neliöruudukkoon

Neliöruudukkoon is the illative form of neliöruudukko in Finnish, used to indicate direction or destination of movement into a square grid. A neliöruudukko, or square grid, is a regular tiling of the plane by congruent squares created by vertical and horizontal lines that intersect at right angles. The intersections form lattice points, and the smallest repeating unit is a single square cell. In many contexts the grid is analyzed as a graph where grid points or cell centers are vertices and grid lines are edges.

In two dimensions, a square grid can be described by integer coordinates. Each cell occupies a unit square, and adjacent cells share a side. The most common connectivity is 4-neighborhood (up, down, left, right), though some models use 8-neighborhood (including diagonals). Distances on a square grid are often measured by Manhattan distance, which counts the minimum number of orthogonal moves between two points. Grids can be finite, with a defined width and height, or infinite, extending without bound. Variants include toroidal grids, where opposite edges are connected to form a surface without boundaries.

Applications of neliöruudukko or square grids span several fields. In mathematics and computer science, they serve as discretizations of continuous spaces for simulations, pathfinding algorithms like A* or Dijkstra, and graph-theoretic studies. In computer graphics and image processing, grids represent pixel arrays and raster data. In games and robotics, square grids underpin movement, obstacle avoidance, and spatial reasoning. The concept also underpins coordinate systems and spatial indexing in various computational tasks.

See also: neliöruudukko, grid graph, lattice, pixel, coordinate system.