scholarly journals A mathematical classification of the one-dimensional deterministic cellular automata

1988 ◽  
Vol 118 (3) ◽  
pp. 529-529
Author(s):  
Michel Dubois-Violette ◽  
Alain Rouet
Keyword(s):  
Cellular Automata ◽  
One Dimensional ◽  
The One

Automatic Texture Based Classification of the Dynamics of One-Dimensional Binary Cellular Automata

2019 ◽  
Vol 8 (4) ◽  
pp. 41-61
Author(s):  
Marcelo Arbori Nogueira ◽  
Pedro Paulo Balbi de Oliveira
Keyword(s):  
Cellular Automata ◽  
Dynamic Behavior ◽  
Temporal Evolution ◽  
Computational Cost ◽  
Great Variability ◽  
Texture Descriptor ◽  
One Dimensional ◽  
Binary Images ◽  
Elementary Cellular Automata

Cellular automata present great variability in their temporal evolutions due to the number of rules and initial configurations. The possibility of automatically classifying its dynamic behavior would be of great value when studying properties of its dynamics. By counting on elementary cellular automata, and considering its temporal evolution as binary images, the authors created a texture descriptor of the images - based on the neighborhood configurations of the cells in temporal evolutions - so that it could be associated to each dynamic behavior class, following the scheme of Wolfram's classic classification. It was then possible to predict the class of rules of a temporal evolution of an elementary rule in a more effective way than others in the literature in terms of precision and computational cost. By applying the classifier to the larger neighborhood space containing 4 cells, accuracy decreased to just over 70%. However, the classifier is still able to provide some information about the dynamics of an unknown larger space with reduced computational cost.

Using the one-dimensional S-transform as a discrimination tool in classification of hyperspectral images

2007 ◽  
Vol 33 (6) ◽  
pp. 551-560 ◽  
Author(s):  
Bhaskar C Sahoo ◽  
Thomas Oommen ◽  
Debasmita Misra ◽  
Gregory Newby
Keyword(s):  
Hyperspectral Images ◽  
One Dimensional ◽  
S Transform ◽  
The One

scholarly journals Large semigroups of cellular automata

2011 ◽  
Vol 32 (6) ◽  
pp. 1991-2010 ◽  
Author(s):  
YAIR HARTMAN
Keyword(s):  
Cellular Automata ◽  
Field Structure ◽  
The Other ◽  
Entire Space ◽  
Dimensional Torus ◽  
Semigroup Action ◽  
Closed Set ◽  
One Dimensional ◽  
Shift Space ◽  
The One

AbstractIn this article, we consider semigroups of transformations of cellular automata which act on a fixed shift space. In particular, we are interested in two properties of these semigroups which relate to ‘largeness’: first, a semigroup has the ID (infinite is dense) property if the only infinite invariant closed set (with respect to the semigroup action) is the entire space; the second property is maximal commutativity (MC). We shall consider two examples of semigroups: one is spanned by cellular automata transformations that represent multiplications by integers on the one-dimensional torus, and the other one consists of all the cellular automata transformations which are linear (when the symbols set is the ring ℤ/sℤ). It will be shown that these two properties of these semigroups depend on the number of symbols s. The multiplication semigroup is ID and MC if and only if s is not a power of a prime. The linear semigroup over the mentioned ring is always MC but is ID if and only if s is prime. When the symbol set is endowed with a finite field structure (when possible), the linear semigroup is both ID and MC. In addition, we associate with each semigroup which acts on a one-sided shift space a semigroup acting on a two-sided shift space, and vice versa, in a way that preserves the ID and the MC properties.

Transformations of the one-dimensional cellular automata rule space

1997 ◽  
Vol 23 (11) ◽  
pp. 1593-1611 ◽  
Author(s):  
G. Cattaneo ◽  
E. Formenti ◽  
L. Margara ◽  
G. Mauri
Keyword(s):  
Cellular Automata ◽  
One Dimensional ◽  
Rule Space ◽  
The One

scholarly journals Self-Organizing Construction Method of Offshore Structures by Cellular Automata Model

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Takeshi Ishida
Keyword(s):  
Cellular Automata ◽  
Living Organism ◽  
Offshore Structures ◽  
Structural Units ◽  
Cellular Automata Model ◽  
One Dimensional ◽  
Transition Rules ◽  
Complex Patterns ◽  
The One ◽  
Self Organizing

