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A simulation of cellular automata on hexagons by cellular automata on rings

Bruno Martin
2001 Theoretical Computer Science  
We prove that cellular automata deÿned over a hexagonal grid can be simulated by cellular automata over a ring.  ...  We consider cellular automata on Cayley graphs and compare their computational power according to their topology.  ...  We extend RÃ oka's simulations results [7, 9] ; we prove that cellular automata deÿned over a hexagonal grid can be simulated by cellular automata over a ring.  ... 
doi:10.1016/s0304-3975(00)00244-9 fatcat:j5c5td5tvngnjfakqnkmepagza

Page 4403 of Mathematical Reviews Vol. , Issue 2002F [page]

2002 Mathematical Reviews  
{For the entire collection see MR 2002d:68011.} 2002f:68121 68Q80 Martin, Bruno (F-NICE-I3S; Sophia Antipolis) A simulation of cellular automata on hexagons by cellular automata on rings.  ...  We prove that cellular automata defined over a hexagonal grid can be simulated by cellular automata over a ring.” 2002f:68122 68Q85 68N25 Barbosa, Valmir C.  ... 

A single-copy minimal-time simulation of a torus of automata by a ring of automata

Bruno Martin, Claudine Peyrat
2007 Discrete Applied Mathematics  
We consider cellular automata on Cayley graphs and we simulate the behavior of a torus of n × m automata (nodes) by a ring of n · m automata (cells).  ...  We prove that it is possible to simulate the behavior of a torus on a ring with a single copy on each cell if and only if n and m satisfy a given condition.  ...  In addition, this simulation together with a result from Róka [16] , permits to prove in a straightforward way that cellular automata defined over a hexagonal grid can be simulated by cellular automata  ... 
doi:10.1016/j.dam.2007.05.019 fatcat:haj2uqepofeodld6j332zf2fb4

Systolic Dissemination in the Arrowhead Family [chapter]

Dominique Désérable
2014 Lecture Notes in Computer Science  
Although cellular automata (CA) are usually driven by a local rule, global communications are often needed either to synchronize a process or to share common data.  ...  Two types of dissemination are presented: a (one-to-all) broadcasting and a (all-to-all) gossiping.  ...  So far, the hexagonal arrowhead underlies a lattice-grain automata network [18] [19] [20] 3] whereas the orthogonal diamond, named "T n " therein, is the subject of several works on cellular multiagent  ... 
doi:10.1007/978-3-319-11520-7_9 fatcat:3pzengjwxbgm7mgp2p3ej6jak4

MODELING OF LIQUID VORTICITY USING CELLULAR AUTOMATON

E. A. Nastenko, A. V. Radahuz
2017 Electronics and Control Systems  
Examples of some signals of electrocardiograms simulated by a two-dimensional cut are given. Also, an evaluation of the performance of a three-dimensional model on a four-member cluster.  ...  A method has been developed for constructing large-scale electrophysiological models using extended cellular automata and for running such models on a cluster of shared memory systems.  ...  , whose solution is based on the use of cellular automata.  ... 
doi:10.18372/1990-5548.54.12337 fatcat:5jhsyh7mnreihns6otrfhf26yq

Cellular automata with almost periodic initial conditions

A Hof, O Knill
1995 Nonlinearity  
We illusmate that in one dimension by rule 18 and in W O dimensions by the Game of Life. The ides, also apply to cellular automata acting on (0, . . ., Nl)zd.  ...  Cellular automata are dynamical system on the compact metric space of subshifls. They leave many classes of sukhifts invariant.  ...  Acknowledgments The work of AH is partially supported by NSERC. AH also would like to thank B Simon for his kind hospitality at Caltech, where this work was completed.  ... 
doi:10.1088/0951-7715/8/4/002 fatcat:6fxidbkujzh6pfmeqhjwmgr4ly

A New Cellular Automata Model Of Cardiac Action Potential Propagation Based On Summation Of Excited Neighbors

F. Pourhasanzade, S. H. Sabzpoushan
2010 Zenodo  
A Cellular Automata is a type of model that can be used to model cardiac action potential propagation.  ...  One of the advantages of this approach against the methods based on differential equations is its high speed in large scale simulations.  ...  In this paper, we presented a new cellular automata model for simulating the propagation of ventricular action potential.  ... 
doi:10.5281/zenodo.1081643 fatcat:uxzzeuwwbzf65alp3loziys2ua

Involving Action Potential Morphology On A New Cellular Automata Model Of Cardiac Action Potential Propagation

F. Pourhasanzade, S. H. Sabzpoushan
2010 Zenodo  
This paper presents a 2-D Cellular Automata model for simulating action potential propagation in cardiac tissue. We demonstrate a novel algorithm in order to use minimum neighbors.  ...  We also preserve the real shape of action potential by using linear curve fitting of one well known electrophysiological model.  ...  The aim of this study is to design a computer model of action potential propagation based on cellular automata theory that simulates complex electrophysiological phenomena and does not require a sophisticated  ... 
doi:10.5281/zenodo.1077484 fatcat:aitbzexdufeihl27cua4ntlh4a

Equilibrium Properties of the Cellular Automata Models for Traffic Flow in a Single Lane [chapter]

