Fractal Art

The inimitable 3Blue1Brown does a far better job illustrating space filling curves than I ever could, take a look [youtube]. Just the first 15 seconds of the video is enough to get a sense of what a space filling curve is: a simple rule applied to a line segment that results in self-similar geometry that fills a 2D space.

The pattern presented here is a Moore curve. It is one continuous line that snakes its way all over the space and returns to its starting point. The line slowly changes colour along its length, which creates the appearance of distinct regions when viewed from afar.

Keen-eyed readers may have noticed that this is also this website's icon.

Technical Notes

This work was produced using Python, numpy and matplotlib were used for generating the curve and plotting. The palette is matplotlib's built-in "twilight" color map.