THE HPP RULE WITH MEMORY AND THE DENSITY CLASSIFICATION TASK

2010 ◽  
Vol 21 (09) ◽  
pp. 1115-1128 ◽  
Author(s):  
RAMÓN ALONSO-SANZ
Keyword(s):  
Cellular Automata ◽  
Initial Configuration ◽  
Classification Task ◽  
Two Dimensional ◽  
With Memory ◽  
Standard Framework ◽  
In Cells

This article considers an extension to the standard framework of cellular automata by implementing memory capability in cells. It is shown that the important block HPP rule behaves as an excellent classifier of the density in the initial configuration when applied to cells endowed with pondered memory of their previous states. If the weighing is made so that the most recent state values are assigning the highest weights, the HPP rule surpasses the performance of the best two-dimensional density classifiers reported in the literature.

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.

RANDOM NUMBER GENERATION BY CELLULAR AUTOMATA WITH MEMORY

2008 ◽  
Vol 19 (02) ◽  
pp. 351-367 ◽  
Author(s):  
RAMÓN ALONSO-SANZ ◽  
LARRY BULL
Keyword(s):  
Cellular Automata ◽  
Random Number ◽  
Random Number Generation ◽  
Random Number Generators ◽  
Potential Value ◽  
Number Generation ◽  
Elementary Cellular Automata ◽  
With Memory ◽  
Standard Framework

This paper considers an extension to the standard framework of cellular automata which implements memory capabilities by featuring cells by elementary rules of its last three states. A study is made of the potential value of elementary cellular automata with elementary memory rules as random number generators.

Response Curves for Cellular Automata in One and Two Dimensions

2010 ◽  
Vol 1 (3) ◽  
pp. 85-99 ◽  
Author(s):  
Henryk Fuks ◽  
Andrew Skelton
Keyword(s):  
Cellular Automata ◽  
Response Curve ◽  
Initial Density ◽  
Two Dimensions ◽  
Initial Configuration ◽  
Two Dimensional ◽  
Response Curves ◽  
Special Case

In this paper, the authors consider the problem of computing a response curve for binary cellular automata, that is, the curve describing the dependence of the density of ones after many iterations of the rule on the initial density of ones. The authors demonstrate how this problem could be approached using rule 130 as an example. For this rule, preimage sets of finite strings exhibit recognizable patterns; therefore, it is possible to compute both cardinalities of preimages of certain finite strings and probabilities of occurrence of these strings in a configuration obtained by iterating a random initial configuration n times. Response curves can be rigorously calculated in both one- and two-dimensional versions of CA rule 130. The authors also discuss a special case of totally disordered initial configurations, that is, random configurations where the density of ones and zeros are equal to 1/2.

Evolution of cellular automata with memory: The Density Classification Task

Biosystems ◽  
2009 ◽  
Vol 97 (2) ◽  
pp. 108-116 ◽  
Author(s):  
Christopher Stone ◽  
Larry Bull
Keyword(s):  
Cellular Automata ◽  
Classification Task ◽  
With 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.

Response Curves for Cellular Automata in One and Two Dimensions

2012 ◽  
pp. 291-305
Author(s):  
Henryk Fuks ◽  
Andrew Skelton
Keyword(s):  
Cellular Automata ◽  
Response Curve ◽  
Initial Density ◽  
Two Dimensions ◽  
Initial Configuration ◽  
Two Dimensional ◽  
Response Curves ◽  
Special Case

In this paper, the authors consider the problem of computing a response curve for binary cellular automata, that is, the curve describing the dependence of the density of ones after many iterations of the rule on the initial density of ones. The authors demonstrate how this problem could be approached using rule 130 as an example. For this rule, preimage sets of finite strings exhibit recognizable patterns; therefore, it is possible to compute both cardinalities of preimages of certain finite strings and probabilities of occurrence of these strings in a configuration obtained by iterating a random initial configuration n times. Response curves can be rigorously calculated in both one- and two-dimensional versions of CA rule 130. The authors also discuss a special case of totally disordered initial configurations, that is, random configurations where the density of ones and zeros are equal to 1/2.

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