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A cellular automaton is a self-reproducing system that consists of a collection of interconnected cells. Each cell can be in one of a finite number of states. The cells change state in a synchronous fashion, according to a fixed set of rules. The rules are typically designed to produce interesting patterns or behaviors.

Cellular automata are often used to model complex systems, such as biological systems. They are also used in computer science, for tasks such as image processing and generating fractals.

Cellular automata were first studied by John von Neumann and Stanislaw Ulam in the 1940s. They are a type of automaton, which is a system that can be in one of a finite number of states and that can transition from one state to another according to some fixed rules.

Cellular automata are usually two-dimensional, but they can be three-dimensional or higher-dimensional. The cells are arranged in a grid, and each cell has a certain number of neighbours. The neighbours of a cell are the cells that are adjacent to it.

The state of a cell can be a number, a symbol, or a Boolean value. The number of states that a cell can be in is usually finite, but it can be infinite.

The rules of a cellular automaton determine how the state of a cell changes over time. The rules are usually based on the states of the cell's neighbours. For example, a rule might say that a cell should be in state 0 if its left neighbour is in state 0 and its right neighbour is in state 1.

Cellular automata can be classified according to the number of states they have and the number of neighbours that they have. For example, a two-state cellular automaton with two neighbours is called a two-state, two-neighbour cellular automaton.

Cellular automata can also be classified according to the way in which the states of the cells are updated. For example, a cellular automaton might be synchronous, meaning that all of the cells are updated at the same time, or asynchronous, meaning that the cells are updated in random order.

Cellular automata are used to model a wide variety of systems, including biological systems, physical systems, and social systems.

Cellular automata are particularly well suited for modelling systems that are composed of many small parts that interact with each other. For example, a cellular automaton can be used to model the spread of a disease through a population.

Cellular automata are also used in computer science, for tasks such as image processing and generating fractals.

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