De Bruijn Sequence - de Bruijn Torus

De Bruijn Torus

A De Bruijn torus is a toroidal array with the property that every k-ary m-by-n matrix occurs exactly once. (It is not necessary that the array be expressed toroidally; the array can be mapped into a 2-dimensional array. Because it is toroidal it "wraps around" on all 4 sides.)

Such a pattern can be used for two-dimensional positional encoding in a fashion analogous to that described above for rotary encoding. Position can be determined by examining the m-by-n matrix directly adjacent to the sensor, and calculating its position on the De Bruijn torus.