Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!sdd.hp.com!usc!apple!netcom!kmc From: kmc@netcom.COM (Kevin McCarty) Newsgroups: comp.theory.cell-automata Subject: Re: Wacky Quantum Theory in CA Message-ID: <23855@netcom.COM> Date: 13 Feb 91 07:53:30 GMT References: Organization: Netcom - Online Communication Services UNIX System {408 241-9760 guest} Lines: 29 Randy O'Reilly asks about wave phenomena in CA systems with continuous state variables, but discrete space and time. This kind of system was mentioned in a general framework in a recent article I saw that dealt with the general phenomenon of pattern formation in the following kinds of systems: Model Space Time State ----- ----- ---- ----- partial diff. eq'ns C C C iterated functional eqn's C D C oscillator chains D C C lattice dynamical systems D D C cellular automata D D D D = discrete C = continuous J. P. Crutchfield, K. Kaneko, "Phenomenology of Spatio-Temporal Chaos", in "Directions in Chaos", Hao Bai-lin, ed., World Scientific, 1987. The lattice dynamical systems are what numerical analysts really study when they discretize P.D.E.'s for computation. Autonomous, non-quiescent behavior of such systems is a botheration to numerical analysts though, and they strive to avoid it by quantizing 'appropriately'. If you're looking for self-organizing wave phenomena, why then begin with a numerical analysis text and learn about 'numerical instability'. The above-referenced article looks at the topic from a fresh perspective though, and presents an interesting catalog of lattice dynamical system phenomena.