Box-Counting Dimension - Estimated fractal dimension obtained by covering a set with boxes of edge epsilon and measuring how the count N(epsilon) scales as epsilon → 0.
Complex Dimensions - Generalization of the real Hausdorff/box-counting dimension to complex values, used by Lapidus et al. to describe oscillatory geometric and spectral asymptotics of fractal sets.
Differential Box-Counting - Extension of box-counting for grayscale images that partitions the intensity axis to estimate the fractal dimension of textured surfaces.
Fractal Dimension - A real-valued (often non-integer) measure of how the detail of a pattern changes with the scale at which it is measured.
Hausdorff Dimension - Rigorous notion of dimension defined as the infimum of d such that the d-dimensional Hausdorff measure of the set is zero.
Lacunarity - Measure of how a fractal fills space, quantifying gap-size distribution.
Multi-Fractal - Generalization of fractal geometry in which different regions of a set exhibit different local scaling exponents, characterized by a spectrum f(alpha).
Open Set Condition - Separation hypothesis on an iterated function system: there exists a nonempty bounded open set U with the union of the maps' images of U contained in U and those images pairwise disjoint.
Topological Dimension - Integer-valued dimension defined via open covers (Lebesgue covering dimension).