of five elements: Cell Space, Cell State, Cell Neighbourhood, Transition Rule and Time [5]. UGMs based on **CA** predict the urban growth with high accuracy than any other mathematical models [6] [7]. SLEUTH, a UGM based on **CA**, is also being widely used to model the urbanization and is implemented to predict the urban growth of the cities of Mashad, Iran [8]. The study implemented the urban growth model with transportation data and highlighted the efficiency of SLEUTH model when other socioeconomic data with high temporal accuracy were not available. SLEUTH was used to predict the urban growth of Matara city, Sri Lanka [9]. It was found out that out of 66 Grama Niladari Divisions (GNDs), 29 GNDs would be urbanized in 2030. This prediction results would be helpful for urban planners to devise further urban planning policies of Sri Lan- kan cities.

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**Cellular** **automata** (**CA**), formally introduced by von Neu- mann in the late 1940s and early 1950s, are a class of spatially and temporally discrete deterministic systems, characterized by local interactions and an inherently pa- rallel form of evolution [1]. In the late 1960s, Conway proposed his now-famous Game of Life, which shows the great potential of **CA** in simulating complex systems [2]. In the 1980s, Wolfram focused on the analysis of dyna- mical systems and studied **CA** in detail [3,4]. In 2002, he introduced the monumental work A New Kind of Science [5]. In fact, mathematical theory of **CA** was firstly deve- loped by Hedlund about two decades after Neumann’s seminal work [6]. Since 2002, Chua et al. provided a ri- gorous nonlinear dynamical approach to Wolfram’s em- pirical observations [7-10]. All elementary **CA** (ECA) rules are reorganized into four groups in terms of finite bit stings. There are 40 topologically-distinct period- rules , 30 topologically-distinct Bernoulli shift rules, 10 complex Bernoulli shift rules, and 8 hyper Bernoulli shift rules. Recently, the dynamical properties of Chua’s periodic rules and robust Bernoulli-shift rules with distinct parameters have been investigated from the viewpoint of symbolic dynamics [11-17].

two solitons including the phase shift is described by the isomorphism from the tensor product of two affine crystals to the other order of the tensor product called the combinatorial R-matrix [1]. The fact that the combinatorial R-matrices satisfy the Yang–Baxter equation ensures that the scattering of three solitons does not depend on the order of scatterings of the two solitons. Subsequently, in [2] new soliton **cellular** **automata** were constructed from affine crystals corresponding to U q ( g n ), where g n = A (2) 2n − 1 , A (2) 2n , B n ( 1 ) ,C n ( 1 ) , **D** n ( 1 ) , **D** n (2) + 1 . The soliton therein

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In this paper, we will show two kinds of **Cellular** **automata**. The rest of the paper is structured as follows: next section show historical background about **Cellular** **automata**; Section **3** gives overview of one dimensional **cellular** **automata** and describe some of its rules; Section 4 illustrates two dimensional **cellular** **automata** and its rules with details; In the last section of the paper we will present some of the important issues and we will present some of discussion concerning about the **cellular** **automata**, including classification of **cellular** automate as Wolfram classification which includes four styles that mainly based on a graphic analysis of the development of one- dimensional **CA** and Li and Packard have established a classification system depending on Wolfram's system. Then, we will discuss classification of **cellular** **Automata** rules based on their Properties in 1-Dim or 2-dim **cellular** **automata**. After that, we will describe some issues in **CA** the density classification problem in both 1-Dim and 2- Dim **CA** and **cellular** **automata** rules in 2-Dim include Toom’s Rule and Reynaga’s rule and discuss the properties of them and determine the most effective one. At the last parts of this paper , we will talk about the assumption that say “ the physical universe is, fundamentally, a discrete computational structure and Self-Reproducing property with von-Neunmann **cellular** **automata**. and finally we conclude the paper.

