Cellular Automaton State Transition Diagrams

2007 ◽  
Keyword(s):  
Cellular Automaton ◽  
State Transition ◽  
Automaton State

scholarly journals Characterization of the Evolution of Nonlinear Uniform Cellular Automata in the Light of Deviant States

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Pabitra Pal Choudhury ◽  
Sudhakar Sahoo ◽  
Mithun Chakraborty
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Boolean Functions ◽  
State Transition ◽  
The State ◽  
Transition Diagram ◽  
One Dimensional ◽  
State Transition Diagram ◽  
Linear Rule

Dynamics of a nonlinear cellular automaton (CA) is, in general asymmetric, irregular, and unpredictable as opposed to that of a linear CA, which is highly systematic and tractable, primarily due to the presence of a matrix handle. In this paper, we present a novel technique of studying the properties of the State Transition Diagram of a nonlinear uniform one-dimensional cellular automaton in terms of its deviation from a suggested linear model. We have considered mainly elementary cellular automata with neighborhood of size three, and, in order to facilitate our analysis, we have classified the Boolean functions of three variables on the basis of number and position(s) of bit mismatch with linear rules. The concept of deviant and nondeviant states is introduced, and hence an algorithm is proposed for deducing the State Transition Diagram of a nonlinear CA rule from that of its nearest linear rule. A parameter called the proportion of deviant states is introduced, and its dependence on the length of the CA is studied for a particular class of nonlinear rules.

Simulating Self-Reproduction of Cells in a Two-Dimensional Cellular Automaton

2010 ◽  
Vol 22 (5) ◽  
pp. 669-676 ◽  
Author(s):  
Takeshi Ishida ◽  
Keyword(s):  
Synthetic Biology ◽  
Cellular Automaton ◽  
State Transition ◽  
Cellular Automaton Model ◽  
Molecular Machine ◽  
Two Dimensional ◽  
Transition Rules ◽  
State Transition Rules

Clarifying generalized self-reproduction is basic to applications in fields such as molecular machine production in nanotechnology and synthetic biology. The two-dimensional cellular automaton model we developed simulated cellular self-reproduction using a few state transition rules.

scholarly journals A Cellular Automaton Model for Pedestrians’ Movements Influenced by Gaseous Hazardous Material Spreading

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
J. Makmul
Keyword(s):  
Cellular Automaton ◽  
Numerical Experiments ◽  
Eikonal Equation ◽  
Arrival Time ◽  
Source Term ◽  
State Transition ◽  
Hazardous Material ◽  
Advection Diffusion ◽  
Moore Neighborhood ◽  
Ca Model

A cellular automaton (CA) model is proposed to simulate the egress of pedestrians while gaseous hazardous material is spreading. The advection-diffusion with source term is used to describe the propagation of gaseous hazardous material. It is incorporated into the CA model. The navigation field in our model is determined by the solution of the Eikonal equation. The state transition of a pedestrian relies on the arrival time of cells in the Moore neighborhood. Numerical experiments are investigated in a room with multiple exits, and their results are shown.

Fungal Automata

2020 ◽  
Vol 29 (4) ◽  
pp. 759-778
Author(s):  
Andrew Adamatzky ◽  
◽  
Eric Goles ◽  
Genaro J. Martínez ◽  
Michail-Antisthenis Tsompanas ◽  
...  
Keyword(s):  
Cellular Automaton ◽  
State Transition ◽  
Fungal Mycelium ◽  
Information Dynamics ◽  
Binary State ◽  
Eca Rules ◽  
Previous State ◽  
Single Hypha ◽  
Elementary Cellular Automaton ◽  
The One

We study a cellular automaton (CA) model of information dynamics on a single hypha of a fungal mycelium. Such a filament is divided in compartments (here also called cells) by septa. These septa are invaginations of the cell wall and their pores allow for the flow of cytoplasm between compartments and hyphae. The septal pores of the fungal phylum of the Ascomycota can be closed by organelles called Woronin bodies. Septal closure is increased when the septa become older and when exposed to stress conditions. Thus, Woronin bodies act as informational flow valves. The one-dimensional fungal automaton is a binary-state ternary neighborhood CA, where every compartment follows one of the elementary cellular automaton (ECA) rules if its pores are open and either remains in state 0 (first species of fungal automata) or its previous state (second species of fungal automata) if its pores are closed. The Woronin bodies closing the pores are also governed by ECA rules. We analyze a structure of the composition space of cell-state transition and pore-state transition rules and the complexity of fungal automata with just a few Woronin bodies, and exemplify several important local events in the automaton dynamics.

An Implementation of von Neumann's Self-Reproducing Machine

1995 ◽  
Vol 2 (4) ◽  
pp. 337-354 ◽  
Author(s):  
Umberto Pesavento
Keyword(s):  
Cellular Automaton ◽  
State Transition ◽  
The State ◽  
Transition Rule ◽  
John Von Neumann ◽  
Von Neumann ◽  
Special Case

This article describes in detail an implementation of John von Neumann's self-reproducing machine. Self-reproduction is achieved as a special case of construction by a universal constructor. The theoretical proof of the existence of such machines was given by John von Neumann in the early 1950s [6], but was first implemented in 1994, by the author in collaboration with R. Nobili. Our implementation relies on an extension of the state-transition rule of von Neumann's original cellular automaton. This extension was introduced to simplify the design of the constructor. The main operations in our constructor can be mapped into operations of von Neumann's machine.

