Models and Paradigms of Cellular Automata With One Active Cell

2021 ◽  
pp. 39-54
Keyword(s):  
Cellular Automata ◽  
Local State ◽  
Active Cell ◽  
Time Step ◽  
Basic Cell ◽  
Transition Functions ◽  
Cell Structures ◽  
A Cell ◽  
Local Transition ◽  
Local Transmission

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.

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.

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.

TWO-DIMENSIONAL CELLULAR AUTOMATA WITH MEMORY: PATTERNS STARTING WITH A SINGLE SITE SEED

2002 ◽  
Vol 13 (01) ◽  
pp. 49-65 ◽  
Author(s):  
RAMÓN ALONSO-SANZ ◽  
MARGARITA MARTÍN
Keyword(s):  
Cellular Automata ◽  
Single Site ◽  
Two Dimensional ◽  
Time Step ◽  
A Cell ◽  
With Memory

Standard Cellular Automata (CA) are ahistoric (memoryless), i.e., the new state of a cell depends on its neighborhood configuration only at the preceding time step. The effect of keeping ahistoric memory of all past iterations in two-dimensional CA, featuring each cell by its most frequent state is analyzed in this work.

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.

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.

EFFECT OF MEMORY ON BOOLEAN NETWORKS WITH DISORDERED DYNAMICS: THE K = 4 CASE

2007 ◽  
Vol 18 (08) ◽  
pp. 1313-1327 ◽  
Author(s):  
RAMÓN ALONSO-SANZ ◽  
JUAN PABLO CÁRDENAS
Keyword(s):  
Cellular Automata ◽  
Boolean Networks ◽  
Ordered Structure ◽  
Time Step ◽  
Damage Spreading ◽  
A Cell ◽  
In Cells

In standard Cellular Automata (CA) and Boolean Networks (BN), the new state of a cell depends on the neighborhood configuration only at the preceding time step. The effect of implementing memory in cells on CA, CA on networks and BN with different degrees of random rewiring is studied in this paper paying attention to the particular case of four inputs. As a rule, memory in cells induces a moderation in the rate of changing cells and in the damage spreading, albeit in the latter case memory turns out ineffective in the control of the damage as the wiring network moves away of the ordered structure that features proper CA.

ONE-DIMENSIONAL r=2 CELLULAR AUTOMATA WITH MEMORY

2004 ◽  
Vol 14 (09) ◽  
pp. 3217-3248 ◽  
Author(s):  
RAMÓN ALONSO-SANZ
Keyword(s):  
Cellular Automata ◽  
Time Step ◽  
One Dimensional ◽  
The Past ◽  
A Cell ◽  
Factor Α ◽  
Update Rules ◽  
With Memory ◽  
Standard Framework ◽  
Dimensional Range

Standard Cellular Automata (CA) are ahistoric (memoryless): i.e. the new state of a cell depends on the neighborhood configuration only at the preceding time step. This article introduces an extension to the standard framework of CA by considering automata implementing memory capabilities. While the update rules of the CA remains the same, each site remembers a weighted mean of all its past states, with a decreasing weight of states farther in the past. The historic weighting is defined by a geometric series of coefficients based on a memory factor (α). This paper considers the time evolution of one-dimensional range-two CA with memory.

Evolutions of Some One-Dimensional Homogeneous Cellular Automata

2021 ◽  
Vol 30 (1) ◽  
pp. 75-92
Author(s):  
Sreeya Ghosh ◽  
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Active Cell ◽  
One Dimensional ◽  
Transition Functions

Evolution patterns of a one-dimensional homogeneous cellular automaton (CA) are investigated for some standard transition functions. The different possible evolution patterns for an elementary CA starting with at most one active cell or ON state cell are discussed. Also, with respect to some initial configurations, evolution-wise equivalent Wolfram codes are investigated. It is shown that these equivalent codes are automorphic.

ONE-DIMENSIONAL CELLULAR AUTOMATA WITH MEMORY: PATTERNS FROM A SINGLE SITE SEED

2002 ◽  
Vol 12 (01) ◽  
pp. 205-226 ◽  
Author(s):  
RAMÓN ALONSO-SANZ ◽  
MARGARITA MARTÍN
Keyword(s):  
Cellular Automata ◽  
Weighted Mean ◽  
Time Step ◽  
Memory Factor ◽  
One Dimensional ◽  
A Cell ◽  
Factor Α ◽  
Update Rules ◽  
With Memory ◽  
Standard Framework

Standard Cellular Automata (CA) are ahistoric (memoryless): i.e. the new state of a cell depends on the neighborhood configuration only at the preceding time step. This article introduces an extension to the standard framework of CA by considering automata implementing memory capabilities. While the update rules of the CA remain the same, each site remembers a weighted mean of all its past states. The historic weighting is defined by a geometric series of coefficients based on a memory factor (α). The time evolution of one-dimensional CA with memory starting with a single live cell is studied. It is found that for α ≤ 0.5, the evolution corresponds to the standard (nonweighted) one, while for α > 0.5, there is a gradual decrease in the width of the evolving pattern, apart from discontinuities which sometimes may occur for certain rules and α values.

Modeling of Dynamic Processes

2021 ◽  
pp. 19-38
Keyword(s):  
Cell Activity ◽  
Active State ◽  
Dynamic Processes ◽  
State Function ◽  
Logical Function ◽  
Time Step ◽  
Cell Structures ◽  
Cad Models ◽  
A Cell ◽  
Function Cell

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.

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