Self-Affine Scaling of Earth's Islands (opens in new tab)

Earth's relief is approximately self-affine, meaning a zoom-in on a small region looks statistically similar to a large region upon a suitable rescaling. Fractional Brownian surfaces give an idealized self-affine model of Earth's relief with one parameter, the Hurst exponent $H$, characterizing the roughness of the surface. To quantitatively assess agreement with Earth elevation data, we compile a large dataset of topographic profiles of islands (N=131,063 with the range of areas covering 8+ ...