Why we Use Hexagonal grids

Hexagons VS square grids.

Why is the HomeLand based on Hexagons and not square grids?
Why we use hexagonal grids

Hexagons vs square grids

Why is the HomeLand based on hexagons and not square grids?
  • Reduced edge effects: a hexagonal grid gives the lowest perimeter to area ratio of any regular tessellation of the plane. In practice, this means that edge effects are minimized when working with hexagonal grids. This is essentially the same reason beehives are built from hexagonal honeycomb: it is the arrangement that minimizes the amount of material used to create a lattice of cells with a given volume.
  • All neighbors are identical: square grids have two classes of neighbors, those in the cardinal directions that share an edge and those in diagonal directions that share a vertex. In contrast, a hexagonal grid cell has six identical neighboring cells, each sharing one of the six equal-length sides. Furthermore, the distance between centroids is the same for all neighbors.
  • Hexagons reduce sampling bias: due to edge effects of the grid shape, this is related to the low perimeter-to-area ratio of the shape of the hexagon. A circle has the lowest ratio but cannot tessellate to form a continuous grid. Hexagons are the most circular-shaped polygon that can tessellate to form an evenly spaced grid.
  • Finding neighbors is more straightforward: since the edge or length of contact is the same on each side, the centroid of each neighbor is equidistant. However, with a fishnet grid, the Queen's Case (above/below/right/left) neighbor's centroids are N units away, while the centroids of the diagonal (Rook) neighbors are farther away (exactly the square root of 2 times N units away).
  • Represents curves naturally: the circularity of a hexagon grid allows it to represent curves more naturally than square grids
  • Natural connectivity and movement: hexagons are preferable when the system includes aspects of connectivity or movement paths
  • Any point closer to the centroid: When comparing polygons with equal areas, the more similar to a circle the polygon is, the closer to the centroid the points near the border are (especially points near the vertices). This means that any point inside a hexagon is closer to the centroid of the hexagon than any given point in an equal-area square or triangle would be (this is due to the more acute angles of the square and triangle versus the hexagon).
  • Easily understood: due to the linear nature of rectangles, fishnet grids can draw our eyes to the straight, unbroken, parallel lines which may inhibit the underlying patterns in the data. Hexagons tend to break up the lines and allow any curvature of the patterns in the data to be seen more clearly and easily. This breakup of artificial linear patterns also diminishes any orientation bias that can be perceived in fishnet grids.
  • Less distortion: when working over a large area, a hexagon grid will suffer less distortion due to the curvature of a circular land than the shape of a fishnet grid.
  • Hexagons look naturally awesome!