The Abelian Sandpile generates complex and beautiful patterns and seems to
display allometry. On the plane, beyond patches, patterns periodic in both
dimensions, we remark the presence of structures periodic in one dimension,
that we call strings. We classify completely their constituents in terms of
their principal periodic vector k, that we call momentum. We derive a simple
relation between the momentum of a string and its density of particles, E,
which is reminiscent of a dispersion relation, E=k^2. Strings interact: they
can merge and split and within these processes momentum is conserved. We reveal
the role of the modular group SL(2,Z) behind these laws.Comment: 4 pages, 4 figures in colo
