Following Bittner 2011, a spatial region can’t simply be recognized to have a quality like forested or polluted, where the intended meaning is distributed across the region. That is, we expect a forested acre of land to be covered by trees; the discovery of only two small trees on that acre would smack of deceit. So by a distributed quality of a spatial region, we understand that quality to be found throughout most, if not all of the region’s parts.
The problem is, the parts of a region aren’t exactly enumerable – you can always specify finer and finer levels of precision by which to identify parts. It turns out that the precision you end up using goes a long way in determining whether a (distributed) quality is actually present. So we define the presence of a quality in a region with the notion of granularity-sensitive homogeneity: Given a granularity W, a quality Q, and a breakdown of a region R into parts, then R is homogeneous with respect to Q when the area of R is roughly the same size (based on W) as the total area of R‘s sub-regions that have Q.
For example, let’s imagine a big tract of mostly-forested land. We break down that tract into parts (like cells in a raster), and decide for each cell whether we’d consider it forested or not (say, using remote sensing). Turns out that we have a few small ponds on our land that each take up one of our parts/cells. To determine whether we can attribute the quality of being forested to this region, we compare its area to the area of parts/cells that are determined to be forested. The answer depends on the level of precision we use, which is tossed into a simple formula to provide our answer.
Distributed qualities like forested are interesting to contrast with a lot of the commonplace holistic qualities we usually run into, like being electronic, sleepy, or profitable. Distributed qualities depend quite a bit on the qualities of their parts in a way that’s irrelevant to holistic qualities. However, some qualities of spatial regions are neither distributed nor holistic: the quality of being a habitat for badgers depends on processes that relate some parts of a region in a variety of ways.