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The Mathematics of Chip-Firing

The Mathematics of Chip-Firing is a textbook in mathematics on chip-firing games and abelian sandpile models. It was written by Caroline Klivans, and published in 2018 by the CRC Press.

Network automaton

A network automaton (plural network automata) is a mathematical system consisting of a network of nodes that evolves over time according to predetermined rules. It is similar in concept to a cellular

Wolfram code

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

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

Curtis–Hedlund–Lyndon theorem

The Curtis–Hedlund–Lyndon theorem is a mathematical characterization of cellular automata in terms of their symbolic dynamics. It is named after Morton L. Curtis, Gustav A. Hedlund, and Roger Lyndon;

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 st

Movable cellular automaton

The movable cellular automaton (MCA) method is a method in computational solid mechanics based on the discrete concept. It provides advantages both of classical cellular automaton and discrete element

Information fluctuation complexity

Information fluctuation complexity is an information-theoretic quantity defined as the fluctuation of information about entropy. It is derivable from fluctuations in the predominance of order and chao

Cam-6

The CAM-6 accelerator is a PC-compatible expansion board designed to simulate cellular automata, presenting the output to an IBM CGA display. It was designed by Tommaso Toffoli and Norman Margolus and

A New Kind of Science

A New Kind of Science is a book by Stephen Wolfram, published by his company Wolfram Research under the imprint Wolfram Media in 2002. It contains an empirical and systematic study of computational sy

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. Cellular automa

Asynchronous cellular automaton

Cellular automata, as with other multi-agent system models, usually treat time as discrete and state updates as occurring synchronously. The state of every cell in the model is updated together, befor

Second-order cellular automaton

A second-order cellular automaton is a type of reversible cellular automaton (CA) invented by Edward Fredkin where the state of a cell at time t depends not only on its neighborhood at time t − 1, but

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

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. Using local transition rules, cells ca

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 that surround it.

Mobile automaton

Mobile automaton (plural: mobile automata) within theoretical computer science, is a class of automata similar to cellular automata but which have a single "active" cell instead of updating all cells

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 John von Neumann. The same name may also re

Speed of light (cellular automaton)

In Conway's Game of Life (and related cellular automata), the speed of light is a propagation rate across the grid of exactly one step (either horizontally, vertically or diagonally) per generation. I

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 co

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. Time can also be continuous, and in

Bootstrap percolation

In statistical mechanics, bootstrap percolation is a percolation process in which a random initial configuration of active cells is selected from a lattice or other space, and then cells with few acti

Reversible cellular automaton

A reversible cellular automaton is a cellular automaton in which every configuration has a unique predecessor. That is, it is a regular grid of cells, each containing a state drawn from a finite set o

Cellular automaton

A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homoge

Calculating Space

Calculating Space (German: Rechnender Raum) is Konrad Zuse's 1969 book on automata theory. He proposed that all processes in the universe are computational. This view is known today as the simulation

Surjunctive group

In mathematics, a surjunctive group is a group such that every injective cellular automaton with the group elements as its cells is also surjective. Surjunctive groups were introduced by . It is unkno

Quantum dot cellular automaton

Quantum dot cellular automata (QDCA, sometimes referred to simply as quantum cellular automata, or QCA) are a proposed improvement on conventional computer design (CMOS), which have been devised in an

Lattice gas automaton

Lattice gas automata (LGCA), or lattice gas cellular automata, are a type of cellular automaton used to simulate fluid flows, pioneered by Hardy–Pomeau–de Pazzis and Frisch–Hasslacher–Pomeau. They wer

Von Neumann neighborhood

In cellular automata, the von Neumann neighborhood (or 4-neighborhood) is classically defined on a two-dimensional square lattice and is composed of a central cell and its four adjacent cells. The nei

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