Binary Synchronization of Complex Dynamics in Cellular Automata and its Applications in Compressed Sensing and Cryptography

2013 ◽  
pp. 81-95
Author(s):  
Radu Dogaru ◽  
Ioana Dogaru
Keyword(s):  
Cellular Automata ◽  
Compressed Sensing ◽  
Complex Dynamics

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.

scholarly journals Classification of Discrete Dynamical Systems Based on Transients

2021 ◽  
pp. 1-26
Author(s):  
Barbora Hudcová ◽  
Tomáš Mikolov
Keyword(s):  
Dynamical Systems ◽  
Cellular Automata ◽  
Complex Dynamics ◽  
Computation Time ◽  
Boolean Networks ◽  
Random Boolean Networks ◽  
Average Computation Time ◽  
Design Systems ◽  
Computational Systems

Abstract In order to develop systems capable of artificial evolution, we need to identify which systems can produce complex behavior. We present a novel classification method applicable to any class of deterministic discrete space and time dynamical systems. The method is based on classifying the asymptotic behavior of the average computation time in a given system before entering a loop. We were able to identify a critical region of behavior that corresponds to a phase transition from ordered behavior to chaos across various classes of dynamical systems. To show that our approach can be applied to many different computational systems, we demonstrate the results of classifying cellular automata, Turing machines, and random Boolean networks. Further, we use this method to classify 2D cellular automata to automatically find those with interesting, complex dynamics. We believe that our work can be used to design systems in which complex structures emerge. Also, it can be used to compare various versions of existing attempts to model open-ended evolution (Channon, 2006; Ofria & Wilke, 2004; Ray, 1991).

Using Cellular Automata to Learn About the Immune System

1998 ◽  
Vol 09 (06) ◽  
pp. 793-799 ◽  
Author(s):  
Rita Maria Zorzenon Dos Santos
Keyword(s):  
Immune System ◽  
Cellular Automata ◽  
Time Evolution ◽  
Collective Behavior ◽  
Complex Dynamics ◽  
Biological Systems ◽  
Immune Repertoire ◽  
Probabilistic Cellular Automata ◽  
Cellular Automata Model ◽  
Simple Systems

Cellular automata are very simple systems that can exhibit complex dynamics on its time evolution. Over the last decade there have been many applications of cellular automata to modeling of biological systems. Those applications have been stimulated by the study of complex systems which has brought many insights into the cooperative and global behavior of the biological systems. Along with this discussion we present two different applications of deterministic and also of probabilistic cellular automata that are used to model the dynamics involved in cooperative and collective behavior of the immune system. In the first example, we use a deterministic cellular automata to model the time evolution of the immune repertoire, as a network, according to the Jerne's theory. Using this model we could reproduce some recent experimental results about immunization and aging of the immune system. In the second example, we use a probabilistic cellular automata model to study the evolution of HIV infection and the onset of AIDS. The results are in excellent agreement with experimental data obtained from infected patients. Besides the examples above, other interesting applications, such as models for cancer and recurrent epidemics, are being considered in the present framework.

Image encryption and compression based on kronecker compressed sensing and elementary cellular automata scrambling

2016 ◽  
Vol 84 ◽  
pp. 118-133 ◽  
Author(s):  
Tinghuan Chen ◽  
Meng Zhang ◽  
Jianhui Wu ◽  
Chau Yuen ◽  
You Tong
Keyword(s):  
Cellular Automata ◽  
Compressed Sensing ◽  
Image Encryption ◽  
Elementary Cellular Automata

A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART III: PREDICTING THE UNPREDICTABLE

2004 ◽  
Vol 14 (11) ◽  
pp. 3689-3820 ◽  
Author(s):  
LEON O. CHUA ◽  
VALERY I. SBITNEV ◽  
SOOK YOON
Keyword(s):  
Nonlinear Dynamics ◽  
Cellular Automata ◽  
Difference Equations ◽  
Complex Dynamics ◽  
Rotation Group ◽  
Equivalence Classes ◽  
Nonlinear Difference Equations ◽  
Dynamic Behaviors ◽  
Local Equivalence ◽  
Science Part

We prove rigorously the four cellular automata local rules 110, 124, 137 and 193 have identical dynamic behaviors capable of universal computations. We exploit Felix Klein's remarkable Vierergruppe to partition the 256 local rules studied empirically by Wolfram into 89 global equivalence classes of which only 50 may exhibit complex dynamics. We define a 24-element rotation group which induces 30 local equivalence classes of nonlinear difference equations whose parameters can be mapped into each other among members of the same class.

scholarly journals Distributed Control of a Manufacturing System with One-Dimensional Cellular Automata

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-15
Author(s):  
Irving Barragan-Vite ◽  
Juan C. Seck-Tuoh-Mora ◽  
Norberto Hernandez-Romero ◽  
Joselito Medina-Marin ◽  
Eva S. Hernandez-Gress
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Distributed Control ◽  
Manufacturing Process ◽  
Manufacturing Systems ◽  
Manufacturing System ◽  
Complex Dynamics ◽  
Initial Conditions ◽  
Global Dynamics ◽  
One Dimensional

We present a distributed control modeling approach for an automated manufacturing system based on the dynamics of one-dimensional cellular automata. This is inspired by the fact that both cellular automata and manufacturing systems are discrete dynamical systems where local interactions given among their elements (resources) can lead to complex dynamics, despite the simple rules governing such interactions. The cellular automaton model developed in this study focuses on two states of the resources of a manufacturing system, namely, busy or idle. However, the interaction among the resources such as whether they are shared at different stages of the manufacturing process determines the global dynamics of the system. A procedure is shown to obtain the local evolution rule of the automaton based on the relationships among the resources and the material flow through the manufacturing process. The resulting distributed control of the manufacturing system appears to be heterarchical, and the evolution of the cellular automaton exhibits a Class II behavior for some given disordered initial conditions.

Complex dynamics of cellular automata rule 119

2009 ◽  
Vol 388 (6) ◽  
pp. 984-990 ◽  
Author(s):  
Fang-Fang Chen ◽  
Fang-Yue Chen
Keyword(s):  
Cellular Automata ◽  
Complex Dynamics

scholarly journals Understanding the complex dynamics of stock markets through cellular automata

2007 ◽  
Vol 75 (4) ◽  
Author(s):  
G. Qiu ◽  
D. Kandhai ◽  
P. M. A. Sloot
Keyword(s):  
Cellular Automata ◽  
Stock Markets ◽  
Complex Dynamics
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