An introduction to symbolic dynamics and coding
An introduction to symbolic dynamics and coding
Action, or the fungibility of computation
Feynman and computation
How to turn a second-order cellular automaton into a lattice gas: a new inversion scheme
Theoretical Computer Science - Special issue: Theoretical aspects of cellular automata
Theory of cellular automata: a survey
Theoretical Computer Science
Methodology and implementation of a software architecture for cellular and lattice-gas automata programming
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The connections between symmetries and conserved quantities of a dynamical system brought to light by Noether's theorem depend in an essential way on the symplectic nature of the underlying kinematics. In the discrete dynamics realm, a rather suggestive analogy for this structure is offered by second-order cellular automata. We ask to what extent the latter systems may enjoy properties analogous to those conferred, for continuous systems, by Noether's theorem. For definiteness, as a second-order cellular automaton we use the Ising spin model with both ferromagnetic and antiferromagnetic bonds. We show that--and why--energy not only acts as a generator of the dynamics for this family of systems, but is also conserved when the dynamics is time-invariant. We then begin to explore the issue of whether, in these systems, it may hold as well that translation invariance entails momentum conservation.