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Discrete Dynamics in Nature and Society
Volume 2015, Article ID 542507, 8 pages
http://dx.doi.org/10.1155/2015/542507
Research Article

Simulation of a Vibrant Membrane Using a 2-Dimensional Cellular Automaton

1Modeling and Simulation Laboratory, Centro de Investigación en Computación, Instituto Politécnico Nacional, Avenida Juan de Dios Bátiz, Esquina Miguel Othón de Mendizábal, Colonia Nueva Industrial Vallejo, 07738 Gustavo A. Madero, DF, Mexico
2Postgraduate and Research Section, Escuela Superior de Cómputo, Instituto Politécnico Nacional, Avenida Juan de Dios Bátiz, Esquina Miguel Othón de Mendizábal, Colonia Lindavista, 07738 Gustavo A. Madero, DF, Mexico
3Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas Norte 152, 07730 Gustavo A. Madero, DF, Mexico

Received 21 April 2015; Revised 4 June 2015; Accepted 8 June 2015

Academic Editor: Tetsuji Tokihiro

Copyright © 2015 I. Huerta-Trujillo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper proposes a 2-dimensional cellular automaton (CA) model and how to derive the model evolution rule to simulate a two-dimensional vibrant membrane. The resulting model is compared with the analytical solution of a two-dimensional hyperbolic partial differential equation (PDE), linear and homogeneous. This models a vibrant membrane with specific conditions, initial and boundary. The frequency spectrum is analysed as well as the error between the data produced by the CA model. Then it is compared to the data provided by the solution evaluation to the differential equation. This shows how the CA obtains a behavior similar to the PDE. Moreover, it is possible to simulate nonclassical initial conditions for which there is no exact solution using PDE. Very interesting information could be obtained from the CA model such as the fundamental frequency.