Random permutations refer to rearranging a set of items or numbers in a completely unpredictable and haphazard manner. It means changing the order of things in a way that is not planned or following any specific rule or pattern. Full definition
An estimate of the nominal p - value was calculated as the fraction of the 1,000 random permutations in which the top pathway gave a larger ES result than that observed in the actual data. (molvis.org)
The show also features a performance piece by Bruce Nauman — a hired actor walks the room as if the ceiling were five feet high, with the public standing outside — along with an arrangement of textured patterns on each wall and a phrase by poet Alfred Starr Hamilton, which gives the show its title and undergoes random permutations by means of an algorithm designed by Robert Pearson, with results displayed on a pile of sheets. (flashartonline.com)
For the mapping function, I'd consider random permutations, and as separate tests, translations & rotations, to preserve the spatial structure of the socio data. (climateaudit.org)