Abstract: A highly scalable cluster of computing nodes simulates large numbers of objects interacting in a space defined by an octree of cubical elements. Each cube of the octree is enclosed within a corresponding padding sphere. Interacting objects are quickly identified by determining which of the padding spheres are candidate spheres that satisfy an interaction criterion, considering candidate objects located in the cubes that correspond to the candidate spheres, and determining which of the candidate objects meet the interaction criterion. The computing workload can be efficiently parallelized among nodes of the cluster by assigning the objects to the nodes in approximately equal numbers, each node being responsible for managing the objects assigned thereto. Inter-node data traffic can be minimized by reassigning frequently interacting objects to the same node. The cluster can be scaled simply by adding more nodes to the cluster, and redistributing the objects equally among the nodes.