Connecting nodes with springs that pull toward a rest length produces force-directed layouts and elastic motion

A spring between two nodes applies a force proportional to how far its current length deviates from a rest length (Hooke’s law): stretched springs pull the nodes together, compressed springs push them apart. Give each node a mass and integrate the accumulated spring forces into velocity and position each frame, adding damping so motion settles. A network of such springs relaxes into a configuration where all rest lengths are best satisfied — the basis of force-directed graph layout and of elastic, cloth-like generative motion. Combining springs (attraction along edges) with global repulsion between all nodes yields readable graph drawings where connected nodes stay near and unconnected ones spread apart.

Examples

M_6_1_02 links two nodes with one spring you can drag; M_6_1_03 extends to many nodes and many springs forming a relaxing mesh. Rest length, stiffness, and damping are the tunable parameters.

Assessment

Explain the role of damping in a spring network and what happens without it. Given three nodes fully connected by equal springs, predict the equilibrium shape they relax into.