Arborescence

Arborescence is a mathematical term defined as a directed rooted tree in which all edges point away from the root, with a tree being defined as a connected acyclic graph. Interestingly, Arborescence is also an album (and corresponding title track) by one my favorite progressive rock bands: Ozric Tentacles.

Inspired by this mesmerizing music, I collected several images of actual mathematical arborescences that I have produced for my own scientific work over the years, complemented by beautiful photographs of real trees that I have taken during my many hiking trips.

The mathematical images include several phylogenetic trees, a minimum-cost arborescence embedded in a more general directed acyclic graph, and a bifurcation diagram. A phylogenetic tree usually has undirected edges, but there often is an explicit root (or otherwise one can be chosen arbitrarily), so the edges can be assumed to be directed away from the root. A bifurcation diagram is strictly speaking not an arborescence, but it does resemble a rooted tree (again implicitly directed) when drawn in full detail.

I’ve put all these images and photographs together in a short slideshow together with the title track from the Arborescence album by Ozric Tentacles. Enjoy the show!