Models and Paradigms of Cellular Automata With an Organized Set of Active Cells

2021 ◽  
pp. 301-322
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Colony Formation ◽  
The State ◽  
Time Step ◽  
Asynchronous Cellular Automata ◽  
Main Cell ◽  
Image Contour

The chapter presents the principles of functioning of asynchronous cellular automata with a group of cells united in a colony. The rules of the formation of colonies of active cells and methods to move them along the field of a cellular automaton are considered. Each formed colony of active cells has a main cell that controls the movement of the entire colony. If several colonies of identical cells meet and combine, then the main cell is selected according to the priority, which is evaluated by the state of the cells of their neighborhoods. Colonies with different active cells can interact, destroying each other. The methods of interaction of colonies with different active states are described. An example of colony formation for solving the problem of describing contour images is presented. The image is described by moving the colony through the cells belonging to the image contour and fixing the cell sectors of the colony, which include the cells of the contour at each time step.

Pseudorandom Number Generators Based on Cellular Automata With the Hexagonal Coverage

2017 ◽  
pp. 139-156
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Random Number ◽  
The State ◽  
Time Step ◽  
Random Number Generators ◽  
Asynchronous Cellular Automata ◽  
Local Functions ◽  
Initial Settings ◽  
The Right

The seventh chapter describes approaches to constructing pseudo-random number generators based on cellular automata with a hexagonal coating. Several variants of cellular automata with hexagonal coating are considered. Asynchronous cellular automata with hexagonal coating are used. To simulate such cellular automata with software, a hexagonal coating was formed using an orthogonal coating. At the same time, all odd lines shifted to the cell floor to the right or to the left. The neighborhood of each cell contains six neighboring cells that have one common side with one cell of neighborhood. The chapter considers the behavior of cellular automata for different sizes and different initial settings. The behavior of cellular automata with various local functions is described, as well as the behavior of the cellular automaton with an additional bit inverting the state of the cell in each time step of functioning.

Pseudorandom Number Generators Based on Asynchronous Cellular Automata and Cellular Automata With Inhomogeneous Cells

2017 ◽  
pp. 127-138
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Local State ◽  
Active Cell ◽  
State Function ◽  
Local Function ◽  
Time Step ◽  
Random Number Generators ◽  
Asynchronous Cellular Automata ◽  
A Cell

The sixth chapter deals with the construction of pseudo-random number generators based on a combination of two cellular automata, which were considered in the previous chapters. The generator is constructed based on two cellular automata. The first cellular automaton controls the location of the active cell on the second cellular automaton, which realizes the local state function for each cell. The active cell on the second cellular automaton is the main cell and from its output bits of the bit sequence are formed at the output of the generator. As the first cellular automaton, an asynchronous cellular automaton is used in this chapter, and a synchronous cellular automaton is used as the second cellular automaton. In this case, the active cell of the second cellular automaton realizes another local function at each time step and is inhomogeneous. The algorithm for the work of a cell of a combined cellular automaton for implementing a generator and its hardware implementation are presented.

Pseudorandom Number Generators Based on Asynchronous Cellular Automata

2017 ◽  
pp. 66-108
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Random Number ◽  
Random Number Generator ◽  
Active Cell ◽  
Time Step ◽  
Random Number Generators ◽  
Von Neumann ◽  
Asynchronous Cellular Automata ◽  
Pseudo Random Number

The fourth chapter deals with the use of asynchronous cellular automata for constructing high-quality pseudo-random number generators. A model of such a generator is proposed. Asynchronous cellular automata are constructed using the neighborhood of von Neumann and Moore. Each cell of such an asynchronous cellular state can be in two states (information and active states). There is only one active cell at each time step in an asynchronous cellular automaton. The cell performs local functions only when it is active. At each time step, the active cell transmits its active state to one of the neighborhood cells. An algorithm for the operation of a pseudo-random number generator based on an asynchronous cellular automaton is described, as well as an algorithm for working a cell. The hardware implementation of such a generator is proposed. Several variants of cell construction are considered.

scholarly journals EVOLUTION OF TWO-DIMENSIONAL CELLULAR AUTOMATA. NEW FORMS OF PRESENTATION

