  This survey addresses pluri-periodic harmonic functions on lattices with
values in a positive characteristic field. We mention, as a motivation, the
game "Lights Out" following the work of Sutner, Goldwasser-Klostermeyer-Ware,
Barua-Ramakrishnan-Sarkar, Hunzikel-Machiavello-Park e.a.; see also 2 previous
author's preprints for a more detailed account. Our approach explores harmonic
analysis and algebraic geometry over a positive characteristic field. The
Fourier transform allows us to interpret pluri-periods of harmonic functions on
lattices as torsion multi-orders of points on the corresponding affine
algebraic variety.
