The Path of a Riderless Bicycle

Credit: Matthew Cook

In 2004, while a graduate student at Caltech, Matthew Cook (PhD ’05) created this evocative illustration that shows various paths a bike with no rider might take before it falls over. Developed as part of a study of how artificial intelligence might learn to ride a bike, the visualization has resurfaced and spread on social media numerous times since its publication.

Each line represents one of 800 simulator runs, each of which ends when the riderless two-wheeler topples. The curves that end in straight segments correspond with paths in which the wheels become horizontal as the bike topples over, which leads to large distances between the points where the wheels touch the ground from instant to instant.

Cook, who recently returned to Caltech as a visiting Moore Distinguished Scholar while on sabbatical from the Institute of Neuroinformatics at the University of Zurich and ETH Zurich, says he receives a flurry of emails about the illustration every few years when it reappears on social media. “Although the segments are visually incongruous with the flowy curves,” he notes, “I still like it because it kind of looks like long hair with split ends.”