A Universal Law for the ‘Blood of the Earth’

Quanta Magazine contributing correspondent Joshua Sokol explains how geophysicists in the EAPS Rothman group combined mathematical principles with geological data to explain how river networks grow and their shape forms.

About five centuries ago, Leonardo da Vinci surveyed the Arno River, likely for a scheme — devised with Niccolò Machiavelli — to divert the strategically important waterway from Pisa to Florence. Their grand plan never went forward. But at some point in the process, da Vinci envisioned what the entire hydrological system would look like from above.

He sketched the Arno’s main stem, which split into upstream branches. Then those branches themselves branched, and so on, fanning out into small spidery veins that fed the entire network. To da Vinci, this patterning looked suspiciously alive. River networks, he wrote, were a separate circulatory system, one that carried the “blood of the Earth.”

Today, branching river networks still lure would-be explainers, many of whom hope to glimpse some underlying mathematical code responsible for etching out these common patterns.