Von Neumann cellular automaton

von Neumann cellular automatavon Neumann's CAvon Neumann's cellular automatacellular automataone he usedvon Neumann's cellular automaton
Von Neumann cellular automata are the original expression of cellular automata, the development of which was prompted by suggestions made to John von Neumann by his close friend and fellow mathematician Stanislaw Ulam.wikipedia
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Cellular automaton

cellular automataCACell games (cellular automaton)
Von Neumann cellular automata are the original expression of cellular automata, the development of which was prompted by suggestions made to John von Neumann by his close friend and fellow mathematician Stanislaw Ulam.
Like Ulam's lattice network, von Neumann's cellular automata are two-dimensional, with his self-replicator implemented algorithmically.

Nobili cellular automata

Nobili's cellular automaton
Nobili's cellular automaton is a variation of von Neumann's cellular automaton, augmented with the ability for confluent cells to cross signals and store information.
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.

Langton's loops

Chou–Reggia loopEvoloopLangton loop
Hutton's cellular automaton is yet another variation, which allows a loop of data, analogous to Langton's loops, to replicate.
In 1968 Edgar F. Codd reduced the number of states from 29 in von Neumann's CA to 8 in his.

John von Neumann

von NeumannJ. von NeumannNeumann, John von
Von Neumann cellular automata are the original expression of cellular automata, the development of which was prompted by suggestions made to John von Neumann by his close friend and fellow mathematician Stanislaw Ulam.
Subsequently, the concept of the Von Neumann universal constructor based on the von Neumann cellular automaton was fleshed out in his posthumously published lectures Theory of Self Reproducing Automata.

Von Neumann neighborhood

orthogonally adjacentVon Neumann neighbourhoodneighborhood
As von Neumann's cellular automaton was the first example to use this arrangement, it is known as the von Neumann neighbourhood.
The neighborhood is named after John von Neumann, who used it to define the von Neumann cellular automaton and the von Neumann universal constructor within it.

Von Neumann universal constructor

universal constructorself-replicating machinesconstruction
Their original purpose was to provide insight into the logical requirements for machine self-replication, and they were used in von Neumann's universal constructor.
The one he used consists of a two-dimensional grid of cells, each of which can be in one of 29 states at any point in time.

Codd's cellular automaton

Codd's automatonhisHis design for a self-replicating computer
It was designed to recreate the computation- and construction-universality of von Neumann's CA but with fewer states: 8 instead of 29.

Stanislaw Ulam

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

Self-replicating machine

Clanking replicatorself-replicatingself-replicating machines
Their original purpose was to provide insight into the logical requirements for machine self-replication, and they were used in von Neumann's universal constructor.

Finite-state machine

finite state machinestate machinefinite automata
In general, cellular automata (CA) constitute an arrangement of finite state automata (FSA) that sit in positional relationships between one another, each FSA exchanging information with those other FSAs to which it is positionally adjacent.

Regular grid

Cartesian gridrectilinear gridstructured grid
In von Neumann's cellular automaton, the finite state machines (or cells) are arranged in a two-dimensional Cartesian grid, and interface with the surrounding four cells.

Bifurcation theory

bifurcationbifurcationsbifurcation point
Therefore, the transition/sensitised states can be thought of as the nodes of a bifurcation tree leading from the ground-state to each of the quiescent transmission and confluent states.

Computational sociology

computational social sciencecomputationalcomputationally
In the post-war era, Vannevar Bush's differential analyser, John von Neumann's cellular automata, Norbert Wiener's cybernetics, and Claude Shannon's information theory became influential paradigms for modeling and understanding complexity in technical systems.

Cybernetics

cyberneticcyberneticiancybernetically
In the early 1940s John von Neumann contributed a unique and unusual addition to the world of cybernetics: von Neumann cellular automata, and their logical follow up, the von Neumann Universal Constructor.