Tätheten

Tätheten is a term used in various scientific and analytical contexts to describe a measure of how completely a space, dataset, or material is filled by a particular content or feature. The meaning of Tätheten is context-dependent: in physical sciences it often aligns with traditional density or packing density; in data analysis it may refer to the proportion of non-missing or nonzero entries; in ecology it can describe habitat occupancy. There is no single universal definition, and practitioners specify the precise formulation for their field.

In a general mathematical framing, Tätheten can be viewed as a density-like function ρ_T defined on a domain X with a reference measure μ. For a subregion R ⊂ X, the Tätheten T(R) is often taken as the fraction of R that is occupied, T(R) = μ(A ∩ R) / μ(R), where A denotes the portion of space meeting the filling criterion. In discrete settings, such as datasets, Tätheten equals the ratio of filled elements to total elements.

Applications include materials science (packing efficiency of powders), geology (ore-body fill density), ecology (habitat occupancy), urban planning (land-use fill), and information science (data density). The concept emphasizes scale and context; Tätheten may vary with resolution, orientation, or sampling strategy, and should be reported with the method and units used.

Related notions include density, concentration, filling fraction, and occupancy rate. See also: porosity, saturation, and fill factor.