CELLULAR AUTOMATA WITH ACCUMULATIVE MEMORY: LEGAL RULES STARTING FROM A SINGLE SITE SEED

2003 ◽  
Vol 14 (05) ◽  
pp. 695-719 ◽  
Author(s):  
RAMÓN ALONSO-SANZ ◽  
MARGARITA MARTÍN
Keyword(s):  
Cellular Automata ◽  
Forgetting Factor ◽  
Weighted Mean ◽  
Time Step ◽  
One Dimensional ◽  
Legal Rules ◽  
The Past ◽  
A Cell ◽  
Update Rules ◽  
Standard Framework

Standard Cellular Automata (CA) are ahistoric (memoryless), i.e., the new state of a cell depends only on the neighborhood configuration at the preceding time step. This article introduces an extension of 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 back in the past. The historic weighting is defined by a potential series of coefficients, tk, k acting as a forgetting factor. This paper considers the time evolution of one-dimensional, legal CA rules with accumulative memory.

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.

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.

MULTIFRACTAL PROPERTIES OF R90 CELLULAR AUTOMATON WITH MEMORY

2004 ◽  
Vol 15 (10) ◽  
pp. 1461-1470 ◽  
Author(s):  
JUAN R. SÁNCHEZ ◽  
RAMÓN ALONSO-SANZ
Keyword(s):  
Cellular Automata ◽  
Complex Behavior ◽  
Time Step ◽  
One Dimensional ◽  
Dynamical Characteristics ◽  
Historic Memory ◽  
A Cell ◽  
Update Rules ◽  
With Memory ◽  
Standard Framework

Standard Cellular Automata (CA) are ahistoric (memoryless Markov process), i.e., the new state of a cell depends on the neighborhood configuration only at the preceding time step. This article considers the fractal and multifractal properties of an extension to the standard framework of CA implemented by the inclusion of memory capabilities. Thus, in CA with memory, while the update rules of the CA remain unaltered, historic memory of all past iterations is retained by featuring each cell by a summary of all its past states. A study is made of the effect of historic memory on the multifractal dynamical characteristics of one-dimensional cellular automata operating under one of the most studied rules, rule 90, which is well known to display a rich complex behavior.

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.

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.

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.

Cellular Automata Communication Models

2010 ◽  
Vol 1 (3) ◽  
pp. 66-84 ◽  
Author(s):  
Predrag T. Tošic
Keyword(s):  
Distributed Computing ◽  
Cellular Automata ◽  
Large Scale ◽  
Relevant Model ◽  
One Dimensional ◽  
Threshold Functions ◽  
Communication Models ◽  
Ca Model ◽  
Asymptotic Dynamics ◽  
Update Rules

In this paper, cellular automata (CA) are viewed as an abstract model for distributed computing. The author argues that the classical CA model must be modified in several important respects to become a relevant model for large-scale MAS. The paper first proposes sequential cellular automata (SCA) and formalizes deterministic and nondeterministic versions of SCA. The author then analyzes differences in possible dynamics between classical parallel CA and various SCA models. The analysis in this paper focuses on one-dimensional parallel and sequential CA with node update rules restricted to simple threshold functions, as arguably the simplest totalistic, yet non-linear (and non-affine) update rules. The author identifies properties of asymptotic dynamics that can be proven to be entirely due to the assumption of perfect synchrony in classical, parallel CA. Finally, the paper discusses what an appropriate CA-based abstraction would be for large-scale distributed computing, insofar as the inter-agent communication models. In that context, the author proposes genuinely asynchronous CA and discusses main differences between genuinely asynchronous CA and various weakly asynchronous sequential CA models found in the literature.

A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART XIV: MORE BERNOULLI στ-SHIFT RULES

2010 ◽  
Vol 20 (08) ◽  
pp. 2253-2425 ◽  
Author(s):  
LEON O. CHUA ◽  
GIOVANNI E. PAZIENZA
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamical Systems ◽  
Cellular Automata ◽  
Present Article ◽  
Initial State ◽  
One Dimensional ◽  
The Past ◽  
Time Patterns ◽  
The One ◽  
Science Part

Over the past eight years, we have studied one of the simplest, yet extremely interesting, dynamical systems; namely, the one-dimensional binary Cellular Automata. The most remarkable results have been presented in a series of papers which is concluded by the present article. The final stop of our odyssey is devoted to the analysis of the second half of the 30 Bernoulli στ-shift rules, which constitute the largest among the six groups in which we classified the 256 local rules. For all these 15 rules, we present the basin-tree diagrams obtained by using each bit string with L ≤ 8 as initial state, a summary of the characteristics of their ω-limit orbits, and the space-time patterns generated from the superstring. Also, in the last section we summarize the main results we obtained by means of our "nonlinear dynamics perspective".

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.

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.

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