Alejandro Salcido
2011 Cellular Automata - Simplicity Behind Complexity  
Acknowledgements We acknowledge the disinterested help and invaluable contributions we received from A. Fierros Palacios (Director, IIE-DEA, Mexico), R. Merino (TECALCO, Mexico), and A. T.  ...  Celada Murillo (IIE-DEA, Mexico) through their encouragements, comments, and enlightening discussions during the preparation of this work.  ...  Frisch, Hasslacher and Pomeau demonstrated that it is possible to simulate the Navier-Stokes fluid flows by using a cellular automata gas model on a hexagonal lattice, with extremely simple translation  ... 
doi:10.5772/15371 fatcat:fniqps6zw5cujooj7acfwivozq

Subdivided Cellular Automata Model Considering Anticipation Floor Field and Analysis of Pedestrian Detour Behavior

Jinrui Liu, Maosheng Li, Panpan Shu
2021 Sustainability  
The micro-pedestrian simulation model represented by the cellular automata model is an important simulation model.  ...  Pedestrian heterogeneity and the influence of predicted field potential energy on the simulated pedestrian trajectory.  ...  Acknowledgments: The authors send their appreciation to the Central South University Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/su131910621 fatcat:fwytau55l5ff7cp4vopxwuxdre

Overview of the KSLA efforts in parallel computing [chapter]

G. A. Zee
1989 Lecture Notes in Computer Science  
The main approach we have taken to achieve this is to develop libraries of parallel routines which can be called from programs in a sequential programming language like Pascal or FORTRAN, running on a  ...  These machines offer supercomputing capabilities at such a favourable cost that we have started research to use them in a dedicated way for applications such as on-line plant optimisation, interactive  ...  Stimulated by the opportunities offered by parallel computing, a completely new approach to fluid flow simulation has come up under the name of cellular automata.  ... 
doi:10.1007/3-540-51604-2_2 fatcat:npjjzxha75abdaglyo3jyaury4

Application of cellular automata modeling to seismic elastodynamics

Michael J. Leamy
2008 International Journal of Solids and Structures  
This article details application of a physics-based cellular automata (CA) computational approach to model seismic events in an idealized linear-elastic medium.  ...  Results are provided for an example ground-shock simulation in which a differentiated Gaussian pulse acts on the surface of a linear-elastic half-space.  ...  ., also of DTRA, for supporting the intellectual development of the ideas presented, for supplying its motivation, and for serving as a source of counsel.  ... 
doi:10.1016/j.ijsolstr.2008.04.021 fatcat:zpqjjuo3rzc4jarf4xyy7mtk2e

Hybrid models of tumor growth

Katarzyna A. Rejniak, Alexander R. A. Anderson
2010 Wiley Interdisciplinary Reviews: Systems Biology and Medicine  
Cancer is a complex, multiscale process, in which genetic mutations occurring at a subcellular level manifest themselves as functional changes at the cellular and tissue scale.  ...  Hybrid models form part of a larger class of individual-based-models that can naturally connect with tumor cell biology and allow for the integration of multiple interacting variables both intrinsically  ...  Acknowledgments Both authors were partially supported by the National Cancer Institute Integrative Cancer Biology Program (U54 CA143970) and by NCI Physical Sciences-Oncology Centers Program (U54 CA143970  ... 
doi:10.1002/wsbm.102 pmid:21064037 pmcid:PMC3057876 fatcat:uxwc6tvvsvd77ewewaolfqs64i

Application of Semitotalistic 2D Cellular Automata on a Triangulated 3D Surface

M. Zawidzki
2011 International Journal of Design & Nature and Ecodynamics  
Cellular automata (CA) can be applied in controlling the state of a freeform building envelope.  ...  This paper presents the application of semi-totalistic, also called outer totalistic cellular automata on any three-dimensional (3D) surface.  ...  The 3D triangulated model was imported from the MeshLab, a tool developed with the support of the 3D-CoForm project http://meshlab.sourceforge.net/.  ... 
doi:10.2495/dne-v6-n1-34-51 fatcat:tlksnezuefgvzjrk3trqpb3l4a

Cytoskeletal Signaling: Is Memory Encoded in Microtubule Lattices by CaMKII Phosphorylation?

Travis J. A. Craddock, Jack A. Tuszynski, Stuart Hameroff, Gustav Bernroider
2012 PLoS Computational Biology  
In long-term potentiation (LTP), a cellular and molecular model for memory, post-synaptic calcium ion (Ca 2+ ) flux activates the hexagonal Ca 2+ -calmodulin dependent kinase II (CaMKII), a dodacameric  ...  Candidate sites for CaMKII phosphorylation-encoded molecular memory include microtubules (MTs), cylindrical organelles whose surfaces represent a regular lattice with a pattern of hexagonal polymers of  ...  To simulate microtubule automata, two-dimensional hexagonal MT lattices are slightly skewed according to lattice geometry and wrapped into a three-dimensional cylinder.  ... 
doi:10.1371/journal.pcbi.1002421 pmid:22412364 pmcid:PMC3297561 fatcat:snwxwrxfnrbg3chjzgou326vyi
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