Phase Transition in Elementary Cellular Automata with Memory

2014 ◽  
Vol 24 (09) ◽  
pp. 1450116 ◽  
Author(s):  
Shigeru Ninagawa ◽  
Andrew Adamatzky ◽  
Ramón Alonso-Sanz
Keyword(s):  
Cellular Automata ◽  
State Transition ◽  
Time Interval ◽  
Complex Behavior ◽  
Weighted Function ◽  
Transition Functions ◽  
Elementary Cellular Automata ◽  
Computational Universality ◽  
With Memory ◽  
Time Automaton

We study elementary cellular automata with memory. The memory is a weighted function averaged over cell states in a time interval, with a varying factor which determines how strongly a cell's previous states contribute to the cell's present state. We classify selected cell-state transition functions based on Lempel–Ziv compressibility of space-time automaton configurations generated by these functions and the spectral analysis of their transitory behavior. We focus on rules 18, 22, and 54 because they exhibit the most intriguing behavior, including computational universality. We show that a complex behavior is observed near the nonmonotonous transition to null behavior (rules 18 and 54) or during the monotonic transition from chaotic to periodic behavior (rule 22).

scholarly journals DESIGNING COMPLEX DYNAMICS IN CELLULAR AUTOMATA WITH MEMORY

2013 ◽  
Vol 23 (10) ◽  
pp. 1330035 ◽  
Author(s):  
GENARO J. MARTÍNEZ ◽  
ANDREW ADAMATZKY ◽  
RAMON ALONSO-SANZ
Keyword(s):  
Cellular Automata ◽  
State Transition ◽  
Complex Dynamics ◽  
Transition Function ◽  
Systematic Analysis ◽  
Time Dynamics ◽  
Controversial Topic ◽  
State Transition Function ◽  
And Behavior ◽  
With Memory

Since their inception at Macy conferences in later 1940s, complex systems have remained the most controversial topic of interdisciplinary sciences. The term "complex system" is the most vague and liberally used scientific term. Using elementary cellular automata (ECA), and exploiting the CA classification, we demonstrate elusiveness of "complexity" by shifting space-time dynamics of the automata from simple to complex by enriching cells with memory. This way, we can transform any ECA class to another ECA class — without changing skeleton of cell-state transition function — and vice versa by just selecting a right kind of memory. A systematic analysis displays that memory helps "discover" hidden information and behavior on trivial — uniform, periodic, and nontrivial — chaotic, complex — dynamical systems.

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.

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.

Invertible behavior in elementary cellular automata with memory

2012 ◽  
Vol 199 ◽  
pp. 125-132 ◽  
Author(s):  
Juan C. Seck-Tuoh-Mora ◽  
Genaro J. Martínez ◽  
Ramon Alonso-Sanz ◽  
Norberto Hernández-Romero
Keyword(s):  
Cellular Automata ◽  
Elementary Cellular Automata ◽  
With Memory

The Fixed String of Elementary Cellular Automata

2010 ◽  
Vol 19 (3) ◽  
pp. 243-262
Author(s):  
Jiang Zhisong ◽  
◽  
Qin Dakang ◽  
Keyword(s):  
Cellular Automata ◽  
Elementary Cellular Automata
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