A note on the optimal labelling of quadtree nodes

Methods of labelling quadtree nodes by extended quaternary numbers are discussed. It is shown that a fixed bit-length technique requires only 2n+1 bits to represent any node in a depth n quadtree. A technique using exactly that number of bits is described. A more useful extension, requiring 2n+2 bits, is compared with the best technique previously published, which typically requires 2n+4 bits.