Fractal Coastline & Richardson Effect

Richardson Effect: Lewis Fry Richardson (1961) discovered that the measured length of a coastline depends on the length of the ruler used — longer rulers cut corners and give shorter measurements. Benoit Mandelbrot (1967, "How Long is the Coast of Britain?") formalized this: if L(ε) ~ ε^{1−D}, then plotting log(L) vs log(ε) gives a straight line with slope 1−D, where D is the Hausdorff (fractal) dimension. For the Koch curve, D = log(4)/log(3) ≈ 1.262. Britain's coastline has D ≈ 1.25; Norway's deeply fjorded coast has D ≈ 1.52. Fractals capture the self-similar roughness that makes coastlines "infinitely long" at infinitesimal resolution.