It's not just a beautiful concept, they have other uses too. It turns out some patterns can be pretty efficient for search if there is a spatial movement cost.

Some questions that interest me:

1. Can you get these search patterns as part of an emergent behaviour?

2. Can multiple searchers work together in order to produce these patterns efficiently?

3. Instead of searching linear 2D and 3D space, what if you want to search non-linear spaces?