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Abstract: One dimensional cellular automata are analyzed via their generalized permutivity. Invariant subalphabets provide a systematic way of identifying periodic and aperiodic tilings as well as stationary distributions invariant under the cellular automaton iteration. In the case of several invariant subalphabets a hierarchy of interaction phenomena arise. In particular the interaction of subalphabets can generate random walks as well as their degenerate forms. A comprehensive scheme emerges that... (Update)
Context of citations to this paper: More
...rigorously using probabilistic methods. This results in a complete classification in the partially permutive case. The paper complements [1] where the general framework of tilings and subpermutivity was introduced and non probabilistic properties were analyzed. Introduction In...
.... the interaction properties of the particles one can build logic gates, from them boolean circuits and higher computational elements ( 1] [2]) But before we go on what does this have to do with alife The fact that some c.a. support universal computation means that they can...
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Algebraic Properties of the Block Transformation on Cellular.. - Moore, Drisko (1995) (Correct)
Commuting Cellular Automata - Moore, Boykett (Correct)
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0.5: Random Walks in Cellular Automata - Eloranta (1993) (Correct)
0.5: Prior Information and Generalized Questions - Lemm (1996) (Correct)
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3: Combinatorial construction of one dimensional reversible cellular automata (context) - Boykett - 1995
3: Cellular automata as algebraic systems (context) - Pedersen - 1992
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BibTeX entry: (Update)
K. Eloranta, "Partially permutive cellular automata." Nonlinearity 6 (1993) 1009. http://citeseer.ist.psu.edu/eloranta93partially.html More
@article{ eloranta93partially,
author = "K Eloranta",
title = "Partially premitive cellular automata",
journal = "Nonlinearity",
volume = "6",
number = "6",
pages = "1009",
year = "1993",
url = "citeseer.ist.psu.edu/eloranta93partially.html" }
Citations (may not include all citations):114 Theory and Applications of Cellular Automata (context) - Wolfram - 1986
62 Studying artificial life with cellular automata (context) - Langton - 1986
46 Endomorphisms and automorphisms of the shift dynamical syste.. (context) - Hedlund - 1969
30 Global order from local sources - Radin - 1991
30 The attractor-basin portrait of a cellular automaton (context) - Hanson, Crutchfield - 1992
13 Applications of ergodic theory and sofic systems to cellular.. (context) - Lind - 1984
10 Mixing properties of substitutions (context) - Dekking, Keane - 1978
10 Soliton-like behavior in automata (context) - Park, Steiglitz et al. - 1986
9 Aperiodicity in one-dimensional cellular automata (context) - Jen - 1990
2 Random walks in cellular automata - Eloranta - 1993
2 The kink of the elementary cellular automaton Rule 18 perfor.. (context) - Eloranta, Nummelin - 1992
2 Random Walks (context) - Fern'andez, Frohlich et al. - 1992
2 The interaction dynamics of the kinks in the cellular automa.. - Eloranta - 1991
1 Properties of the directed entropy function for cellular aut.. (context) - Smillie - 1987
1 An equilibrium state for a 1-dimensional life game (context) - Miyamoto - 1979
Documents on the same site (http://dopey.hut.fi/~kve/research.html.en): More
Cellular Automata for Contour Dynamics - Eloranta (1995) (Correct)
Random Walks in Cellular Automata - Eloranta (1993) (Correct)
Voter Dynamics In Deterministic Cellular Automata - Eloranta (1995) (Correct)
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