2021 ◽  
Vol 3 (1) ◽  
pp. 85-90
Author(s):  
S. M. Bilan ◽  
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Color Image ◽  
The State ◽  
Dynamic Processes ◽  
State Change ◽  
Two Dimensional ◽  
Time Step ◽  
Von Neumann ◽  
Elementary Cellular Automata

The paper considers cellular automata and forms of reflection of their evolution. Forms of evolution of elementary cellular automata are known and widely used, which allowed specialists to model different dynamic processes and behavior of systems in different directions. In the context of the easy construction of the form of evolution of elementary cellular automata, difficulties arise in representing the form of evolution of two-dimensional cellular automata, both synchronous and asynchronous. The evolution of two-dimensional cellular automata is represented by a set of states of two-dimensional forms of cellular automata, which complicates the perception and determination of the dynamics of state change. The aim of this work is to solve the problem of a fixed mapping of the evolution of a two-dimensional cellular automaton in the form of a three-dimensional representation, which is displayed in different colors on a two-dimensional image The paper proposes the evolution of two-dimensional cellular automata in the form of arrays of binary codes for each cell of the field. Each time step of the state change is determined by the state of the logical "1" or "0". Moreover, each subsequent state is determined by increasing the binary digit by one. The resulting binary code identifies the color code that is assigned to the corresponding cell at each step of the evolution iteration. As a result of such coding, a two-dimensional color matrix (color image) is formed, which in its color structure indicates the evolution of a two-dimensional cellular automaton. To represent evolution, Wolfram coding was used, which increases the number of rules for a two-dimensional cellular automaton. The rules were used for the von Neumann neighborhood without taking into account the own state of the analyzed cell. In accordance with the obtained two-dimensional array of codes, a discrete color image is formed. The color of each pixel of such an image is encoded by the obtained evolution code of the corresponding cell of the two-dimensional cellular automaton with the same coordinates. The bitness of the code depends on the number of time steps of evolution. The proposed approach allows us to trace the behavior of the cellular automaton in time depending on its initial states. Experimental analysis of various rules for the von Neumann neighborhood made it possible to determine various rules that allow the shift of an image in different directions, as well as various affine transformations over images. Using this approach, it is possible to describe various dynamic processes and natural phenomena.

Models and Paradigms of Cellular Automata With Several Active Cells

2021 ◽  
pp. 55-74
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Local State ◽  
State Function ◽  
State Control ◽  
Time Step ◽  
Transition Functions ◽  
Asynchronous Cellular Automata ◽  
Control Schemes ◽  
Local Transition

The chapter describes the models and paradigms of asynchronous cellular automata with several active cells. Variants of active states are considered in which an asynchronous cellular automaton functions without loss of active cells. Structures that allow the coincidence of several active states in one cell of a cellular automaton are presented. The cell scheme is complicated by adding several active triggers and state control schemes for active triggers. The VHDL models of such cells were developed. Attention is paid to the choice of local state functions and local transition functions. The local transition functions are different for each active state. This allows you to transmit active signals in different directions. At each time step, two cells can change their information state according to the local state function. Asynchronous cellular automata have a long lifecycle.

scholarly journals Characterization of the Evolution of Nonlinear Uniform Cellular Automata in the Light of Deviant States

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Pabitra Pal Choudhury ◽  
Sudhakar Sahoo ◽  
Mithun Chakraborty
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Boolean Functions ◽  
State Transition ◽  
The State ◽  
Transition Diagram ◽  
One Dimensional ◽  
State Transition Diagram ◽  
Linear Rule

Dynamics of a nonlinear cellular automaton (CA) is, in general asymmetric, irregular, and unpredictable as opposed to that of a linear CA, which is highly systematic and tractable, primarily due to the presence of a matrix handle. In this paper, we present a novel technique of studying the properties of the State Transition Diagram of a nonlinear uniform one-dimensional cellular automaton in terms of its deviation from a suggested linear model. We have considered mainly elementary cellular automata with neighborhood of size three, and, in order to facilitate our analysis, we have classified the Boolean functions of three variables on the basis of number and position(s) of bit mismatch with linear rules. The concept of deviant and nondeviant states is introduced, and hence an algorithm is proposed for deducing the State Transition Diagram of a nonlinear CA rule from that of its nearest linear rule. A parameter called the proportion of deviant states is introduced, and its dependence on the length of the CA is studied for a particular class of nonlinear rules.

