As a conclusion, the results presented here can
be interpreted as a kind of "uniform tiling" by digits.
The uniformity would be defined by the symmetries. The
shapes of tiles would be the values of the digits.
The decomposed digit-matrices can cover 
-plane
periodically. We can crop any 
-matrix from the
covered plane so as to satisfy the "pan-magic square condition".
Some pair of such digit-matrices gives pan-magic square.
In the case of usual shape-tiling, we have limited set of tiles
which can cover the two dimensional plane. Then, does such limited
set exist in the case of number-tiling?
For example, 4m+2-perfect magic square does not exist.
Can we find other conditions for the "shape" of number-tiles?