Revisão Bibliográfica: Autômatos Celulares


Title: A New Self-Reproducing Cellular Automaton



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Title: A New Self-Reproducing Cellular Automaton


Author: Gianluca Tempesti (1995)

Abstract: We present a new self-reproducing cellular automaton capable of construction and computation beyond self-reproduction. Our automaton makes use of some of the concepts developed by Langton for his self-reproducing automaton, but provides the added advantage of being able to perform independent constructional and computational tasks alongside self-reproduction. Our automaton is capable, like Langton's automaton and with comparable complexity, of simple self-replication, but it also provides (at the cost, naturally, of increased complexity) the option of attaching to the automaton an executable program which will be duplicated and executed in each of the copies of the automaton.


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Studying Artificial Life Using a Simple, General Cellular Model - Sipper (1995)  
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Cellular Automata and Artificial Life - Computation and Life in.. - Morita (1998)  
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An introduction to Cellular Automata - Delorme (1998)  
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Discovery of Self-Replicating Structures Using A Genetic.. - Lohn, Reggia (1995)  
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Spatial analysis of vector-borne disease: a four-species model - Boleslaw Szymanski Tom (1994)  
Self-Reproduction in a Reversible Cellular Space - Kenichi Morita (1996)  
Special Purpose Parallel Computing - McColl (1993)  
Co-evolving Non-Uniform Cellular Automata to Perform Computations - Sipper (1996)  
An Implementation of von Neumann's Self-Reproducing Machine - Pesavento (1996)  
A Survey of Artificial Life and Evolutionary Robotics - Walker, Oliver (1997)  
Logical Universality and Self-Reproduction in Reversible.. - Kenichi Morita

Voltar

2) Utilização na Computação

Exemplo de construção de um autômato celular


Os autômatos celulares são muito úteis para resolver alguns problemas de forma distribuída. Por exemplo, uma maneira muito simples de desenhar o triângulo de Sierpinski é simplesmente construir um autômato celular 1D em que cada célula segue a seguinte regra de transição: ou exclusivo dos estados das células vizinhas. Cada linha horizontal do triângulo de Sierpinski é um momento durante a evolução do autômato celular.


FIGURA - Vista de uma região do Triângulo de Sierpinski. Cada parte do triângulo revela estrutura semelhante ao seu todo.


Outra maneira de gerar o triângulo de Sierpinski é simplesmente construir um autômato celular em que cada célula é programada da seguinte forma: o próximo estado de cada célula será o resto da divisão por 2 da soma dos estados das células vizinhas.
Implementação de autômatos celulares 1D e 2D
Temos aqui autômatos celulares 1D e 2D implementados em Turbo Pascal V. 5.5 baseados no resto da divisão por números naturais inferiores a 255.

Para efeito de notação, c[x,y] é o autômato de índices x e y pertencente a um autômato celular 3D. Ainda para efeito de notação, o operador mod é o operador de resto da divisão. Na tabela seguinte, podemos ver as fórmulas usadas para implementação dos autômatos.




Nome

N. Dimensões

C[x,y]=

DANTE1.PAS

2

C[x-1] xor C[x+1]

DANTE2.PAS

2

(C[x-1] + C[x+1]) mod 10

DANTE3.PAS

3

(C[x-1,y] + C[x+1,y] + C[x,y-1] + C[x,y+1] ) mod 119

DANTE4.PAS

3

(C[x-1,y] + C[x+1,y] + C[x,y-1] + C[x,y+1] +C[x-1,y-1] + C[x+1,y-1] + C[x+1,y-1] + C[x+1,y+1] ) mod 4

DANTE5.PAS

3

(C[x-1,y] + C[x+1,y] + C[x,y-1] + C[x,y+1] +C[x-1,y-1] + C[x+1,y-1] + C[x+1,y-1] + C[x+1,y+1] ) mod 2

DANTE7.PAS

3

(C[x-1,y] + C[x+1,y] + C[x,y-1] + C[x,y+1] ) mod 200

DANTE8.PAS

3

(C[x-1,y] + C[x+1,y] + C[x,y-1] + C[x,y+1] ) mod 100

DANTE9.PAS

3

(C[x-1,y] + C[x+1,y] + C[x,y-1] + C[x,y+1] ) mod 20

DANTE10.PAS

3

(C[x-1,y] +C[x+1,y]+C[x,y-1]+C[x,y+1]+C[x-1,y-1]*2 +C[x+1,y-1]*2+C[x+1,y-1]*2+C[x+1,y+1]*2) mod 2

As fórmulas de geração dos programas DANTE2.PAS e DANTE3.PAS são semelhantes às fórmulas encontradas no livro Chaos and Fractals[PEIT] .


Implementação de Autômato 2D
type TVIDEO = array[0..199,0..319] of byte;

procedure Automato2D(var R:TVIDEO); // DANTE4.PAS

var I,J:integer;

D:TVIDEO;

begin

D:=R;


for I:=1 to 318 do

for J:=1 to 198 do

D[J,I]:=(R[J,I-1] + R[J,I+1] +

R[J-1,I] + R[J+1,I] +

R[J-1,I-1] + R[J+1,I+1] +

R[J-1,I+1] + R[J+1,I-1]

) mod 4;

R:=D;


end;

Dante1.pas Dante2.pas



Dante3.pas Dante4.pas



Dante7.pas Dante7.pas



Voltar
2.1) Computação em Geral
Fonte: www.ifs.tuwien.ac.at/~aschatt/info/ca/ca.html


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