There are phenomena that do not spread in all directions, but move or “flows” along a given, least-cost path, determined by characteristics of local terrain. The typical case arises when we want to determine drainage patterns in a catchment area: rain water “chooses” a way to leave the area.
We can illustrate the principles involved in this typical case with a simple elevation raster. For each cell in that raster, the steepest downward slope to a neighbour cell is computed and its direction is stored in a new raster. This computation determines the elevation difference between the cell and the neighbour cell and it takes into account cell distance - 1 for neighbour cells in N–S or W–E direction, 2 for cells in a NE–SW or NW–SE direction. From among its eight neighbour cells, it picks the one with the steepest path to it. The directions thus obtained in an output raster are encoded in integer values, which can be called the flow-direction raster. From this raster, the GIS can compute the accumulated flow-count raster, a raster that for each cell indicates how many cells have their water flow into that cell.
Cells with a high accumulated flow count represent areas of concentrated flow and may, thus, belong to a stream. By using some appropriately chosen threshold value in a map algebra expression, we may decide whether they do or not. Cells with an accumulated flow count of zero are local topographic highs and can be used to identify ridges.