patchesruudukolla

Patchesruudukolla is a concept used in grid-based design, tiling, and image or data partitioning. The Finnish term combines patch with ruudukko (grid) and describes the arrangement, subdivision, or coverage of a grid by smaller units called patches. It can refer to both a practical approach to laying out patches on a grid and a formal framework for analyzing such layouts.

Formal definition: A patch is a finite, connected set of grid cells. A patch layout is a partition of a finite region of the grid into disjoint patches whose union equals the region. Patches are characterized by their shapes, sizes, and attributes, such as color or label. Common requirements include non-overlap, complete coverage, and sometimes additional constraints on contiguity, boundary structure, symmetry, or color distribution.

Variants and constraints: Patches can be simple rectangles, polyominoes, or more irregular shapes. Depending on the application, constraints may specify fixed patch sizes, minimum or maximum areas, or allowable transformations (rotation, reflection). Some frameworks impose hierarchical or multi-scale patching, where patches themselves are subdivided into smaller patches.

Applications: Patch-based tiling supports puzzle design, mosaic art, and quilt planning. It is used in texture atlas creation, image compression, and computer graphics to group pixels into patches for processing. In geographic information systems and game design, patches represent regions or tiles with shared properties, aiding efficient rendering and analysis.

Related concepts include tiling, mosaic art, polyomino tiling, and patch-based coding.