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Epidemic modeling is utilized to mimic the dissemination of infectious illness for a given crowd, such as influenza, H1N1, and SARS. Contaminated persons propagate the infection to healthy individuals that they contact with. Since computer worms are similar to such biological viruses in their self-replicating and diffusion behaviors, epidemiological models for examining the propagation of malware, especially worms is not a new criteria [12]. Studying computer worms overall, and Internet worms specifically, is a popular subject for analysts. Numerous endeavors have been made to model the spread behaviors of malwares in different networks [5],[6],[7],[8].The epidemic models can be categorized into two primary groups. The first is the deterministic model, which is represented by the ordinary differential equation [9].The second is the stochastic model which contains two types: one is based on Markov chain [8],[10] and the other is based on **cellular** **automata**. Most models have focused on the technology of differential equations and the Markov chain [8].Models based on differential equations fail to catch the local features of propagation processes .They also neglect to interaction behaviors among individuals. On the other hand, the models based on the Markov chain are complex to explain the spatial temporal process of worm propagation. **Cellular** **automata** [13] is the answer for this problems. Because **Cellular** **automata** (**CA**)can dominate these issues, it has been used as an effective alternative method to describe epidemic spreading and malware propagation[12],[14],[13],[15],[16],[17].In fact, **cellular** **automata** can model the physical computation capabilities, biological, or environme- ntal complex phenomena, such as growth processes, reaction–diffusion systems, epidemic models, and the spread of forest fire.

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This wire is a horizontal row of QCA cells and emits a binary signal from the input to the output due to electrostatic interactions between adjacent cells [5]. If the cell is charged with two additional electrons, the electrons would be arranged in a diagonal way.This type of placement is due to the Coulomb's repulsive forces that do not allow them to be arranged in any other order. When an electron is placed in a cell in a special diameter (logic 1), this polarity consists of electrons located in the vicinity of the QCA with the same polarity. As shown in Figures 2 and **3**, wires are made using two types of cells such as ordinary cells and rotated cells. In a 45 degree wire, the propagation of a binary signal between two polarities is alternated [6].

Sheng-Uei Guan and Shu Zhang [17], proposed a novel **CA**-dynamical system. A block cipher and key stream generator based on that novel **CA** were introduced. Lafe [6,18], proposed to use one-dimensional **CA** transforms for data compression and encryption, where the transformations can be obtained from basic basis functions. The basis functions are related to evolving the states of the **CA**. Jes ủ s Ur ỉ as, et al. [19], introduced a cryptosystem based on **CA**, where the mechanism based on synchronization in **CA** is presented. They provide two primitives system, the pseudorandom generator of keys and the indexed families of permutation. Chunren Lai [20], introduced **CA** based block cipher algorithm (CA256-2) which was designed to provide the high-speed encryption/decryption. Two-dimensional **CA** used for design hash function to provide the digital signature and serve as "check-sums" for error detection/correction. He used four transformations with four cycle length to encryption and decryption message.

A **cellular** automaton (**CA**) is a dynamical system with arbitrarily complex global behavior, despite being governed by very simple local rules [1]. In order to better under- stand how that kind of complex behavior emerges, many explorations have been made in the context of the power implicit in **CA** rules. For instance, classical benchmark problems have been used for this, including the density classification task [2, **3**] and the parity problem [4]. The density classification task tries to discover the most frequent bit in the initial configuration of the lattice; the parity problem tries to find the parity of the number of 1s in the initial configuration of the lattice. One of the approaches in these contexts is to evaluate every possible **CA** of a given family in terms of its capabilities to solve the target problem. This approach is possible in small **CA** families, like the elementary space (composed of 256 CAs), but is not feasible in larger families, like the one-dimensional binary **CA** family with radius **3**, composed of 2 128 rules.

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[5]. S. Angizi, E. Alkaldy, N. Bagherzadeh and K. Navi, “Novel Robust Single Layer Wire Crossing Approach for Exclusive OR Sum of Products Logic Design with Quantum -Dot **Cellular** **Automata**,” Journal of Low Power Electronics, vol.10, pp.256– 271, 2014.