Languages, equicontinuity and attractors in cellular automata

1997 ◽  
Vol 17 (2) ◽  
pp. 417-433 ◽  
Author(s):  
PETR KŮRKA
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
State Space ◽  
Finite Type ◽  
Measure Zero ◽  
Initial Conditions ◽  
The State ◽  
Subshift Of Finite Type ◽  
Topologically Transitive ◽  
The Third

We consider three related classifications of cellular automata: the first is based on the complexity of languages generated by clopen partitions of the state space, i.e. on the complexity of the factor subshifts; the second is based on the concept of equicontinuity and it is a modification of the classification introduced by Gilman [9]. The third one is based on the concept of attractors and it refines the classification introduced by Hurley [16]. We show relations between these classifications and give examples of cellular automata in the intersection classes. In particular, we show that every positively expansive cellular automaton is conjugate to a one-sided subshift of finite type and that every topologically transitive cellular automaton is sensitive to initial conditions. We also construct a cellular automaton with minimal quasi-attractor, whose basin has measure zero, answering a question raised in Hurley [16].

Processing and Recognition of Images Based on Asynchronous Cellular Automata

2021 ◽  
pp. 194-242
Keyword(s):  
Image Processing ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Pulse Sequence ◽  
Pulse Signal ◽  
Software Implementation ◽  
Image Description ◽  
Image Objects ◽  
Asynchronous Cellular Automata ◽  
Geometric Objects

This chapter discusses the use of asynchronous cellular automata with controlled movement of active cells for image processing and recognition. A time-pulsed image description method is described. Various models and structures of cellular automata for transmitting active signals are presented. The image of the figure is binarized and an active signal moves along its edges. At every moment in time, the active cell of an asynchronous cellular automaton generates a pulse signal. The shape of the generated pulse sequence describes the geometric shape of a flat figure. Methods for describing images of individual plane figures, as well as a method for describing images consisting of many separate geometric objects, are proposed. Cellular automaton is considered as an analogue of the retina of the human visual canal. The circuitry structures of cells of such asynchronous cellular automata are presented, and the software implementation of the proposed methods is also performed. Methods allow one to classify individual geometric image objects.

Models and Paradigms of Cellular Automata With a Variable Set of Active Cells

2021 ◽  
pp. 75-98
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Variable Number ◽  
Point Of View ◽  
Modes Of Operation ◽  
Von Neumann ◽  
Asynchronous Cellular Automata ◽  
Cad Models

The chapter describes the functioning model of an asynchronous cellular automaton with a variable number of active cells. The rules for the formation of active cells with new active states are considered. Codes of active states for the von Neumann neighborhood are presented, and a technique for coding active states for other forms of neighborhoods is described. Several modes of operation of asynchronous cellular automata from the point of view of the influence of active cells are considered. The mode of coincidence of active cells and the mode of influence of neighboring active cells are considered, and the mode of influence of active cells of the surroundings is briefly considered. Algorithms of cell operation for all modes of the cellular automata are presented. Functional structures of cells and their CAD models are constructed.

scholarly journals Asynchronous Cellular Automata and Brownian Motion

2007 ◽  
Vol DMTCS Proceedings vol. AH,... (Proceedings) ◽  
Author(s):  
Philippe Chassaing ◽  
Lucas Gerin
Keyword(s):  
Asymptotic Behavior ◽  
Brownian Motion ◽  
Cellular Automata ◽  
Interacting Particle Systems ◽  
Particle Systems ◽  
Time Step ◽  
Interacting Particle ◽  
Asynchronous Cellular Automata ◽  
International Audience ◽  
A Cell

International audience This paper deals with some very simple interacting particle systems, \emphelementary cellular automata, in the fully asynchronous dynamics: at each time step, a cell is randomly picked, and updated. When the initial configuration is simple, we describe the asymptotic behavior of the random walks performed by the borders of the black/white regions. Following a classification introduced by Fatès \emphet al., we show that four kinds of asymptotic behavior arise, two of them being related to Brownian motion.

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