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Cellular automaton

Index Cellular automaton

A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model studied in computer science, mathematics, physics, complexity science, theoretical biology and microstructure modeling. [1]

165 relations: A New Kind of Science, Agent-based model, Alan Turing, Alexander Dewdney, Alvy Ray Smith, Anatol Zhabotinsky, Arturo Rosenblueth, Asynchronous cellular automaton, Automata theory, Belousov–Zhabotinsky reaction, Bidirectional traffic, Bijection, Block cellular automaton, Block cipher, Boris Pavlovich Belousov, Brian's Brain, Calculating Space, Cambridge University Press, Cephalopod, Chromatophore, Codd's cellular automaton, CoDi, Complex system, Complex Systems (journal), Computational irreducibility, Computer science, Cone snail, Continuous automaton, Continuous function, Continuous spatial automaton, Conus textile, Conway's Game of Life, Coupled map lattice, Cryptography, Curtis–Hedlund–Lyndon theorem, Cyclic cellular automaton, Cymbiola, Digital physics, Dimension, Discrete mathematics, Dov Gabbay, Dynamical system, ECC memory, Edge (geometry), Edge of chaos, Edward Fredkin, Elementary cellular automaton, Endomorphism, Excitable medium, Fibroblast, ..., Firing squad synchronization problem, Fourier transform, Garden of Eden (cellular automaton), Gerard 't Hooft, Graph paper, Graph rewriting, Greenberg–Hastings cellular automaton, Gustav A. Hedlund, Hamming distance, Heart arrhythmia, Hexagonal tiling, Homogeneity and heterogeneity, Hypercube, IEEE Transactions on Computers, ILabs, Ilya Prigogine, Image (mathematics), James P. Crutchfield, Jarkko Kari, John Horton Conway, John von Neumann, Konrad Zuse, Langton's ant, Langton's loops, Lattice model (physics), Lloyd A. Jeffress, Los Alamos National Laboratory, Majority problem (cellular automaton), Malonic acid, Martin Gardner, Marvin Minsky, Mathematical and theoretical biology, Mathematics, Matthew Cook, Microstructure, Mirek's Cellebration, MIT Press, Modular arithmetic, Moore neighborhood, Movable cellular automaton, Nature (journal), Neural network, Neuron, Nils Aall Barricelli, Nobili cellular automata, Norbert Wiener, Norman Margolus, One-way function, Open access, Orthogonality, Oxford University Press, Partial differential equation, Particle physics, Penrose tiling, Phase transition, Phonon, Physics, Pigment, Public-key cryptography, Quantum cellular automaton, Quantum mechanics, Random number generation, Randomness, Reaction–diffusion system, Reviews of Modern Physics, Rule 110, Rule 184, Rule 30, Rule 90, Santa Fe Institute, Science (journal), Scientific American, Seashell, Second law of thermodynamics, Second-order cellular automaton, Secretion, Self-replication, Shift space, Spatial decision support system, Springer Science+Business Media, Stanislaw Ulam, State (computer science), Stephen Wolfram, Stochastic cellular automaton, Stoma, Symbolic dynamics, Systolic array, Tessellation, The Economist, The New York Review of Books, The New York Times, The New York Times Company, Thermodynamics, Tommaso Toffoli, Torus, Trapdoor function, Turing completeness, Turing machine, Turmite, Undecidable problem, Unit interval, Universal Turing machine, University of Illinois Press, Vertex (geometry), Von Neumann architecture, Von Neumann cellular automaton, Von Neumann neighborhood, Von Neumann universal constructor, Wang tile, Wireworld, Wolfram code, Wolfram Research, World Scientific, Z3 (computer), Zebra. Expand index (115 more) »

A New Kind of Science

A New Kind of Science is a best-selling, controversial book by Stephen Wolfram, published by his own company in 2002.

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Agent-based model

An agent-based model (ABM) is a class of computational models for simulating the actions and interactions of autonomous agents (both individual or collective entities such as organizations or groups) with a view to assessing their effects on the system as a whole.

