# Von Neumann neighborhood > [[PORTAL_Cellular_automaton|Cellular automaton]] spine. ## Microsims — three.js <div class="microsim-player"> <iframe src="https://wikitube-3d-microsims.netlify.app/Von_Neumann_neighborhood_3D.html" width="100%" height="520" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Von Neumann neighborhood — three.js microsim"></iframe> </div> <p class="wt-pending"><strong>Note:</strong> staged, awaiting CDN deploy — one of [[PORTAL_Cellular_automaton]]'s five hand-built three.js stations.</p> Every cellular automaton rule needs a definition of "neighbour," and the Von Neumann neighborhood is one of the two most common choices: the cells within Manhattan (L1) distance r of a given cell — its orthogonal face-neighbours, 2d of them at radius r=1 in d dimensions. It is named for [[John_von_Neumann|John von Neumann]], who used a neighbourhood of this kind in his pioneering work on self-replicating automata. ## Overview The Von Neumann neighbourhood's diamond shape contrasts with the cube-shaped Moore neighbourhood, the other standard choice, which instead takes every cell within Chebyshev (L-infinity) distance r — the full (2r+1)^d − 1 hypercube minus the centre. This build renders a 3D lattice with whichever neighbour set is selected highlighted and connected to the centre cell by lines, so the diamond-versus-cube difference is immediately visible, with a toggle for radius (r=1 or r=2) and for collapsing to a 2D slice versus the full 3D lattice; the HUD shows the live neighbour count next to the closed-form formula for whichever definition is active. The choice of neighbourhood is a design decision baked into every [[Cellular_automaton|cellular automaton]] rule, from the two-neighbour row of an [[Elementary_cellular_automaton|elementary cellular automaton]] to the eight-neighbour Moore grid of [[Conway's_Game_of_Life|Conway's Game of Life]]. **On the spine:** [[Cellular_automaton]] · [[Elementary_cellular_automaton]] · [[Conway's_Game_of_Life]] · [[John_von_Neumann]] · [[Langton's_ant]]. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Von_Neumann_neighborhood) : [Wikitube](https://en.wikitube.io/wiki/Von_Neumann_neighborhood) --- *Repopulated 2026-08-05 · existing three.js asset renamed + wired, Wikipedia-sourced overview · 0 deletions.*