A processor includes a decode unit to decode an instruction that is to indicate a source packed data operand to include Morton coordinates, a dimensionality of a multi-dimensional space having points that the Morton coordinates are to be mapped to, a given dimension of the multi-dimensional space, and a destination. The execution unit is coupled with the decode unit. The execution unit, in response to the decode unit decoding the instruction, stores a result packed data operand in the destination. The result operand is to include Morton coordinates that are each to correspond to a different one of the Morton coordinates of the source operand. The Morton coordinates of the result operand are to be mapped to points in the multi-dimensional space that differ from the points that the corresponding Morton coordinates of the source operand are to be mapped to by a fixed change in the given dimension.