Bittorio revisited: structural coupling in the Game of Life

2019 ◽  
Vol 28 (4) ◽  
pp. 197-212 ◽  
Author(s):  
Randall D Beer
Keyword(s):  
Cellular Automaton ◽  
State Transition ◽  
The State ◽  
Theoretical Frameworks ◽  
Transition Graph ◽  
Structural Coupling ◽  
Game Of Life ◽  
Interaction Graphs ◽  
State Transition Graph ◽  
Autopoietic System

The notion of structural coupling plays a central role in Maturana and Varela’s biology of cognition framework and strongly influenced Varela’s subsequent enactive elaboration of this framework. Building upon previous work using a glider in the Game of Life (GoL) cellular automaton as a toy model of a minimal autopoietic system with which to concretely explore these theoretical frameworks, this article presents an analysis of structural coupling between a glider and its environment. Specifically, for sufficiently small GoL universes, we completely characterize the nonautonomous dynamics of both a glider and its environment in terms of interaction graphs, derive the set of possible glider lives determined by the mutual constraints between these interaction graphs, and show how such lives are embedded in the state transition graph of the entire GoL universe.

PHENOMENOLOGY OF RETAINED EXCITATION

2007 ◽  
Vol 17 (11) ◽  
pp. 3985-4014 ◽  
Author(s):  
ANDREW ADAMATZKY
Keyword(s):  
Cellular Automaton ◽  
Resting State ◽  
State Transition ◽  
Space Time ◽  
Two Dimensional ◽  
Time Activity ◽  
Cell State ◽  
Resting Cell ◽  
Refractory State ◽  
Activity Dynamics

In a two-dimensional cellular automaton model of retained excitation every excited cell stays excited if the number of excited neighbors belong to some interval, the cell takes refractory state otherwise. Every resting cell is excited if the number of excited cells in its neighborhood belong to some other interval; cell-state transition from refractory to resting state is unconditional. We classify 1296 rules of retained excitation based on how dynamics of excitable lattices develop after initial stimulation. Several modes of space-time activity dynamics are discovered: not growing but persistent domains of activity, domains with rectangular, octagonal and almost circular growth, amoeba-like growing patterns, mobile and still localizations.

A Probabilistic Cellular Automaton for Evolution

1995 ◽  
Vol 5 (9) ◽  
pp. 1129-1134 ◽  
Author(s):  
Nikolaus Rajewsky ◽  
Michael Schreckenberg
Keyword(s):  
Cellular Automaton ◽  
Probabilistic Cellular Automaton

Autómatas Celulares Aplicados al Comportamiento de Células de Cáncer Cervicouterino

2019 ◽  
Vol 6 (1) ◽  
pp. 44-49
Author(s):  
Tania Muñoz Jiménez ◽  
Aurora Torres Soto ◽  
María Dolores Torres Soto
Keyword(s):  
Cellular Automaton ◽  
Medical Model ◽  
Research Process ◽  
Simulation Algorithm ◽  
Stages Of Development ◽  
Literary Research ◽  
Migration Dynamics ◽  
Three Stages ◽  
And Migration ◽  
Best Parameters

En este documento se describe el desarrollo e implementación de un modelo para simular computacionalmente la dinámica del crecimiento y migración del cáncer cervicouterino, considerando sus principales características: proliferación, migración y necrosis, así como sus etapas de desarrollo. El modelo se desarrolló mediante un autómata celular con enfoques paralelo y secuencial. El autómata celular se basó en el modelo de Gompertz para simular las etapas de desarrollo de este cáncer, el cual se dividió en tres etapas cada una con diferentes comportamientos durante la simulación. Se realizó un diseño experimental con parámetros de entrada que se seleccionaron a partir de la investigación literaria y su discusión con médicos expertos. Al final del proceso de investigación, se logró obtener un algoritmo computacional de simulación muy bueno comparado con el modelo médico de Gompertz y se encontraron los mejores parámetros para su ejecución mediante un diseño factorial soportado estadísticamente. This paper describes the development and implementation of a model to computationally simulate the growth and migration dynamics of cervical cancer, considering its main characteristics: proliferation, migration and necrosis, as well as its stages of development. The model was developed by means of a cellular automaton with parallel and sequential approaches. The cellular automaton was based on the model of Gompertz to simulate the stages of development of this cancer, which was divided into three stages, each with different behaviors during the simulation. An experimental design was carried out with input parameters that were selected from literary research and its discussion with expert physicians. At the end of the research process, a very good simulation algorithm was obtained compared to the Gompertz medical model and the best parameters for its execution were found by means of a statistically supported factorial design.

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