Extended Data Fig. 2: Geometric theory for surface habitats.
From: A geometric basis for surface habitat complexity and biodiversity
a, Schematic showing mean height variation as a function of scale. ΔH is the height range of the habitat surface for the extent L. ΔH0 is the mean height range of the surface at the smallest scale: the resolution L0. The two slopes S represent fractal dimensions D of 2 and 3 according to Eq. 2. For example, high D results when mean height ranges at the scale of the grain are large (that is, in the vicinity of ΔH), suggesting a highly convoluted surface. Conversely, low D occurs when mean height variations at the scale of the grain are very small, suggesting an approximately flat surface. b, Area A0 at the scale of the grain L0 is calculated as the minimum surface area given the mean height range at this scale.
