People walk where others have walked before, and the footpath network designs itself
A park with no paved walkways develops a clear network of worn trails over weeks. Nobody designs them.
Each pedestrian trades off the shortest geometric path against the already-worn trail, which is firmer and faster. Worn trails win more often, get worn more, and win more often still — the feedback loop that makes desire paths.
Dirk Helbing's "active walker" framework: each pedestrian lays down wear, and subsequent walkers prefer worn ground over grass. A single parameter — path preference — sets the balance between shortcut-seeking and trail-following.
Low path preference makes walkers beeline, scattering faint marks. High preference collapses traffic onto a few trunk routes with branches near destinations. The middle produces efficient, natural-looking networks.
Figure 1. Pedestrians pick destinations and walk. Trail intensity accumulates with each crossing. Higher path preference means walkers deviate more toward worn ground. Trail coverage measures the fraction of ground with significant wear.
A path used by 10 attracts the 11th more strongly than a path used by 2, so small early fluctuations get amplified. Reset and the exact layout differs, but the overall structure does not.
Early walkers take wandering routes because there are few trails to compromise with. As the network matures, the trail-to-straight-line ratio drops toward 1.0.
Nobody optimized the network. Each walker optimized only their own next step. The aggregate is a nearly optimal transport graph.
Figure 2. Ratio of trail distance to straight-line distance, averaged over sliding windows of 10 pedestrians. As the network matures, the ratio approaches 1.0. Spikes correspond to walkers headed to distant destinations where detours along trunk trails cost more.
Add a new destination and new branches sprout to reach it. The existing network stays mostly intact and acts as scaffolding for the new connections.
Click anywhere on the field to drop a destination where you want, or use the button for a random one
Figure 3. A new destination forces new trail branches to grow. The existing network acts as scaffolding: new paths often branch off old ones rather than cutting entirely new routes.
Some campus planners wait a year before paving walkways on a new quad — they let students wear desire paths into the grass, then pave those. Michigan State, Virginia Tech, and the University of Oregon have all used the approach.