It goes much further into the mathematics than I did, and probably much further than I could (even if I tried). The Slartibartfast opening is difficult to beat.
I respectfully submit that Mandelbrot probably did not really expect infinity. That might be the answer for a mathematical fractal, but for a physical thing such as an island, the fractal self-similarity breaks down when you get down the scale of individual atoms (or before that). A completely separate issue is that the length of a coastline cannot even *have* a definite value, even in principle. Say you define the coast as the outer-most point with an altitude of the mean sea level at that point. Every time a grain of sand shifts by a fraction of an angstrom, which is constantly, the length of the "coastline" changes. One cannot measure something with a greater precision than the thing possesses. Of course the 'coast' used to define territorial waters and economic zones is merely defined by official charts with special rules for islands and inlets and such.
You wrote that Richardson wrote in 1961… but he died in 1953 (see https://en.wikipedia.org/wiki/Lewis_Fry_Richardson)
Thanks for the catch! You're absolutely right: Richardson died in 1953, and the article was published posthumously in 1961.
I've already corrected the text to make that clear.
Sorry. Wasn’t trying to be adversarial.
Fry Richardson is a hero of mine
See https://craigavad.org/2026/01/09/where-do-weather-forecasts-come-from-and-why-are-they-sometimes-so-wrong/
No! The comment was greatly appreciated! I rather be corrected in time than just keep going with the mistake. :)
Here’s a discussion of this topic that I wrote a few weeks ago
https://craigavad.org/2026/05/09/how-long-is-a-coastline-well-it-all-depends/
Thanks for sharing this, it is a great piece!
It goes much further into the mathematics than I did, and probably much further than I could (even if I tried). The Slartibartfast opening is difficult to beat.
I respectfully submit that Mandelbrot probably did not really expect infinity. That might be the answer for a mathematical fractal, but for a physical thing such as an island, the fractal self-similarity breaks down when you get down the scale of individual atoms (or before that). A completely separate issue is that the length of a coastline cannot even *have* a definite value, even in principle. Say you define the coast as the outer-most point with an altitude of the mean sea level at that point. Every time a grain of sand shifts by a fraction of an angstrom, which is constantly, the length of the "coastline" changes. One cannot measure something with a greater precision than the thing possesses. Of course the 'coast' used to define territorial waters and economic zones is merely defined by official charts with special rules for islands and inlets and such.