A Cellular Automaton Model of Excitable Media Including Curvature and Dispersion

Gerhardt, Martin; Schuster, Heike; Tyson, John J.

doi:10.1126/science.2321017

Cited by 264 publications

(104 citation statements)

References 21 publications

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“…The term 'cellular automaton' is often used to describe the spatio-temporal evolution of chemical or biological systems that are capable of switching sequentially between several discrete states [29,30]. In regard to cell proliferation and morphogenesis, cellular automata have been used to model tumour growth [31,32] and pattern formation [33].…”

Section: Discussionmentioning

confidence: 99%

An automaton model for the cell cycle

et al. 2010

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We consider an automaton model that progresses spontaneously through the four successive phases of the cell cycle: G1, S (DNA replication), G2 and M (mitosis). Each phase is characterized by a mean duration t and a variability V. As soon as the prescribed duration of a given phase has passed, the transition to the next phase of the cell cycle occurs. The time at which the transition takes place varies in a random manner according to a distribution of durations of the cell cycle phases. Upon completion of the M phase, the cell divides into two cells, which immediately enter a new cycle in G1. The duration of each phase is reinitialized for the two newborn cells. At each time step in any phase of the cycle, the cell has a certain probability to be marked for exiting the cycle and dying at the nearest G1/S or G2/M transition. To allow for homeostasis, which corresponds to maintenance of the total cell number, we assume that cell death counterbalances cell replication at mitosis. In studying the dynamics of this automaton model, we examine the effect of factors such as the mean durations of the cell cycle phases and their variability, the type of distribution of the durations, the number of cells, the regulation of the cell population size and the independence of steady-state proportions of cells in each phase with respect to initial conditions. We apply the stochastic automaton model for the cell cycle to the progressive desynchronization of cell populations and to their entrainment by the circadian clock. A simple deterministic model leads to the same steady-state proportions of cells in the four phases of the cell cycle.

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Section: Discussionmentioning

confidence: 99%

An automaton model for the cell cycle

et al. 2010

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“…These latticegas automata are probabilistic cellular automata that employ a particle description of the dynamics and should be distinguished from other cellular automata that are designed to simulate reaction-diffusion equation dynamics. [13][14][15] While most of the phenomena of interest occur on sufficiently long space and time scales that a continuum description using reaction-diffusion equations is appropriate, the cellular automaton models have the advantage that they naturally incorporate fluctuations that are responsible for the nucleation events that play a role in the process and, as well, can be extended to smaller scales where continuum models are no longer appropriate. Cellular automaton models allow one to describe the system at a mesoscopic level which incorporates the essential mechanistic features of the reaction dynamics.…”

Section: Introductionmentioning

confidence: 99%

Surface structure and catalytic CO oxidation oscillations

Danielak

Perera²,

Moreau³

et al. 1996

Physica A: Statistical Mechanics and its Applications

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A cellular automaton model is used to describe the dynamics of the catalytic oxidation of CO on a P t(100) surface. The cellular automaton rules account for the structural phase transformations of the P t substrate, the reaction kinetics of the adsorbed phase and diffusion of adsorbed species. The model is used to explore the spatial structure that underlies the global oscillations observed in some parameter regimes. The spatiotemporal dynamics varies significantly within the oscillatory regime and depends on the harmonic or relaxational character of the global oscillations. Diffusion of adsorbed CO plays an important role in the synchronization of the patterns on the substrate and this effect is also studied.

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“…Among the more recent research, the study of excitable media is one domain that attracted wide attention, where CA models have been found useful for approximating real life behavior. Gerhardt et al [9] designed a CA model that adheres to the curvature and dispersion properties found experimentally in excitable media [25]. A detailed survey on CA up to this date is presented by Ganguly et al [6].…”

Section: Definition and A Brief History Of Camentioning

confidence: 99%

GPGPU computation and visualization of three-dimensional cellular automata

Gobron

Çöltekin

Bonafos³

et al. 2010

Vis Comput

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This paper presents a general-purpose simulation approach integrating a set of technological developments and algorithmic methods in cellular automata (CA) domain. The approach provides a general-purpose comput-ing on graphics processor units (GPGPU) implementation for computing and multiple rendering of any direct-neighbor three-dimensional (3D) CA. The major contributions of this paper are: the CA processing and the visualization of large 3D matrices computed in real time; the proposal of an original method to encode and transmit large CA functions to the graphics processor units in real time; and clarification of the notion of top-down and bottom-up approaches to CA that non-CA experts often confuse. Additionally a practical technique to simplify the finding of CA functions is implemented using a 3D symmetric configuration on an interac-tive user interface with simultaneous inside and surface visualizations. The interactive user interface allows for testing the system with different project ideas and serves as a test bed for performance evaluation. To illustrate the flexibility of the proposed method, visual outputs from diverse areas are demonstrated. Computational performance data are also provided to demonstrate the method's efficiency. Results indicate that when large matrices are processed, computations using GPU are two to three hundred times faster than the identical algorithms using CPU. Abstract This paper presents a general-purpose simulation approach integrating a set of technological developments and algorithmic methods in cellular automata (CA) domain. The approach provides a general-purpose computing on graphics processor units (GPGPU) implementation for computing and multi-rendering of any direct-neighbor three dimensional (3D) CA. The major contributions of this paper are; the CA processing and the visualization of large 3D matrices computed in real-time; the proposal of an original method to encode and transmit large CA functions to the graphics processor units in real time; and clarification of the notion of top-down and bottom-up approaches to CA that non-CA experts often confuse. Additionally a practical technique to simplify the finding of CA functions is implemented using a 3D symmetric configuration on an interactive user interface with simultaneous inside and surface visualizations. The interactive user interface allows for testing the system with different project ideas and serves as a test bed for performance evaluation. To illustrate the flexibility of the proposed method, visual outputs from diverse areas are demonstrated. Computational performance data are also provided to demonstrate the method's efficiency. Results indicate that when large matrices are processed, computations using GPU are two to three hundred times faster than the identical algorithms using CPU.

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A Cellular Automaton Model of Excitable Media Including Curvature and Dispersion

Cited by 264 publications

References 21 publications

An automaton model for the cell cycle

An automaton model for the cell cycle

Surface structure and catalytic CO oxidation oscillations

GPGPU computation and visualization of three-dimensional cellular automata

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