How Great is Great Britain?

How long is the coastline of Great Britain?

Go on. Have a guess.

It sounds like the sort of question that should have a straightforward answer. Surely someone, at some point, has walked around Britain with a very long tape measure and worked it out.

Unfortunately, the coastline has other ideas.

The problem is that Britain's coast is full of bays, headlands, inlets and innumerable little squiggly bits. Measure it using a fairly large ruler and you'll skip over much of that detail. Use a smaller ruler and suddenly you're measuring around all those extra twists and turns - and Britain's coastline mysteriously gets longer.

This is the Coastline Paradox: the awkward fact that there isn't really one definitive answer to the question How long is the coastline of Great Britain?

In 1967, mathematician Benoit Mandelbrot famously explored exactly this problem in his paper How Long Is the Coast of Britain? His attempts to understand why coastlines reveal ever more complexity the more closely you examine them helped popularize the idea of fractals - shapes and patterns whose complexity can continue to emerge at different scales.

Coastal Paradox lets you explore this geographical and mathematical conundrum for yourself.

The interactive map starts by measuring Great Britain using just 50 measurement points. Draw straight lines between those points (using a very large ruler) and you get one approximation of the coastline. But then things start getting interesting.

As you scroll through the story, the number of measurement points increases - from 50 to 100, then 250, 500 and eventually into the thousands. The measuring line starts following more and more of Britain's coastal wiggles, and the measured coastline keeps growing.

The visualization is built from a GeoJSON outline of Great Britain. Turf js is used to generate evenly spaced measurement points along the coast and calculate the distances between them, while SVG draws the coastline and the increasingly detailed measuring lines.

There's also a free-play mode, where you can choose your own number of measurement points with a slider. Pick a resolution and see for yourself how much longer Britain becomes when you decide to measure it more carefully.

So, how long is the coastline of Great Britain? 

How long is a length of string?