  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.
