Empirical fractal

There’s a common saying in discussion of fractals that the length of a coastline depends on how small a device you use to measure it. I thought this was a hypothetical, say as applied to the steps in the construction of the Koch snowflake. But the saying has its roots in actually surveying. Lewis Fry Richardson discovered in 1803 that the length of the coast of Scotland depended on a the size of segments used to measure it. And he found that the length followed a power law, i.e. that there’s a linear relation between the log of the coastline length and the log of the ruler length. Here’s a copy of Richardson’s plot, taken from [1]. Richardson’s discovery predated Mandelbrot’s work on fractals by nearly two centuries. Mandelbrot built on Richardson’s observation and defined the idea of fractal dimension. Related posts Minimalist Mandelbrot set The fractal nature of Brownian motion Randomly generated dragon [1] Eoghan Bradley and Mark McCartney. Four hundred years of the fractal…