Lifelike Self-Replicators

2010 ◽  
pp. 210-247
Author(s):  
Eleonora Bilotta ◽  
Pietro Pantano
Keyword(s):  
Cellular Automaton ◽  
Turing Machine ◽  
Digital Computer ◽  
Initial Conditions ◽  
Von Neumann ◽  
One Dimensional ◽  
Game Of Life ◽  
Universal Computation

The concept of a cellular automaton derives from John von Neumann’s studies of the logic of life. In these studies, von Neumann focused on self-replicating structures with universal computational capabilities. Given the appropriate initial conditions, a universal computer can perform any finite computation, reproducing even the most complex biological behaviors. It is well known that the ECAs described in (Wolfram, 2002) and the Game of Life (Gardner, 1970; Evans, 2003; Adachi et al., 2008) have universal computational capabilities. It has been shown, furthermore, that certain one-dimensional CAs can generate structures that are equivalent to the components of an idealized digital computer, and that, by connecting these components in different ways, it is possible to implement any kind of algorithm. In brief, these CAs are equivalent to the better known - and simpler - Turing machine and share its ability to perform universal computation (Smith 1971).

On the stability of lattice boltzmann equations for one-dimensional diffusion equation

2017 ◽  
Vol 08 (01) ◽  
pp. 1750013 ◽  
Author(s):  
Gerasim Vladimirovich Krivovichev
Keyword(s):  
Lattice Boltzmann ◽  
Initial Conditions ◽  
Kinetic Equations ◽  
Differential Approximation ◽  
Boltzmann Equations ◽  
Von Neumann ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
The Cauchy Problem ◽  
Lattice Boltzmann Equations

Stability analysis of lattice Boltzmann equations (LBEs) on initial conditions for one-dimensional diffusion is performed. Stability of the solution of the Cauchy problem for the system of linear Bhatnaghar–Gross–Krook kinetic equations is demonstrated for the cases of D1Q2 and D1Q3 lattices. Stability of the scheme for D1Q2 lattice is analytically analyzed by the method of differential approximation. Stability of parametrical scheme is numerically investigated by von Neumann method in parameter space. As a result of numerical analysis, the correction of the hypothesis on transfer of stability conditions of the scheme for macroequation to the system of LBEs is demonstrated.

scholarly journals Axiomatizing Rectangular Grids with no Extra Non-unary Relations

2020 ◽  
Vol 176 (2) ◽  
pp. 129-138
Author(s):  
Eryk Kopczyński
Keyword(s):  
Cellular Automaton ◽  
Turing Machine ◽  
Binary Relations ◽  
One Dimensional ◽  
First Order ◽  
Finite Models ◽  
Rectangular Grids ◽  
Deterministic Turing Machine

We construct a first-order formula φ such that all finite models of φ are non-narrow rectangular grids without using any binary relations other than the grid neighborship relations. As a corollary, we prove that a set A ⊆ ℕ is a spectrum of a formula which has only planar models if numbers n ∈ A can be recognized by a non-deterministic Turing machine (or a one-dimensional cellular automaton) in time t(n) and space s(n), where t(n)s(n) ≤ n and t(n); s(n) = Ω(log(n)).

Classifying elementary cellular automata using compressibility, diversity and sensitivity measures

2014 ◽  
Vol 25 (03) ◽  
pp. 1350098 ◽  
Author(s):  
Shigeru Ninagawa ◽  
Andrew Adamatzky
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Initial Conditions ◽  
Morphological Diversity ◽  
Compression Algorithm ◽  
One Dimensional ◽  
Elementary Cellular Automata ◽  
Eca Rules ◽  
Substantial Correlation ◽  
Elementary Cellular Automaton

An elementary cellular automaton (ECA) is a one-dimensional, synchronous, binary automaton, where each cell update depends on its own state and states of its two closest neighbors. We attempt to uncover correlations between the following measures of ECA behavior: compressibility, sensitivity and diversity. The compressibility of ECA configurations is calculated using the Lempel–Ziv (LZ) compression algorithm LZ78. The sensitivity of ECA rules to initial conditions and perturbations is evaluated using Derrida coefficients. The generative morphological diversity shows how many different neighborhood states are produced from a single nonquiescent cell. We found no significant correlation between sensitivity and compressibility. There is a substantial correlation between generative diversity and compressibility. Using sensitivity, compressibility and diversity, we uncover and characterize novel groupings of rules.

Universal Computation in a Simplified Brownian Cellular Automaton with von Neumann Neighborhood

2019 ◽  
Vol 165 (2) ◽  
pp. 139-156 ◽  
Author(s):  
Wen-Li Xu ◽  
Jia Lee ◽  
Hui-Hui Chen ◽  
Teijiro Isokawa
Keyword(s):  
Cellular Automaton ◽  
Von Neumann ◽  
Universal Computation

HOW TO SIMULATE TURING MACHINES BY INVERTIBLE ONE-DIMENSIONAL CELLULAR AUTOMATA

1995 ◽  
Vol 06 (04) ◽  
pp. 395-402 ◽  
Author(s):  
JEAN-CHRISTOPHE DUBACQ
Keyword(s):  
Dynamical Systems ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Turing Machine ◽  
Turing Machines ◽  
One Dimensional

The issue of testing invertibility of cellular automata has been often discussed. Constructing invertible automata is very useful for simulating invertible dynamical systems, based on local rules. The computation universality of cellular automata has long been positively resolved, and by showing that any cellular automaton could be simulated by an invertible one having a superior dimension, Toffoli proved that invertible cellular automaton of dimension d≥2 were computation-universal. Morita proved that any invertible Turing Machine could be simulated by a one-dimensional invertible cellular automaton, which proved computation-universality of invertible cellular automata. This article shows how to simulate any Turing Machine by an invertible cellular automaton with no loss of time and gives, as a corollary, an easier proof of this result.

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.

scholarly journals An Investigation into the Origin of Autopoiesis

2020 ◽  
Vol 26 (1) ◽  
pp. 5-22 ◽  
Author(s):  
Randall D. Beer
Keyword(s):  
Statistical Mechanics ◽  
Cellular Automaton ◽  
Origin Of Life ◽  
Time Evolution ◽  
Initial Conditions ◽  
Game Of Life ◽  
Random Initial Conditions ◽  
The Origin Of Life ◽  
Over Time

Using a glider in the Game of Life cellular automaton as a toy model of minimal persistent individuals, this article explores how questions regarding the origin of life might be approached from the perspective of autopoiesis. Specifically, I examine how the density of gliders evolves over time from random initial conditions and then develop a statistical mechanics of gliders that explains this time evolution in terms of the processes of glider creation, persistence, and destruction that underlie it.

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