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

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.

Advances in Systems Analysis, Software Engineering, and High Performance Computing - Formation Methods, Models, and Hardware Implementation of Pseudorandom Number Generators ◽

Pseudorandom Number Generators Based on Asynchronous Cellular Automata

10.4018/978-1-5225-2773-2.ch004 ◽

2017 ◽

pp. 66-108

Keyword(s):

Cellular Automata ◽

Cellular Automaton ◽

Random Number ◽

Random Number Generator ◽

Active Cell ◽

Time Step ◽

Von Neumann ◽

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.

Reliable Self-Replicating Machines in Asynchronous Cellular Automata

Artificial Life ◽

10.1162/artl.2007.13.4.397 ◽

2007 ◽

Vol 13 (4) ◽

pp. 397-413 ◽

Cited By ~ 5

Author(s):

Jia Lee ◽

Susumu Adachi ◽

Ferdinand Peper

Keyword(s):

Cellular Automata ◽

Cellular Automaton ◽

Essential Property ◽

Two Dimensional ◽

Von Neumann ◽

Self Replication

We propose a self-replicating machine that is embedded in a two-dimensional asynchronous cellular automaton with von Neumann neighborhood. The machine dynamically encodes its shape into description signals, and despite the randomness of cell updating, it is able to successfully construct copies of itself according to the description signals. Self-replication on asynchronously updated cellular automata may find application in nanocomputers, where reconfigurability is an essential property, since it allows avoidance of defective parts and simplifies programming of such computers.

Advances in Systems Analysis, Software Engineering, and High Performance Computing - Formation Methods, Models, and Hardware Implementation of Pseudorandom Number Generators ◽

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

10.4018/978-1-5225-2773-2.ch006 ◽

2017 ◽

pp. 127-138

Keyword(s):

Cellular Automata ◽

Cellular Automaton ◽

Local State ◽

Active Cell ◽

State Function ◽

Local Function ◽

Time Step ◽

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.

Advances in Computer and Electrical Engineering - New Methods and Paradigms for Modeling Dynamic Processes Based on Cellular Automata ◽

Processing and Recognition of Images Based on Asynchronous Cellular Automata

10.4018/978-1-7998-2649-1.ch007 ◽

2021 ◽

pp. 194-242

Keyword(s):

Image Processing ◽

Cellular Automata ◽

Cellular Automaton ◽

Pulse Sequence ◽

Pulse Signal ◽

Software Implementation ◽

Image Description ◽

Image Objects ◽

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.

Limit sets of stable cellular automata

Ergodic Theory and Dynamical Systems ◽

10.1017/etds.2013.72 ◽

2013 ◽

Vol 35 (3) ◽

pp. 673-690 ◽

Cited By ~ 2

Author(s):

ALEXIS BALLIER

Keyword(s):

Cellular Automata ◽

Cellular Automaton ◽

Point Of View ◽

Limit Set ◽

Limit Sets ◽

Sofic Shift ◽

Almost Everywhere ◽

Sofic Shifts ◽

Full Shift ◽

Factor Map

AbstractWe study limit sets of stable cellular automata from a symbolic dynamics point of view, where they are a special case of sofic shifts admitting a steady epimorphism. We prove that there exists a right-closing almost-everywhere steady factor map from one irreducible sofic shift onto another one if and only if there exists such a map from the domain onto the minimal right-resolving cover of the image. We define right-continuing almost-everywhere steady maps, and prove that there exists such a steady map between two sofic shifts if and only if there exists a factor map from the domain onto the minimal right-resolving cover of the image. To translate this into terms of cellular automata, a sofic shift can be the limit set of a stable cellular automaton with a right-closing almost-everywhere dynamics onto its limit set if and only if it is the factor of a full shift and there exists a right-closing almost-everywhere factor map from the sofic shift onto its minimal right-resolving cover. A sofic shift can be the limit set of a stable cellular automaton reaching its limit set with a right-continuing almost-everywhere factor map if and only if it is the factor of a full shift and there exists a factor map from the sofic shift onto its minimal right-resolving cover. Finally, as a consequence of the previous results, we provide a characterization of the almost of finite type shifts (AFT) in terms of a property of steady maps that have them as range.

Advances in Computer and Electrical Engineering - New Methods and Paradigms for Modeling Dynamic Processes Based on Cellular Automata ◽

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

10.4018/978-1-7998-2649-1.ch009 ◽

2021 ◽

pp. 301-322

Keyword(s):

Cellular Automata ◽

Cellular Automaton ◽

Colony Formation ◽

The State ◽

Time Step ◽

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.

Advances in Computer and Electrical Engineering - New Methods and Paradigms for Modeling Dynamic Processes Based on Cellular Automata ◽

Methods and Models for the Formation of Pseudo-Random Number Sequences Based on Cellular Automata

10.4018/978-1-7998-2649-1.ch006 ◽

2021 ◽

pp. 99-193

Keyword(s):

Cellular Automata ◽

Statistical Tests ◽

Variable Number ◽

Pseudorandom Number ◽

High Quality ◽

Hybrid Cellular Automata ◽

Pseudorandom Number Generators ◽

Number Sequences

The chapter describes well-known models and implementation options for pseudorandom number generators based on cellular automata. Pseudorandom number generators based on synchronous and asynchronous cellular automata are briefly reviewed. Pseudorandom number generators based on one-dimensional and two-dimensional cellular automata, as well as using hybrid cellular automata, are described. New structures of pseudorandom number generators based on asynchronous cellular automata with a variable number of active cells are proposed. Testing of the proposed generators was carried out, which showed the high quality of the generators. Testing was conducted using graphical and statistical tests.

Advances in Systems Analysis, Software Engineering, and High Performance Computing - Formation Methods, Models, and Hardware Implementation of Pseudorandom Number Generators ◽

Pseudorandom Number Generators Based on Cellular Automata With the Hexagonal Coverage

10.4018/978-1-5225-2773-2.ch007 ◽

2017 ◽

pp. 139-156

Keyword(s):

Cellular Automata ◽

Cellular Automaton ◽

Random Number ◽

The State ◽

Time Step ◽

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.

Advances in Systems Analysis, Software Engineering, and High Performance Computing - Formation Methods, Models, and Hardware Implementation of Pseudorandom Number Generators ◽

Fundamental of Cellular Automata Theory

10.4018/978-1-5225-2773-2.ch002 ◽

2017 ◽

pp. 26-51

Keyword(s):

Cellular Automata ◽

Automata Theory ◽

Linear Feedback ◽

Von Neumann ◽

One Dimensional ◽

Local Functions ◽

Definition Of

In this chapter, the author reviews the main historical aspects of the development of cellular automata. The basic structures of cellular automata are described. The classification of cellular automata is considered. A definition of a one-dimensional cellular automaton is given and the basic rules for one-dimensional cellular automata are described that allow the implementation of pseudo-random number generators. One-dimensional cellular automata with shift registers with linear feedback are compared. Synchronous two-dimensional cellular automata are considered, as well as their behavior for various using local functions. An analysis of the functioning of synchronous cellular automata for the neighborhoods of von Neumann and Moore is carried out. A lot of attention is paid to asynchronous cellular automata. The necessary definitions and rules for the behavior of asynchronous cellular automata are given.

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

Ukrainian Journal of Information Technology ◽

10.23939/ujit2021.03.085 ◽

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.