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Alan Turing

Alan Mathison Turing (23 June 1912 – 7 June 1954) was an English computer scientist, mathematician, logician, cryptanalyst, philosopher, and theoretical biologist.

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Alexander Dewdney

Alexander Keewatin Dewdney (born August 5, 1941, in London, Ontario) is a Canadian mathematician, computer scientist, author, filmmaker, and conspiracy theorist.

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Alvy Ray Smith

Alvy Ray Smith III is an American computer scientist who cofounded Lucasfilm's Computer Division, and Pixar, participating in the 1980s and 1990s expansion of computer animation into feature film.

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Anatol Zhabotinsky

Anatol Markovich Zhabotinsky (Анато́лий Ма́ркович Жаботи́нский) (January 17, 1938 – September 16, 2008) was a Soviet biophysicist who created a theory of the chemical clock known as Belousov-Zhabotinsky reaction in the 1960s and published a comprehensive body of experimental data on chemical wave propagation and pattern formation in nonuniform media.

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Arturo Rosenblueth

Arturo Rosenblueth Stearns (October 2, 1900 – September 20, 1970) was a Mexican researcher, physician and physiologist, who is known as one of the pioneers of cybernetics.

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Asynchronous cellular automaton

Cellular automata, as with other multi-agent system models, usually treat time as discrete and state updates as occurring synchronously.

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Automata theory

Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them.

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Belousov–Zhabotinsky reaction

A Belousov–Zhabotinsky reaction, or BZ reaction, is one of a class of reactions that serve as a classical example of non-equilibrium thermodynamics, resulting in the establishment of a nonlinear chemical oscillator.

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Bidirectional traffic

In transportation infrastructure, a bidirectional traffic system divides travelers into two streams of traffic that flow in opposite directions.

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Bijection

In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.

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Block cellular automaton

A block cellular automaton or partitioning cellular automaton is a special kind of cellular automaton in which the lattice of cells is divided into non-overlapping blocks (with different partitions at different time steps) and the transition rule is applied to a whole block at a time rather than a single cell.

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Block cipher

In cryptography, a block cipher is a deterministic algorithm operating on fixed-length groups of bits, called a block, with an unvarying transformation that is specified by a symmetric key.

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Boris Pavlovich Belousov

Boris Pavlovich Belousov (Бори́с Па́влович Белоу́сов; 19 February 1893 – 12 June 1970) was a Soviet chemist / biophysicist who discovered the Belousov-Zhabotinsky reaction (BZ reaction) in the early 1950s.

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Brian's Brain

Brian's Brain is a cellular automaton devised by Brian Silverman, which is very similar to his Seeds rule.

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Calculating Space

Calculating Space is the title of MIT's English translation of Konrad Zuse's 1969 book Rechnender Raum (literally: "space that is computing"), the first book on digital physics.

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Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

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Cephalopod

A cephalopod is any member of the molluscan class Cephalopoda (Greek plural κεφαλόποδα, kephalópoda; "head-feet") such as a squid, octopus or nautilus.

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Chromatophore

Chromatophores are pigment-containing and light-reflecting cells, or groups of cells, found in a wide range of animals including amphibians, fish, reptiles, crustaceans and cephalopods.

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Codd's cellular automaton

Codd's cellular automaton is a cellular automaton (CA) devised by the British computer scientist Edgar F. Codd in 1968.

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CoDi

CoDi is a cellular automaton (CA) model for spiking neural networks (SNNs).

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Complex system

A complex system is a system composed of many components which may interact with each other.

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Complex Systems (journal)

Complex Systems is a quarterly peer-reviewed open access scientific journal covering subjects ranging across a number of scientific and engineering fields, including computational biology, computer science, mathematics, and physics.

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Computational irreducibility

Computational irreducibility is one of the main ideas proposed by Stephen Wolfram in his book A New Kind of Science.

