Lab / 05
Draw it, then let the circles draw it
The maps in this lab were drawn by chains of spinning arms. Now it is your turn. Draw any closed shape in one stroke, or start from a heart or a star, and the machine turns it into 128 rotating circles that trace it back. Start with one arm and add more until it looks like yours. Save it or share it when it does.
What happens to your stroke
The line you draw is resampled into 128 evenly spaced points and closed back on itself. Each point becomes a complex number, the discrete Fourier transform turns the list into 128 coefficients, and each coefficient is one arm: a circle of a fixed radius turning at a fixed speed. Sorted biggest first, so the first few arms catch the rough shape and the last ones add the wobbles.
With all 128 arms the machine passes through every one of your points, so the error reads exact. The interesting part is how few it needs to be recognisable.
Sharing a drawing
The share link carries the drawing itself, packed into about 500 characters, not a picture of it. Whoever opens it gets the same machine and can turn the arms up and down. The saved image is rendered on the server from the same points.
Try a letter, a cat, or something with a hole in it and watch what one single loop can and cannot do. Then see why South Africa needs two chains.
Maths: the same discrete Fourier transform as the map experiments. Source on GitHub