# Additive Cellular Automata and Volume Growth

@article{Ward2000AdditiveCA, title={Additive Cellular Automata and Volume Growth}, author={Thomas Ward}, journal={Entropy}, year={2000}, volume={2}, pages={142-167} }

A class of dynamical systems associated to rings of S-integers in rational function fields is described. General results about these systems give a rather complete description of the well-known dynamics in one-dimensional additive cellular automata with prime alphabet, including simple formulae for the topological entropy and the number of periodic configurations. For these systems the periodic points are uniformly distributed along some subsequence with respect to the maximal measure, and in…

## 31 Citations

The Complexity of Permutive Cellular Automata

- MathematicsJ. Cell. Autom.
- 2011

This paper studies cellular automata in two aspects: Ergodic and topological behavior. For ergodic aspect, the formulae of measure-theoretic entropy, topological entropy and topological pressure are…

Some Properties of topological pressure on cellular automata

- Mathematics
- 2014

This paper investigates the ergodicity and the power rule of the topological pressure of a cellular automaton. If a cellular automaton is either leftmost or rightmost premutive (due to the…

On the Measure Entropy of Additive Cellular Automata f∞

- Computer Science, MathematicsEntropy
- 2003

The measure-theoretic entropy of the additive one-dimensional cellular automata f∞ with respect to μ is equal to hμ (f∞) = 2klog r, where k ≥ 1, r-1∈S.

The Topological Pressure of Linear Cellular Automata

- MathematicsEntropy
- 2009

This elucidation studies ergodicity and equilibrium measures for additive cellular automata with prime states and concludes that Parry measure is inferred to be an equilibrium measure.

The topological entropy of nth iteration of an additive cellular automata

- Computer Science, MathematicsAppl. Math. Comput.
- 2006

Mean dimension of continuous cellular automata

- Mathematics
- 2021

We investigate the mean dimension of a cellular automaton (CA for short) with a compact non-discrete space of states. A formula for the mean dimension is established for (near) strongly permutative,…

Stream cipher using two dimensional Cellular Automata

- Computer Science
- 2015

The pseudo-random early in cryptography systems, the important of cellular automata has properties which are considered a state machine, high periods, the binary sequences that are generated form CA generator are characterized by their success in random tests.

Theory of Additive Cellular Automata

- Computer Science
- 2007

An analytical framework is developed to characterize the cyclic vector subspaces gene rat d by anACA with reference toLCA and provides the theoretical analysis of the nature of d ifference.

2 4 Ja n 20 06 Measure rigidity for algebraic bipermutative cellular automata

- Mathematics
- 2006

Let (A Z , F) be a bipermutative algebraic cellular automaton. We present conditions which force a probability measure which is invariant for the N × Z-action of F and the shift map σ to be the Haar…

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