The Never-Ending Coastline

Today's 30DayMapChallenge task is Borgesian Map – a map so detailed it becomes the territory. The challenge takes its inspiration from Jorge Luis Borges' short story On Exactitude in Science, in which cartographers create a map so accurate and detailed that it eventually becomes the same size as the empire it represents.

For my contribution, I've created The Never-Ending Coastline, an interactive map exploring one of cartography's most intriguing curiosities: the coastline paradox.

How long is a coastline? It sounds like a straightforward geographical question, but the answer depends entirely on how closely you look.

My map illustrates this using three different versions of the same stretch of coastline. At the first level, we trace the broad outline, smoothing over small bays, inlets and headlands. Zoom in and we capture more of the shoreline's twists and turns. Zoom in again and we discover yet more detail, producing an even longer coastline.

As you scroll through the map, each successive level reveals a more detailed version of the same shore. The map zooms in as the resolution increases, while the measured coastline grows longer. At each stage, the polyline can be gradually straightened out horizontally, preserving its measured length and making it easy to compare the different results.

The fascinating thing is that all three lines represent exactly the same physical stretch of coastline, with identical starting and ending points. Yet simply by measuring it at different resolutions, we get three different lengths.

This is the coastline paradox. The smaller the measuring stick, the more coastal detail we capture, and the longer our measurement becomes. In an ideal mathematical fractal, this process can continue indefinitely: the coastline has no finite perimeter, even though it encloses a finite area.

And that brings us back to Borges. His fictional cartographers created a map that eventually became as large as the territory itself. My coastline map explores a similar idea: the closer we try to make our representation match the real world, the more detail we have to include – and the longer our map becomes.

This isn't the first time I've mapped this subject. In fact you may even prefer The Coastline Paradox map.