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Computer science

Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.

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Cone snail

Cone snails, cone shells, or cones are common names for a large group of small to large-sized extremely venomous predatory sea snails, marine gastropod molluscs.

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Continuous automaton

A continuous automaton can be described as a cellular automaton extended so the valid states a cell can take are not just discrete (for example, the states consist of integers between 0 and 3), but continuous, for example, the real number range.

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Continuous function

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.

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Continuous spatial automaton

Continuous spatial automata, unlike cellular automata, have a continuum of locations, while the state of a location still is any of a finite number of real numbers.

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Conus textile

Conus textile, common name the textile cone or the cloth of gold cone is a venomous species of sea snail, a marine gastropod mollusk in the family Conidae, the cone snails, cone shells or cones.

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Conway's Game of Life

The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970.

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Coupled map lattice

A coupled map lattice (CML) is a dynamical system that models the behavior of non-linear systems (especially partial differential equations).

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Cryptography

Cryptography or cryptology (from κρυπτός|translit.

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Curtis–Hedlund–Lyndon theorem

The Curtis–Hedlund–Lyndon theorem is a mathematical characterization of cellular automata in terms of their symbolic dynamics.

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Cyclic cellular automaton

A cyclic cellular automaton is a kind of cellular automaton rule developed by David Griffeath and studied by several other cellular automaton researchers.

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Cymbiola

Cymbiola is a genus of large predatory sea snail, a marine gastropod mollusk in the family Volutidae, the volutes.

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Digital physics

In physics and cosmology, digital physics (also referred to as digital ontology or digital philosophy) is a collection of theoretical perspectives based on the premise that the universe is describable by information.

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Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.

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Discrete mathematics

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.

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Dov Gabbay

Dov M. Gabbay (born October 23, 1945) is a British logician.

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Dynamical system

In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space.

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ECC memory

Error-correcting code memory (ECC memory) is a type of computer data storage that can detect and correct the most common kinds of internal data corruption.

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Edge (geometry)

In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.

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Edge of chaos

The term edge of chaos is used to denote a transition space between order and disorder that is hypothesized to exist within a wide variety of systems.

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Edward Fredkin

Edward Fredkin (born 1934) is a distinguished career professor at Carnegie Mellon University (CMU), Pennsylvania, and an early pioneer of Digital physics.

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Elementary cellular automaton

In mathematics and computability theory, an elementary cellular automaton is a one-dimensional cellular automaton where there are two possible states (labeled 0 and 1) and the rule to determine the state of a cell in the next generation depends only on the current state of the cell and its two immediate neighbors.

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Endomorphism

In mathematics, an endomorphism is a morphism (or homomorphism) from a mathematical object to itself.

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Excitable medium

An excitable medium is a nonlinear dynamical system which has the capacity to propagate a wave of some description, and which cannot support the passing of another wave until a certain amount of time has passed (known as the refractory time).

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Fibroblast

A fibroblast is a type of biological cell that synthesizes the extracellular matrix and collagen, the structural framework (stroma) for animal tissues, and plays a critical role in wound healing.

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Firing squad synchronization problem

The firing squad synchronization problem is a problem in computer science and cellular automata in which the goal is to design a cellular automaton that, starting with a single active cell, eventually reaches a state in which all cells are simultaneously active.

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Fourier transform

The Fourier transform (FT) decomposes a function of time (a signal) into the frequencies that make it up, in a way similar to how a musical chord can be expressed as the frequencies (or pitches) of its constituent notes.

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Garden of Eden (cellular automaton)

In a cellular automaton, a Garden of Eden is a configuration that has no predecessor.

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Gerard 't Hooft

Gerardus (Gerard) 't Hooft (born July 5, 1946) is a Dutch theoretical physicist and professor at Utrecht University, the Netherlands.

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Graph paper

Graph paper, coordinate paper, grid paper, or squared paper is writing paper that is printed with fine lines making up a regular grid.

