Fouradjacency

Fouradjacency is a concept used in graph theory, particularly when discussing grids or lattices. It describes a relationship between cells or nodes where two cells are considered adjacent if they share an edge. In a two-dimensional grid, this means a cell has at most four neighbors: one directly above, one directly below, one to its left, and one to its right. This is in contrast to eightadjacency, where cells sharing a corner are also considered adjacent.

The concept of fouradjacency is fundamental in algorithms that operate on grids, such as pathfinding algorithms like Breadth-First Search (BFS) or Dijkstra's algorithm when applied to grid maps. It is also relevant in image processing, cellular automata, and discrete simulations where the state of a cell depends on its immediate neighbors. For instance, in Conway's Game of Life, a cell's survival or birth is determined by the number of living neighbors under the fouradjacency rule. When analyzing a grid, it's important to clarify whether fouradjacency or eightadjacency is being used, as the choice significantly impacts the connectivity and the behavior of algorithms.