We show that multiple filamentation patterns in high-power laser beams, can be described by means of two statistical physics concepts, namely self-similarity of the patterns over two nested scales, and nearest-neighbor interactions of classical rotators. The resulting lattice spin model perfectly reproduces the evolution of intense laser pulses as simulated by the Non-Linear Schr"odinger Equation, shedding a new light on multiple filamentation. As a side benefit, this approach drastically reduces the computing time by two orders of magnitude as compared to the standard simulation methods of laser filamentation.