nineregions

Nineregions is a partitioning concept used in spatial analysis and related fields to divide a bounded area into nine distinct regions. The most common arrangement places a central region at the middle with eight surrounding regions arranged in a 3x3 grid.

Construction and variants: The standard method overlays a 3x3 lattice on the domain, yielding nine cells that are typically contiguous and cover the area without overlap. Regions can be defined as equal-sized squares, or boundaries can be adapted to fit irregular geography while preserving the nine-region count. Some uses emphasize the central region as a focal point and study interactions between the core and peripheral regions, while others treat all regions symmetrically.

Applications: Nineregions provides a simple, standardized framework for comparing metrics across zones, testing spatial interaction models, or visualizing data on a compact map. It is used in urban planning, transportation analysis, epidemiology, market research, and education to illustrate partitioning effects and to benchmark algorithms that operate on zonal data.

Limitations and considerations: The choice of boundaries and the grid orientation can substantially influence results. The nine-region partition is not unique; different implementations can yield different conclusions. It is typically sensitive to scale and edge effects, and may be less suitable for highly irregular domains.

See also: 3x3 grid, grid-based partitioning, spatial analysis, zonal statistics.