Abstract
MGS is an experimental programming language for the modeling and the simulation of discrete dynamical systems. The modeling approach is based on the explicit specification of the interaction structure between the system parts. This interaction structure is adequately described by topological notions. The topological approach enables a unified view on several computational mechanisms initially inspired by biological or chemical processes (Gamma and cellular automata). The expressivity of the language is illustrated by the modeling of a diffusion limited aggregation process on a wide variety of spatial domain: from cayley graphs to arbitrary quasi-manifolds.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Banâtre, J.-P., Fradet, P., Le Métayer, D.: Gamma and the chemical reaction model: Fifteen years after. In: Calude, C.S., Pun, G., Rozenberg, G., Salomaa, A. (eds.) Multiset Processing. LNCS, vol. 2235, p. 17. Springer, Heidelberg (2001)
Giavitto, J.-L.: Invited talk: Topological collections, transformations and their application to the modeling and the simulation of dynamical systems. In: Nieuwenhuis, R. (ed.) RTA 2003. LNCS, vol. 2706, pp. 208–233. Springer, Heidelberg (2003)
Giavitto, J.-L., Michel, O.: Declarative definition of group indexed data structures and approximation of their domains. In: Proceedings of the 3rd International ACM SIGPLAN Conference on Principles and Practice of Declarative Programming (PPDP 2001). ACM Press, New York (2001)
Giavitto, J.-L., Michel, O.: The topological structures of membrane computing. Fundamenta Informaticae 49, 107–129 (2002)
Giavitto, J.-L., Michel, O.: Modeling the topological organization of cellular processes. BioSystems 70(2), 149–163 (2003)
Giavitto, J.-L., Malcolm, G., Michel, O.: Rewriting systems and the modelling of biological systems. Comparative and Functional Genomics 5, 95–99 (2004)
Giavitto, J.-L., Michel, O., Sansonnet, J.-P.: Group based fields. In: Queinnec, C., Halstead Jr., R.H., Ito, T. (eds.) PSLS 1995. LNCS, vol. 1068, pp. 209–215. Springer, Heidelberg (1996)
Leroy, X.: The Objective Caml system (1996), Software and documentation available on the web at http://pauillac.inria.fr/ocaml/
Lienhardt, P.: Topological models for boundary representation: a comparison with n-dimensional generalized maps. Computer-Aided Design 23(1), 59–82 (1991)
Lindenmayer, A.: Mathematical models for cellular interaction in development, Parts I and II. Journal of Theoretical Biology 18, 280–315 (1968)
Munkres, J.: Elements of Algebraic Topology. Addison-Wesley, Reading (1984)
Róka, Z.: One-way cellular automata on Cayley graphs. Theoretical Computer Science 132(1-2), 259–290 (1994)
Shafarevich, I.: Basic Notions of Algebra. Springer, Heidelberg (1990)
Toffoli, T., Margolus, N.: Cellular automata machines: a new environment for modeling. MIT Press, Cambridge (1987)
Tonti, E.: The algebraic-topological structure of physical theories. In: Glockner, P.G., Sing, M.C. (eds.) Symmetry, similarity and group theoretic methods in mechanics, Calgary, Canada, August 1974, pp. 441–467 (1974)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Spicher, A., Michel, O., Giavitto, JL. (2004). A Topological Framework for the Specification and the Simulation of Discrete Dynamical Systems. In: Sloot, P.M.A., Chopard, B., Hoekstra, A.G. (eds) Cellular Automata. ACRI 2004. Lecture Notes in Computer Science, vol 3305. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30479-1_25
Download citation
DOI: https://doi.org/10.1007/978-3-540-30479-1_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23596-5
Online ISBN: 978-3-540-30479-1
eBook Packages: Springer Book Archive