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within it. It is one of the two most commonly used neighborhood types for two-dimensional cellular automata, the other one being the
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An extension of the simple von
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and is composed of a central cell and its four adjacent cells. The neighborhood is named after
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The concept can be extended to higher dimensions, for example forming a 6-cell
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The von
Neumann neighbourhood of a cell is the cell itself and the cells at a
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122:. The number of cells in a 2-dimensional von Neumann neighborhood of range
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Historical
Encyclopedia of Natural and Mathematical Sciences, Volume 1
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neighborhood for a cubic cellular automaton in three dimensions.
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Cellular automaton neighborhood consisting of four adjacent cells
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Cellular
Automata Machines: A New Environment for Modeling
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Handbook of
Computer Vision Algorithms in Image Algebra
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This neighbourhood can be used to define the notion of
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205:-dimensional von Neumann neighborhood of range
182:-dimensional von Neumann neighborhood of range
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47:) is classically defined on a two-dimensional
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515:Replicator
495:Oscillator
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254:Chain code
93:octahedral
530:Spaceship
510:Reflector
400:MathWorld
688:LifeWiki
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563:Highlife
520:Sawtooth
280:(1987),
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59:and the
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