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Qu'est-ce (qui) est von Neumann integer - définition

IN CELLULAR AUTOMATA

Von Neumann neighbourhood; Von Neumann neighbohood; Von Neumann neighbor

von Neumann integer

<mathematics> A finite von Neumann ordinal. The von Neumann integer N is a finite set with N elements which are the von Neumann integers 0 to N-1. Thus 0 = } = { 1 = 0 = {} 2 = 0, 1 = {, {}} 3 = 0, 1, 2 = {, {}, {, {}}} ... The set of von Neumann integers is infinite, even though each of its elements is finite. [Origin of name?] (1995-03-30)

John von Neumann Theory Prize

AWARD

John Von Neumann Theory Prize; Von Neumann Theory Prize; John von neumann prize

The John von Neumann Theory Prize of the Institute for Operations Research and the Management Sciences (INFORMS)

https://en.wikipedia.org/wiki/John_von_Neumann_Theory_Prize

von Neumann architecture

COMPUTER ARCHITECTURE

Von Neumann bottleneck; Von Neumann computer; Von Neumann model; Princeton architecture; Von neumann architecture; Von Neumann Model; Stored program concept; Stored-program architecture; Von Neumann style; Non-Von Neumann architecture; Von Neumann computer architecture; Von Neumann Architecture; Non-von Neumann architecture; Neumann architecture; Van Neumann architecture; Von Neuman architecture; Van Neuman architecture

<architecture, computability> A computer architecture conceived by mathematician John von Neumann, which forms the core of nearly every computer system in use today (regardless of size). In contrast to a Turing machine, a von Neumann machine has a random-access memory (RAM) which means that each successive operation can read or write any memory location, independent of the location accessed by the previous operation. A von Neumann machine also has a central processing unit (CPU) with one or more registers that hold data that are being operated on. The CPU has a set of built-in operations (its instruction set) that is far richer than with the Turing machine, e.g. adding two binary integers, or branching to another part of a program if the binary integer in some register is equal to zero (conditional branch). The CPU can interpret the contents of memory either as instructions or as data according to the {fetch-execute cycle}. Von Neumann considered parallel computers but recognized the problems of construction and hence settled for a sequential system. For this reason, parallel computers are sometimes referred to as non-von Neumann architectures. A von Neumann machine can compute the same class of functions as a universal Turing machine. [Reference? Was von Neumann's design, unlike Turing's, originally intended for physical implementation?] von Neumann architecturetevans/VonNeuma.htm">http://salem.mass.edu/von Neumann architecturetevans/VonNeuma.htm. (2003-05-16)

Wikipédia

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 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. It is one of the two most commonly used neighborhood types for two-dimensional cellular automata, the other one being the Moore neighborhood.

This neighbourhood can be used to define the notion of 4-connected pixels in computer graphics.

The von Neumann neighbourhood of a cell is the cell itself and the cells at a Manhattan distance of 1.

The concept can be extended to higher dimensions, for example forming a 6-cell octahedral neighborhood for a cubic cellular automaton in three dimensions.

https://en.wikipedia.org/wiki/Von Neumann neighborhood