We propose a new algorithm to build self-organizing and self-repairing marine structures on the ocean floor, where humans and remotely operated robots cannot operate. The proposed algorithm is based on the one-dimensional cellular automata model and uses simple transition rules to produce various complex patterns. This cellular automata model can produce various complex patterns like sea shells with simple transition rules. The model can simulate the marine structure construction process with distributed cooperation control instead of central control. Like living organism is constructed with module called cell, we assume that the self-organized structure consists of unified modules (structural units). The units pile up at the bottom of the sea and a structure with the appropriate shape eventually emerges. Using the attribute of emerging patterns in the one-dimensional cellular automata model, we construct specific structures based on the local interaction of transition rules without using complex algorithms. Furthermore, the model requires smaller communication data among the units because it only relies on communication between adjacent structural units. With the proposed algorithm, in the future, it will be possible to use self-assembling structural modules without complex built-in computers.

Complex Order from Disorder and from Simple Order in Coarse-Graining Invariant Orbits of Certain Two-Dimensional Linear Cellular Automata

1997 ◽  
Vol 07 (07) ◽  
pp. 1451-1496 ◽  
Author(s):  
André Barbé
Keyword(s):  
Cellular Automata ◽  
Three Dimensional ◽  
Coarse Graining ◽  
Dimensional Case ◽  
Two Dimensional ◽  
One Dimensional ◽  
Complex Order ◽  
Simple Order ◽  
Problems And Solutions ◽  
The One

This paper considers three-dimensional coarse-graining invariant orbits for two-dimensional linear cellular automata over a finite field, as a nontrivial extension of the two-dimensional coarse-graining invariant orbits for one-dimensional CA that were studied in an earlier paper. These orbits can be found by solving a particular kind of recursive equations (renormalizing equations with rescaling term). The solution starts from some seed that has to be determined first. In contrast with the one-dimensional case, the seed has infinite support in most cases. The way for solving these equations is discussed by means of some examples. Three categories of problems (and solutions) can be distinguished (as opposed to only one in the one-dimensional case). Finally, the morphology of a few coarse-graining invariant orbits is discussed: Complex order (of quasiperiodic type) seems to emerge from random seeds as well as from seeds of simple order (for example, constant or periodic seeds).

scholarly journals Remarks on the Structure of Clifford Quantum Cellular Automata

2009 ◽  
Vol 16 (02n03) ◽  
pp. 269-279
Author(s):  
Dirk-Michael Schlingemann
Keyword(s):  
Phase Space ◽  
Cellular Automata ◽  
Symplectic Group ◽  
Tensor Products ◽  
Projective Representation ◽  
Dimensional Case ◽  
Additional Restriction ◽  
Quantum Cellular Automata ◽  
One Dimensional ◽  
The One

We report here on the structure of reversible quantum cellular automata with the additional restriction that these are also Clifford operations. This means that tensor products of Weyl operators (projective representation of a finite abelian symplectic group) are mapped to multiples of tensor products of Weyl operators. Therefore Clifford quantum cellular automata are induced by symplectic cellular automata in phase space. We characterize these symplectic cellular automata and find that all possible local rules must be, up to some global shift, reflection-invariant with respect to the origin. In the one-dimensional case we also find that all 1D Clifford quantum cellular automata are generated by a few elementary operations.

scholarly journals Yang-Baxter and the Boost: splitting the difference

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Marius de Leeuw ◽  
Chiara Paletta ◽  
Anton Pribytok ◽  
Ana L. Retore ◽  
Paul Ryan
Keyword(s):  
Hilbert Space ◽  
Sigma Model ◽  
Spin Chains ◽  
Baxter Equation ◽  
Regular Solutions ◽  
One Dimensional ◽  
Difference Form ◽  
The Difference ◽  
The One

In this paper we continue our classification of regular solutions of the Yang-Baxter equation using the method based on the spin chain boost operator developed in [1]. We provide details on how to find all non-difference form solutions and apply our method to spin chains with local Hilbert space of dimensions two, three and four. We classify all 16\times1616×16 solutions which exhibit \mathfrak{su}(2)\oplus \mathfrak{su}(2)𝔰𝔲(2)⊕𝔰𝔲(2) symmetry, which include the one-dimensional Hubbard model and the SS-matrix of the {AdS}_5 \times {S}^5AdS5×S5 superstring sigma model. In all cases we find interesting novel solutions of the Yang-Baxter equation.

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