Processing and Recognition of Images Based on Asynchronous Cellular Automata

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

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.

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

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.

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

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.

Models and Paradigms of Cellular Automata With Several Active Cells

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.

New Evolutionary Model of Life Based on Cellular Automata

The chapter presents software that implements models of asynchronous cellular automata with a variable set of active cells. The software is considering one of the modifications of the game Conway “Life”. In the proposed model “New Life,” the possibility of functioning of a separate “living” cell is realized, which, when meeting with other “living” cells, participates in the “birth” of new “living” cells with a different active state. Each active state is determined by a code that is formed by the state values of the cells of the neighborhood. Variants of the evolution of the universe based on the surroundings of von Neumann and Moore are considered. This program uses restrictions on the number of “born” cells in order to limit the overpopulation of the universe. Possible goals and objectives to be solved in the use of “New Life” are also considered.

Models and Paradigms of Cellular Automata With One Active Cell

The chapter describes the basic models and paradigms for constructing asynchronous cellular automata with one active cell. The rules for performing local state functions and local transition functions are considered. The basic cell structures during the transmission of active signals for various local transmission functions are presented. The option is considered when the cell itself selects among the cells in the neighborhood of the cell, a cell that will become active in the next time step, and also the structure with active cells under control is considered. The analysis of cycles that occur in cellular automata with one active cell is carried out, and approaches to eliminating cycles are formulated. Cell structures are constructed and recommendations for their modeling in modern CAD are formulated.

Modeling of Dynamic Processes

The chapter describes the existing approach to modeling dynamic systems. The rules of the transfer of properties and conditions from cell to cell in cellular automata of various organizations are considered. The basic cell structures are presented in the transfer of only states, as well as properties of cell activity and states. The options are considered when the cell itself selects a cell among the cells in the neighborhood that will become active in the next time step. Also is considered is the option when the cell analyzes the state of neighboring cells and, based on the results of the local state function, makes a decision about the transition to the active state or not. An embodiment of a cell for transmitting an active state is described, only to cells with a given local logical function. Cell structures and their CAD models are constructed.

About Cellular Automata

The chapter describes the basic theoretical principles for the theory of cellular automata. The history of the emergence of cellular automata based on an analysis of existing information sources is presented. The modern classification of cellular automata is presented. The structures of elementary and two-dimensional cellular automata are described. In terms of the rules for the functioning of cellular automata, synchronous, asynchronous, and probabilistic cellular automata are briefly described. Researchers are presented who have made a significant contribution to the development of the theory of cellular automata.