New methods for estimating fractal dimensions of coastlines

A coastline is an example of a statistically self-similar fractal. A standard characterization walks a ruler of fixed size along the coast and estimates fractal dimension from the power-law relationship between length and ruler size. Multiple intersection can lead to ambiguity in choosing the next step. The standard method always chooses the first intersection along the curve. Variations were developed to choose intersections which highlight geographic properties. The land method measures accessibility to the coast from land at each size while the water method probes water access. Measurements on sections of the East and West Coasts of the United States typically showed the land length exceeding water. Jumps in water length as step size decreased were often caused by narrow rivers or bays which have few corresponding land features. Simple recursive constructions were inadequate to model this asymmetry.