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Graph rewriting

In computer science, graph transformation, or graph rewriting, concerns the technique of creating a new graph out of an original graph algorithmically.

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Greenberg–Hastings cellular automaton

The Greenberg–Hastings Cellular Automaton (abbrev. GH model) is a three state two dimensional cellular automaton (abbrev CA) named after James M. Greenberg and Stuart Hastings, designed to model excitable media, One advantage of a CA model is ease of computation.

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Gustav A. Hedlund

Gustav Arnold Hedlund (May 7, 1904 – March 15, 1993), an American mathematician, was one of the founders of symbolic and topological dynamics.

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Hamming distance

In information theory, the Hamming distance between two strings of equal length is the number of positions at which the corresponding symbols are different.

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Heart arrhythmia

Heart arrhythmia (also known as arrhythmia, dysrhythmia, or irregular heartbeat) is a group of conditions in which the heartbeat is irregular, too fast, or too slow.

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Hexagonal tiling

In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which three hexagons meet at each vertex.

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Homogeneity and heterogeneity

Homogeneity and heterogeneity are concepts often used in the sciences and statistics relating to the uniformity in a substance or organism.

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Hypercube

In geometry, a hypercube is an ''n''-dimensional analogue of a square and a cube.

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IEEE Transactions on Computers

IEEE Transactions on Computers is a monthly peer-reviewed scientific journal covering all aspects of computer design.

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ILabs

iLabs is a non-profit Milan-based organization pursuing multidisciplinary research on radical extension of human life-span.

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Ilya Prigogine

Viscount Ilya Romanovich Prigogine (Илья́ Рома́нович Приго́жин; 28 May 2003) was a physical chemist and Nobel laureate noted for his work on dissipative structures, complex systems, and irreversibility.

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Image (mathematics)

In mathematics, an image is the subset of a function's codomain which is the output of the function from a subset of its domain.

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James P. Crutchfield

James P. Crutchfield (born 1955) is an American mathematician and physicist.

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Jarkko Kari

Jarkko J. Kari is a Finnish mathematician and computer scientist, known for his contributions to the theory of Wang tiles and cellular automata.

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John Horton Conway

John Horton Conway FRS (born 26 December 1937) is an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.

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John von Neumann

John von Neumann (Neumann János Lajos,; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, and polymath.

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Konrad Zuse

Konrad Zuse (22 June 1910 – 18 December 1995) was a German civil engineer, inventor and computer pioneer.

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Langton's ant

Langton's ant is a two-dimensional universal Turing machine with a very simple set of rules but complex emergent behavior.

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Langton's loops

Langton's loops are a particular "species" of artificial life in a cellular automaton created in 1984 by Christopher Langton.

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Lattice model (physics)

In physics, a lattice model is a physical model that is defined on a lattice, as opposed to the continuum of space or spacetime.

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Lloyd A. Jeffress

Lloyd Alexander Jeffress (November 15, 1900 – April 2, 1986) was an acoustical scientist, a professor of Experimental Psychology at the University of Texas at Austin, a developer of mine-hunting models for the US Navy during World War II and after, and the man Nobel Laureate Linus Pauling credited with getting him interested in chemistry.

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Los Alamos National Laboratory

Los Alamos National Laboratory (Los Alamos or LANL for short) is a United States Department of Energy national laboratory initially organized during World War II for the design of nuclear weapons as part of the Manhattan Project.

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Majority problem (cellular automaton)

The majority problem, or density classification task is the problem of finding one-dimensional cellular automaton rules that accurately perform majority voting.

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Malonic acid

Malonic acid (IUPAC systematic name: propanedioic acid) is a dicarboxylic acid with structure CH2(COOH)2.

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Martin Gardner

Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer, with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literature—especially the writings of Lewis Carroll, L. Frank Baum, and G. K. Chesterton.

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Marvin Minsky

Marvin Lee Minsky (August 9, 1927 – January 24, 2016) was an American cognitive scientist concerned largely with research of artificial intelligence (AI), co-founder of the Massachusetts Institute of Technology's AI laboratory, and author of several texts concerning AI and philosophy.

