von Neumann neighborhood
E656652
The von Neumann neighborhood is a grid-based notion of adjacency in cellular automata and lattice models where each cell interacts only with the four orthogonally adjacent cells (up, down, left, right).
All labels observed (1)
| Label | Occurrences |
|---|---|
| von Neumann neighborhood canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7337921 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: von Neumann neighborhood Context triple: [Moore neighborhood, contrastedWith, von Neumann neighborhood]
-
A.
Game of Life
Game of Life is a famous cellular automaton devised by mathematician John H. Conway that simulates complex patterns and behaviors using simple grid-based rules.
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B.
Langton
Langton is an English surname historically associated with notable figures such as medieval church leaders and scholars.
-
C.
NKS
NKS is the ICAO airline designator used in aviation to identify Spirit Airlines in flight operations and air traffic control.
-
D.
Ulam spiral
The Ulam spiral is a graphical arrangement of the positive integers in a spiral pattern that reveals striking diagonal alignments of prime numbers, suggesting unexpected structure in their distribution.
-
E.
ConwayLife.com
ConwayLife.com is a dedicated online hub for enthusiasts of Conway's Game of Life, featuring forums, pattern collections, tools, and discussions about cellular automata.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: von Neumann neighborhood Target entity description: The von Neumann neighborhood is a grid-based notion of adjacency in cellular automata and lattice models where each cell interacts only with the four orthogonally adjacent cells (up, down, left, right).
-
A.
Game of Life
Game of Life is a famous cellular automaton devised by mathematician John H. Conway that simulates complex patterns and behaviors using simple grid-based rules.
-
B.
Langton
Langton is an English surname historically associated with notable figures such as medieval church leaders and scholars.
-
C.
NKS
NKS is the ICAO airline designator used in aviation to identify Spirit Airlines in flight operations and air traffic control.
-
D.
Ulam spiral
The Ulam spiral is a graphical arrangement of the positive integers in a spiral pattern that reveals striking diagonal alignments of prime numbers, suggesting unexpected structure in their distribution.
-
E.
ConwayLife.com
ConwayLife.com is a dedicated online hub for enthusiasts of Conway's Game of Life, featuring forums, pattern collections, tools, and discussions about cellular automata.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
concept in cellular automata theory
ⓘ
local neighborhood structure ⓘ neighborhood (cellular automata) ⓘ |
| canBeExtendedTo | higher-dimensional lattices ⓘ |
| contrastsWith | Moore neighborhood ⓘ |
| correspondsTo | 4-connectedness in digital topology ⓘ |
| definedOn |
regular grid
ⓘ
square lattice ⓘ |
| excludesAdjacencyType | diagonal adjacency ⓘ |
| generalizesTo | von Neumann neighborhood of radius r ⓘ |
| hasAdjacencyType | orthogonal adjacency ⓘ |
| hasAlternativeName | 4-neighborhood ⓘ |
| hasCardinality | 4 (in 2D, radius 1) ⓘ |
| hasDimension | 2 (standard case) ⓘ |
| hasFewerNeighborsThan | Moore neighborhood (in 2D, radius 1) ⓘ |
| hasGraphTheoreticInterpretation | neighbors in the 2D grid graph ⓘ |
| hasNeighborDirection |
down
ⓘ
left ⓘ right ⓘ up ⓘ |
| hasRadius | 1 (standard definition) ⓘ |
| hasSymmetryGroup | dihedral group of the square (D4) in 2D ⓘ |
| inducesMetric | Manhattan distance (L1 metric) ⓘ |
| inHigherDimensionsHasCardinality | 2d (for dimension d, radius 1) ⓘ |
| isCommonDefaultIn | early cellular automata models ⓘ |
| isIsotropicWithRespectTo | Manhattan distance ⓘ |
| isLocal | true ⓘ |
| isSubsetOf |
Moore neighborhood (for same radius in 2D)
ⓘ
linked to:
Chebyshev distance (L-infinity metric)
|
| isTranslationInvariantOn | regular lattices ⓘ |
| namedAfter | John von Neumann ⓘ |
| usedFor |
defining connectivity in grid graphs
ⓘ
defining local update rules in cellular automata ⓘ modeling diffusion on grids ⓘ modeling nearest-neighbor interactions ⓘ |
| usedIn |
Ising model on a square lattice (nearest-neighbor version)
ⓘ
linked to:
Ising models
cellular automata ⓘ discrete dynamical systems ⓘ grid-based simulations ⓘ image processing ⓘ lattice gas automata ⓘ lattice models ⓘ percolation theory ⓘ reaction-diffusion cellular automata ⓘ statistical mechanics models ⓘ |
| wasIntroducedInContextOf | von Neumann’s work on self-reproducing automata ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: von Neumann neighborhood Description of subject: The von Neumann neighborhood is a grid-based notion of adjacency in cellular automata and lattice models where each cell interacts only with the four orthogonally adjacent cells (up, down, left, right).
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.