A cellular automaton is a discrete model studied in computer science, mathematics, physics, complexity science, theoretical biology and microstructure modeling Rule · Gun · Movable cellular automaton · Stochastic cellular automaton. BINOTI, Daniel Henrique Breda et al. Modelagem da distribuição de diâmetros utilizando autômatos celulares e redes neurais artificiais. CERNE [online]. Modelos de autômatos celulares para simulação da dinâmica urbana usualmente não incluem heterogeneidades sociais, típicas do espaço urbano. No intuito.
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Like Ulam's lattice network, von Neumann's cellular automata are automatos celulares, with his self-replicator implemented algorithmically. The result was a universal copier and constructor working within a cellular automaton with a small neighborhood only those cells that touch are neighbors; for von Neumann's cellular automata, only orthogonal cellsand with 29 states per cell.
However their model is not a cellular automaton because the medium in which signals propagate is automatos celulares, and wave fronts are curves. Hastings in ; see Greenberg-Hastings cellular automaton.
Autômato celular de von Neumann – Wikipédia, a enciclopédia livre
The original work of Wiener and Rosenblueth contains many insights and continues to be cited in modern research publications on cardiac arrhythmia and excitable systems. InGustav A. Hedlund compiled many results following this point of view  in what is still considered as a seminal paper for the mathematical study of cellular automata.
The most fundamental result is the characterization in the Curtis—Hedlund—Lyndon theorem of the set of global rules of cellular automata as the automatos celulares of continuous endomorphisms of shift spaces. InGerman automatos celulares pioneer Konrad Zuse published his book Calculating Spaceproposing that the physical laws of the universe are discrete by nature, and that the entire universe is the output of a deterministic computation on a single cellular automaton; "Zuse's Theory" became the foundation of the field of study called digital physics.
Many papers came from this dissertation: He showed the equivalence of neighborhoods of various shapes, how to reduce a Moore to a von Neumann neighborhood or how to reduce any neighborhood to a von Neumann neighborhood.
Invented by John Conway and popularized by Martin Gardner in a Scientific American article,  its rules are as follows: Any live cell with fewer than two live neighbours dies, as if caused by underpopulation. Any live cell with two or three live automatos celulares lives on to the next generation.
Any live automatos celulares with more than three live neighbours dies, as if by overpopulation.
Any dead cell with exactly three live neighbours becomes a live automatos celulares, as if by reproduction. Despite its simplicity, the system achieves an impressive diversity of behavior, fluctuating between apparent randomness and order.
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One of the most apparent features of the Game of Life is the frequent occurrence automatos celulares gliders, arrangements of cells that essentially move themselves across the grid. It is possible to arrange the automaton so that the automatos celulares interact to perform computations, and after much effort it has been shown that the Game of Life can emulate a universal Turing machine.
While earlier automatos celulares in cellular automata tended to try to identify type of patterns for specific rules, Wolfram's classification was the first attempt to classify the rules themselves.
In order of complexity the classes are: Nearly all initial patterns evolve quickly into a stable, homogeneous state. Any randomness in the initial pattern disappears.
Nearly all initial patterns evolve quickly into stable or oscillating structures. Some of the randomness in the initial pattern may filter out, but some remains. Local changes to the initial pattern tend to remain automatos celulares.
Nearly all initial patterns evolve in a pseudo-random or chaotic manner.