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Mathematical and theoretical biology

Mathematical and theoretical biology is a branch of biology which employs theoretical analysis, mathematical models and abstractions of the living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of experiments to prove and validate the scientific theories.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Matthew Cook

Matthew Cook (born February 7, 1970) is a mathematician and computer scientist who proved Stephen Wolfram's conjecture that the Rule 110 cellular automaton is Turing-complete.

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Microstructure

Microstructure is the very small scale structure of a material, defined as the structure of a prepared surface of material as revealed by a microscope above 25× magnification.

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Mirek's Cellebration

Mirek's Cellebration (abbreviated MCell) is a 32-bit Windows freeware program designed by Polish computer programmer Mirek Wójtowicz for running one-dimensional and two-dimensional cellular automata (CA).

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MIT Press

The MIT Press is a university press affiliated with the Massachusetts Institute of Technology (MIT) in Cambridge, Massachusetts (United States).

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Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus (plural moduli).

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Moore neighborhood

In cellular automata, the Moore neighborhood is defined on a two-dimensional square lattice and is composed of a central cell and the eight cells which surround it.

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Movable cellular automaton

The Movable cellular automaton (MCA) method is a method in computational solid mechanics based on the discrete concept.

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Nature (journal)

Nature is a British multidisciplinary scientific journal, first published on 4 November 1869.

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Neural network

The term neural network was traditionally used to refer to a network or circuit of neurons.

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Neuron

A neuron, also known as a neurone (British spelling) and nerve cell, is an electrically excitable cell that receives, processes, and transmits information through electrical and chemical signals.

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Nils Aall Barricelli

Nils Aall Barricelli (24 January 1912 – 27 January 1993) was a Norwegian-Italian mathematician.

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Nobili cellular automata

Nobili cellular automata (NCA) are a variation of von Neumann cellular automata (vNCA), in which additional states provide means of memory and the interference-free crossing of signal.

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Norbert Wiener

Norbert Wiener (November 26, 1894 – March 18, 1964) was an American mathematician and philosopher.

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Norman Margolus

Norman H. Margolus (born 1955) is a Canadian-American physicist and computer scientist, known for his work on cellular automata and reversible computing.

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One-way function

In computer science, a one-way function is a function that is easy to compute on every input, but hard to invert given the image of a random input.

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Open access

Open access (OA) refers to research outputs which are distributed online and free of cost or other barriers, and possibly with the addition of a Creative Commons license to promote reuse.

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Orthogonality

In mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms.

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Oxford University Press

Oxford University Press (OUP) is the largest university press in the world, and the second oldest after Cambridge University Press.

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Partial differential equation

In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.

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Particle physics

Particle physics (also high energy physics) is the branch of physics that studies the nature of the particles that constitute matter and radiation.

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Penrose tiling

A Penrose tiling is an example of non-periodic tiling generated by an aperiodic set of prototiles.

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Phase transition

The term phase transition (or phase change) is most commonly used to describe transitions between solid, liquid and gaseous states of matter, and, in rare cases, plasma.

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Phonon

In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, like solids and some liquids.

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Physics

Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.

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Pigment

A pigment is a material that changes the color of reflected or transmitted light as the result of wavelength-selective absorption.

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Public-key cryptography

Public-key cryptography, or asymmetric cryptography, is any cryptographic system that uses pairs of keys: public keys which may be disseminated widely, and private keys which are known only to the owner.

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Quantum cellular automaton

A quantum cellular automaton (QCA) is an abstract model of quantum computation, devised in analogy to conventional models of cellular automata introduced by von Neumann.

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Quantum mechanics

Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.

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Random number generation

Random number generation is the generation of a sequence of numbers or symbols that cannot be reasonably predicted better than by a random chance, usually through a hardware random-number generator (RNG).

