Pseudocode
Each node has x,y position and dx,dy velocity and mass m. There is usually a spring constant, s, and damping: 0 < damping < 1. The force toward and away from nodes is calculated according to Hooke's Law and Coulomb's law or similar as discussed above. The example can be trivially expanded to include a z position for 3D representation.
set up initial node velocities to (0,0) set up initial node positions randomly // make sure no 2 nodes are in exactly the same position loop total_kinetic_energy := 0 // running sum of total kinetic energy over all particles for each node net-force := (0, 0) // running sum of total force on this particular node for each other node net-force := net-force + Coulomb_repulsion( this_node, other_node ) next node for each spring connected to this node net-force := net-force + Hooke_attraction( this_node, spring ) next spring // without damping, it moves forever this_node.velocity := (this_node.velocity + timestep * net-force) * damping this_node.position := this_node.position + timestep * this_node.velocity total_kinetic_energy := total_kinetic_energy + this_node.mass * (this_node.velocity)^2 next node until total_kinetic_energy is less than some small number // the simulation has stopped moving
Read more about this topic: Force-based Algorithms (graph Drawing)