The Golden Ratio and the Entropy of Braids

Here’s a cute connection between topological entropy, braids, and the golden ratio. I learned about it in this paper:

• Jean-Luc Thiffeault and Matthew D. Finn, Topology, braids, and mixing in fluids.

Topological entropy

I’ve talked a lot about entropy on this blog, but not much about topological entropy. This is a way to define the entropy of a continuous map from a compact topological space to itself. The idea is that a map that mixes things up a lot should have a lot of entropy. In parti...