Figure 8.

Explanation of upwards complexity. The color gradient indicates height. (A) To study upwards complexity, we slide a horizontal plane downwards. If we denote by X_h the part of the tree that sits above the horizontal plane at distance h from the top of the image, then ${\mathit{X}}_{\mathit{h}}\subseteq {\mathit{X}}_{\mathit{h}\text{'}}$ whenever $\mathit{h}\le {\mathit{h}}^{\prime }$, obtaining a sequence of nested graphs approximating the bronchial tree more accurately as we increase h. (B) The right part of the panel shows the degree-0 barcode of the sequence of nested graphs in (A). In this picture, the correspondence between bars in the barcode and branches that change trajectory upwards becomes apparent. In particular, the length of a bar indicates for how long a branch follows that upwards trajectory.