Generalized Jeans-like Gravitational Term in a Nodes Universe Simulation

In classical astrophysics, the Jeans instability describes the conditions under which a homogeneous gas cloud becomes gravitationally unstable and collapses to form structures such as stars. Here, we extend this concept to a nodes universe simulation, where matter and energy are represented as interconnected nodes following universal laws. We define a Jeans-like gravitational term Ji that generalizes classical gravitational collapse to a network of energy nodes, with a specific pairwise coupling function f(ρi, ρj, dij) = Gijρiρj / dij² and an effective propagation speed cs derived from node coupling parameters. A linear stability analysis yields a critical node spacing λJ,i analogous to the classical Jeans length. This framework allows the study of structure formation, clustering, and instability dynamics in systems governed by inter-node interactions.