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Randomness

Randomness is the lack of pattern or predictability in events.

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Reaction–diffusion system

Reaction–diffusion systems are mathematical models which correspond to several physical phenomena: the most common is the change in space and time of the concentration of one or more chemical substances: local chemical reactions in which the substances are transformed into each other, and diffusion which causes the substances to spread out over a surface in space.

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Reviews of Modern Physics

Reviews of Modern Physics is a quarterly peer-reviewed scientific journal published by the American Physical Society.

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Rule 110

The Rule 110 cellular automaton (often simply Rule 110) is an elementary cellular automaton with interesting behavior on the boundary between stability and chaos.

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Rule 184

Rule 184 is a one-dimensional binary cellular automaton rule, notable for solving the majority problem as well as for its ability to simultaneously describe several, seemingly quite different, particle systems.

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Rule 30

Rule 30 is a one-dimensional binary cellular automaton rule introduced by Stephen Wolfram in 1983.

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Rule 90

In the mathematical study of cellular automata, Rule 90 is an elementary cellular automaton based on the exclusive or function.

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Santa Fe Institute

The Santa Fe Institute (SFI) is an independent, nonprofit theoretical research institute located in Santa Fe (New Mexico, United States) and dedicated to the multidisciplinary study of the fundamental principles of complex adaptive systems, including physical, computational, biological, and social systems.

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Science (journal)

Science, also widely referred to as Science Magazine, is the peer-reviewed academic journal of the American Association for the Advancement of Science (AAAS) and one of the world's top academic journals.

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Scientific American

Scientific American (informally abbreviated SciAm) is an American popular science magazine.

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Seashell

A seashell or sea shell, also known simply as a shell, is a hard, protective outer layer created by an animal that lives in the sea.

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Second law of thermodynamics

The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time.

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Second-order cellular automaton

A second-order cellular automaton is a type of reversible cellular automaton (CA) invented by Edward Fredkin.

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Secretion

Secretion is the movement of material from one point to another, e.g. secreted chemical substance from a cell or gland.

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Self-replication

Self-replication is any behavior of a dynamical system that yields construction of an identical copy of itself.

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Shift space

In symbolic dynamics and related branches of mathematics, a shift space or subshift is a set of infinite words that represent the evolution of a discrete system.

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Spatial decision support system

A spatial decision support system (SDSS) is an interactive, computer-based system designed to assist in decision making while solving a semi-structured spatial problem.

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Springer Science+Business Media

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

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Stanislaw Ulam

Stanisław Marcin Ulam (13 April 1909 – 13 May 1984) was a Polish-American scientist in the fields of mathematics and nuclear physics.

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State (computer science)

In information technology and computer science, a program is described as stateful if it is designed to remember preceding events or user interactions; the remembered information is called the state of the system.

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Stephen Wolfram

Stephen Wolfram (born August 29, 1959) is a British-American computer scientist, physicist, and businessman.

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Stochastic cellular automaton

Stochastic cellular automata or 'probabilistic cellular automata' (PCA) or 'random cellular automata' or locally interacting Markov chains are an important extension of cellular automaton.

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Stoma

In botany, a stoma (plural "stomata"), also called a stomata (plural "stomates") (from Greek στόμα, "mouth"), is a pore, found in the epidermis of leaves, stems, and other organs, that facilitates gas exchange.

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Symbolic dynamics

In mathematics, symbolic dynamics is the practice of modeling a topological or smooth dynamical system by a discrete space consisting of infinite sequences of abstract symbols, each of which corresponds to a state of the system, with the dynamics (evolution) given by the shift operator.

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Systolic array

In parallel computer architectures, a systolic array is a homogeneous network of tightly coupled data processing units (DPUs) called cells or nodes.

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Tessellation

A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.

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The Economist

The Economist is an English-language weekly magazine-format newspaper owned by the Economist Group and edited at offices in London.

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The New York Review of Books

The New York Review of Books (or NYREV or NYRB) is a semi-monthly magazine with articles on literature, culture, economics, science and current affairs.

