Lab / 02
Denmark needs fifteen machines
Norway gets one Fourier series. Denmark is a peninsula and a pile of islands, so it gets 15 separate chains of spinning arms, all hanging off the same hub in the Kattegat-ish middle of the country and all drawing at the same time. Jutland does the heavy lifting. Anholt does very little, but it does it beautifully.
One series per landmass
A Fourier series is a single closed loop, so every island needs its own. Each outline is sampled as evenly spaced points, turned into complex numbers, and run through a discrete Fourier transform. The coefficients become arms, sorted longest first.
The first arm of every chain is the long straight one from the hub to the middle of that island. That is why the drawing looks like a starburst before any coast appears. Small islands only have 64 sample points, so they top out at 64 arms - turn N up and Jutland keeps improving while Fanø is already done.
Which islands
This map knows fifteen landmasses.
Denmark has more than 400 named islands. The 1:10m world map used here only knows these fifteen - Falster is not on it at all, and most of the South Funen archipelago is missing. Which is a nice lead-in to the coastline paradox: how much Denmark there is depends on how closely you look.
Outline data: Natural Earth 1:10m (public domain). Source on GitHub