Toffoli, Tommaso Cellular automata as an alternative to (rather than an approximation of) differential equations in modeling physics. (English) Zbl 0563.68054 Cellular automata, Proc. Interdisc. Workshop, Los Alamos/N.M. 1983, Physica D 10, No. 1-2, 117-127 (1984). Summary: Cellular automata are models of distributed dynamical systems whose structure is particularly well suited to ultrafast, exact numerical simulation. On the other hand, they constitute a radical departure from the traditional partial-differential-equation approach to distributed dynamics. Here we discuss the problem of encoding the state-variables and evolution laws of a physical system into this new setting, and of giving suitable correspondence rules for interpreting the model’s behavior. [For the entire collection see Zbl 0556.00013.] Cited in 29 Documents MSC: 68Q80 Cellular automata (computational aspects) 00A79 Physics (Use more specific entries from Sections 70-XX through 86-XX when possible) Keywords:distributed dynamical systems; physical system PDF BibTeX XML References:  Borel, Émile: Probabilities and life. (1962) · Zbl 0103.35701  Everett, Hugh: The theory of the universal wave function. The many world interpretation of quantum mechanics, 3-140 (1973)  Labudde, R. A.; Greenspan, Donald: Discrete mechanics–A general treatment. J. comput. Physics 15, 134-167 (1974) · Zbl 0301.70006  Hedlund, G. A.: Endomorphysms and automorphisms of the shift dynamical system. Math. syst. Theory 3, 320-375 (1969) · Zbl 0182.56901  Keynes, H. B.; Robertson, J. B.: Generators for topological entropy and expansiveness. Math. syst. Theory 3, 51-59 (1969) · Zbl 0176.20603  Margolus, Norman: Physics-like models of computation. Physica 0D (1984) · Zbl 0563.68051  Richardson, D.: Tesselations with local transformations. J. comput. System sci. 6, 373-388 (1972) · Zbl 0246.94037  Toffoli, Tommaso: Cellular automata mechanics. Logic of computers group (November 1977) · Zbl 0364.94085  Toffoli, Tommaso: Cam: A high performance cellular automata machine. Physica 10D, 195 (1984) · Zbl 0563.68054  Vichniac, Gérard: Simulating physics with cellular automata. Physica 0D (1984) · Zbl 0563.68053 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.