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The New York Times

The New York Times (sometimes abbreviated as The NYT or The Times) is an American newspaper based in New York City with worldwide influence and readership.

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The New York Times Company

The New York Times Company is an American media company which publishes its namesake, The New York Times.

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Thermodynamics

Thermodynamics is the branch of physics concerned with heat and temperature and their relation to energy and work.

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Tommaso Toffoli

Tommaso Toffoli is a professor of electrical and computer engineering at Boston University where he joined the faculty in 1995.

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Torus

In geometry, a torus (plural tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.

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Trapdoor function

A trapdoor function is a function that is easy to compute in one direction, yet difficult to compute in the opposite direction (finding its inverse) without special information, called the "trapdoor".

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Turing completeness

In computability theory, a system of data-manipulation rules (such as a computer's instruction set, a programming language, or a cellular automaton) is said to be Turing complete or computationally universal if it can be used to simulate any Turing machine.

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Turing machine

A Turing machine is a mathematical model of computation that defines an abstract machine, which manipulates symbols on a strip of tape according to a table of rules.

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Turmite

In computer science, a turmite is a Turing machine which has an orientation as well as a current state and a "tape" that consists of an infinite two-dimensional grid of cells.

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Undecidable problem

In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is known to be impossible to construct a single algorithm that always leads to a correct yes-or-no answer.

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Unit interval

In mathematics, the unit interval is the closed interval, that is, the set of all real numbers that are greater than or equal to 0 and less than or equal to 1.

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Universal Turing machine

In computer science, a universal Turing machine (UTM) is a Turing machine that can simulate an arbitrary Turing machine on arbitrary input.

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University of Illinois Press

The University of Illinois Press (UIP) is a major American university press and is part of the University of Illinois system.

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Vertex (geometry)

In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.

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Von Neumann architecture

The von Neumann architecture, which is also known as the von Neumann model and Princeton architecture, is a computer architecture based on the 1945 description by the mathematician and physicist John von Neumann and others in the First Draft of a Report on the EDVAC.

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Von Neumann cellular automaton

Von Neumann cellular automata are the original expression of cellular automata, the development of which were prompted by suggestions made to John von Neumann by his close friend and fellow mathematician Stanislaw Ulam.

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Von Neumann neighborhood

In cellular automata, the von Neumann neighborhood is classically defined on a two-dimensional square lattice and is composed of a central cell and its four adjacent cells.

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Von Neumann universal constructor

John von Neumann's universal constructor is a self-replicating machine in a cellular automata (CA) environment.

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Wang tile

Wang tiles (or Wang dominoes), first proposed by mathematician, logician, and philosopher Hao Wang in 1961, are a class of formal systems.

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Wireworld

Wireworld is a cellular automaton first proposed by Brian Silverman in 1987, as part of his program Phantom Fish Tank.

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Wolfram code

Wolfram code is a naming system often used for one-dimensional cellular automaton rules, introduced by Stephen Wolfram in a 1983 paper and used in his book A New Kind of Science.

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Wolfram Research

Wolfram Research is a private company that creates computational technology.

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World Scientific

World Scientific Publishing is an academic publisher of scientific, technical, and medical books and journals headquartered in Singapore.

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Z3 (computer)

The Z3 was a German electromechanical computer designed by Konrad Zuse.

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Zebra

Zebras are several species of African equids (horse family) united by their distinctive black and white striped coats.

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Applications of cellular automata, Cell games (cellular automaton), Cellular Automata, Cellular Automata machine, Cellular Automaton, Cellular automata, Cellular automata in popular culture, Cellular automata machine, Cellular automota, Cellular autonoma, Cellular image processing, Cellular robotics, Celullar automaton, Fuzzy cellular automata, Fuzzy cellular automaton, Non-totalistic, Seluler Atomatons.

References

[1] https://en.wikipedia.org/wiki/Cellular_automaton

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