dimension exactly 2). He notes that the approximation of these curves with segments of length G have lengths of the form . The resemblance with Richardson's law is striking. The paper does not claim that any coastline or geographic border actually has fractional dimension. Instead, it notes that Richardson's empirical law is compatible with the idea that geographic curves, such as coastlines, can be modelled by random self-similar figures of fractional dimension. Near the end of the paper Mandelbrot briefly discusses how one might approach the study of fractal-like objects in nature that look random rather than regular. For this he defines statistically self-similar figures and says that these are encountered in nature. The paper is important because it is a "turning point" in Mandelbrot's early thinking on fractals. It is an example of the linking of mathematical objects with natural forms that was a theme of much of his later work. See also Coastline paradox List of countries by length of coastline References Mathematics papers Works originally published in Science (journal) Fractals