The coastline paradox

The #coastline #paradox demonstrates that coastline length is not a fixed value but scale-dependent, a phenomenon rooted in fractal geometry. A new BBC article takes an interesting deep dive and, among other things, explores who first documented this paradox, and why – and why it matters.
Author

Ralph Straumann

Published

June 12, 2026

How long is it?

Maybe you have encountered the coastline paradox before. It basically states that a coastline appears longer the more finely you measure it. In other words, the length of a coastline is not well-defined, but scale-dependent.

I vividly remember reading about this phenomenon for the first time in a section about fractal dimensions1 in O’Sullivan and Unwin’s “Geographic Information Analysis” 2 during my studies.

Measuring a curve using rulers

Now, the BBC have an in-depth and very interesting article about the phenomenon. I learned quite some new aspects about this paradox, among others who encountered and documented it for the first time and why. Interesting stuff!

Footnotes

  1. Another concept that tends to show up in this context is that of space-filling curves, such as the Hilbert curve, often used in spatial indexing. It’s all connected!↩︎

  2. Recommended!↩︎