Square and hexagonal grids
A grid divides space into cells of equal size and shape, and is used as a set of zones for aggregating data (see Statistical Units for the predefined grids). Only three regular shapes tile a plane: triangles, squares and hexagons. Squares and hexagons are the two in practical use, and the choice between them matters.
Neighbours
In a square grid a cell has two kinds of neighbour: four that share an edge, and four that touch it only at a corner. The corner neighbours are about 1.41 times as far away, centre to centre, as the edge neighbours. Whether two cells are “next to each other” therefore depends on a rule (rook or queen contiguity), and distances along the grid differ by direction.
In a hexagonal grid all six neighbours share an edge with the cell, and all six are at the same distance, centre to centre. There is only one kind of neighbour, so analyses of neighbourhood, movement, connectivity and spatial clustering treat every direction alike.
Shape and edges
A hexagon is closer to a circle than a square is: for the same area it has a shorter boundary, and every point in it is nearer its centre. A cell’s value is then less influenced by what lies in its corners, and fewer points fall near a cell edge. Patterns that do not follow a north–south and east–west direction, such as coastlines, roads and valleys, look less blocky on a hexagonal map.
Why squares are still the standard
- They nest. Four 500 m squares make a 1 km square, and a hundred 1 km squares a 10 km square. Statistics can be published at several resolutions that add up exactly. Hexagons do not nest: a large hexagon cannot be made of small ones.
- They are the official grids. Danmarks Statistik’s grid statistics use the Danish square grid (Det Danske Kvadratnet), and Eurostat’s use the European square grid. Data published on those grids can only be compared with data on the same squares.
- They match rasters. A raster is a square grid; square zones line up with raster cells, hexagons never do.
- A cell can be named from a coordinate. In the Danish grid a cell’s name is its lower-left corner, truncated to the cell size, so any coordinate gives its cell without an overlay.
Choosing
| Question | Grid |
|---|---|
| Results to compare with official statistics or other studies | the predefined square grid (Danish or European), aligned exactly |
| Several resolutions that must add up | square, nested |
| Combining with raster data | square, on the raster’s grid |
| Neighbourhood, movement, connectivity, clustering | hexagon |
| A map whose pattern should not be shaped by the cells | hexagon |
Whichever shape is chosen, its size and origin are choices too: moving the same grid half a cell gives different values (the zoning effect of the Modifiable areal unit problem).