# Dimension Theory

* [Box-Counting Dimension](box-counting-dimension.md) - 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](complex-dimensions.md) - 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](differential-box-counting.md) - Extension of box-counting for grayscale images that partitions the intensity axis to estimate the fractal dimension of textured surfaces.
* [Fractal Dimension](fractal-dimension.md) - 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](hausdorff-dimension.md) - Rigorous notion of dimension defined as the infimum of d such that the d-dimensional Hausdorff measure of the set is zero.
* [Lacunarity](lacunarity.md) - Measure of how a fractal fills space, quantifying gap-size distribution.
* [Multi-Fractal](multi-fractal.md) - 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](open-set-condition.md) - 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](topological-dimension.md) - Integer-valued dimension defined via open covers (Lebesgue covering dimension).