Abstract
We consider two formulations of a cellular automata: the first one uses a gather-update paradigm and the second one a collision-propagation paradigm. We show the equivalence of both descriptions and, using the latter paradigm, we propose a simple way to define a Cellular Automata on a graph with arbitrary topology. Finally, we exploit the duality of formulation to reconsider the problem of characterizing invertible cellular automata.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Caiazzo, A., Falcone, J.-L., Chopard, B., Hoekstra, A.: Error investigations in complex automata models for reaction-diffusion systems. In: Umeo, H., et al. (eds.) ACRI 2008. LNCS, vol. 5191, pp. 260–267. Springer, Heidelberg (2008)
Caldarelli, G.: Scale-Free Networks. Oxford University Press, Oxford (2007)
Chopard, B., Droz, M.: Cellular Automata Modeling of Physical Systems. Cambridge University Press, Cambridge (1998)
Durand-Lose, J.: Representing reversible cellular automata with reversible block cellular automata. In: Discrete Mathematics and Theoretical Computer Sciences Proceedings AA (DM-CCG), pp. 145–154 (2001)
Hoekstra, A., Lorenz, E., Falcone, J.-L., Chopard, B.: Towards a complex automata formalism for multuscale modeling. Int. J. Multiscale Computational Engineering 5(6), 491–502 (2008)
Hoekstra, A.G., Falcone, J.-L., Caiazzo, A., Chopard, B.: Multi-scale modeling with cellular automata: The complex automata approach. In: Umeo, H., et al. (eds.) ACRI 2008. LNCS, vol. 5191, pp. 192–199. Springer, Heidelberg (2008)
Marconi, S., Chopard, B.: Discrete physics, cellular automata and cryptography. In: El Yacoubi, S., Chopard, B., Bandini, S. (eds.) ACRI 2006. LNCS, vol. 4173, pp. 617–626. Springer, Heidelberg (2006)
Razakanirina, R.M.: Cellular automata on graphs applied to financial flow simulation. Master’s thesis, University of Geneva, Computer Science department, Master thesis (2007)
Toffoli, T., Margolus, N.: Cellular Automata Machines: a New Environment for Modeling. MIT Press, Cambridge (1987)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chopard, B., Falcone, JL., Razakanirina, R., Hoekstra, A., Caiazzo, A. (2008). On the Collision-Propagation and Gather-Update Formulations of a Cellular Automata Rule. In: Umeo, H., Morishita, S., Nishinari, K., Komatsuzaki, T., Bandini, S. (eds) Cellular Automata. ACRI 2008. Lecture Notes in Computer Science, vol 5191. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79992-4_19
Download citation
DOI: https://doi.org/10.1007/978-3-540-79992-4_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79991-7
Online ISBN: 978-3-540-79992-4
eBook Packages: Computer ScienceComputer Science (R0)