Abstract
A vertical profile of landform looks similar to the one-dimensional Brownian motion trace. It is regarded as a self-affine curve characterized by the Hurst scaling exponent, H (0< H <1). The fractal dimension D e for the pattern of entire contour lines including all islands, and D c for a single contour line can be both calculated from H as D e =2- H and D c =2/(1+ H ). The size distribution of islands follows the power-law (the Korcak's law) with the exponent, ζ, characterized by D e as ζ= D e /2. We confirmed these scaling laws both on computer-simulated landforms and real coastlines, although the former is dependent on the system size and the latter includes disturbing effects of coastal processes. The value of H , which expresses a relief characteristic of the three dimensional self-affine surface such as landform, can be calculated from a horizontal section by these three scaling laws.
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