This discussion inspired me to look a little more closely at the short-range project. Here is what I have come up with so far:

31 short-range pieces

I will briefly look at 31 possible 1-2 square short range pieces that are on a square board. Basically, here is an ASCII diagram of the five possible places where a given piece may or may not be allowed to move:

3 2 1 2 3
2 5 4 5 2
1 4 . 4 1
2 5 4 5 2
3 2 1 2 3

1 is the Dababa; 2 is the Knight; 3 is the Alfil (Interesting fact: 'Alfil' is the Spanish word for what we call a Bishop); 4 is the wazir; and 5 is the ferz.

Here is a look at all 31 combinations of these possible moves, or, if you will, 'atom' pieces:

D N A W F

1 2 3 4 5       Name                                            Colorbound
N N N N Y       Ferz                                            2-way
N N N Y N       Wazir                                           No
N N N Y Y       Guard; Commoner                                 No
N N Y N N       Alfil                                           8-way
N N Y N Y       Alfil-Ferz                                      2-way
N N Y Y N       Waffle; Phoenix                                 No
N N Y Y Y       Guard + Alfil                                   No
N Y N N N       Knight                                          No
N Y N N Y       Knight + Ferz (Augmented knight)                No
N Y N Y N       Knight + Wazir (Augmented knight); Vicar        No
N Y N Y Y       Crowned Knight; Centaur                         No
N Y Y N N       Knight + Alfil (Augmented knight)               No
N Y Y N Y       High Priestess                                  No
N Y Y Y N       Alfil Knight Wazir                              No
N Y Y Y Y       Crowned Knight + Alfil                          No
Y N N N N       Dababa                                          4-way
Y N N N Y       Ferz + Dababa                                   2-way
Y N N Y N       Woody rook                                      No
Y N N Y Y       Guard + Dababa                                  No
Y N Y N N       Alibaba; Deacon                                 4-way
Y N Y N Y       Alibaba + Ferz                                  2-way
Y N Y Y N       Alibaba + Wazir                                 No
Y N Y Y Y       Mastodon                                        No
Y Y N N N       Knight + Dababa (Augmented knight)              No
Y Y N N Y       Knight + Dababa + Ferz                          No
Y Y N Y N       Minister                                        No
Y Y N Y Y       Minister + Ferz                                 No
Y Y Y N N       Squirrel                                        No
Y Y Y N Y       Squirrel + Ferz                                 No
Y Y Y Y N       Squirrel + Wazir                                No
Y Y Y Y Y       Lion                                            No

The power of these pieces depends on the size of board we are using. The Alfil is clearly the weakest piece; probably worth less than a pawn. The Lion is clearly the most powerful piece; probably worth about two queens. Seven of the pieces are colorbound; an 8-way colorbound piece needs eight of the piece to cover the entire board, a 4-way colorbound piece four pieces to cover the board, and a 2-way colorbound piece needs two pieces to cover the board (such as the Bishop in FIDE chess). There is one 8-way colorbound piece (the Alfil), two 4-way colorbound pieces, and four 2-way colorbound pieces in our mix. The other 24 possible pieces are not colorbound.

The pinwheel piece

You may observe that the knight is a unique 'atom'; all other four 'atoms' can move four squares; the knight can move eight squares. One possible way to divide up the knight in to two 'subatomic' pieces is to make what I call 'pinwheel' pieces. There are two possible pinwheel pieces; the two pinwheel pieces combined make a knight. Here is a diagram of the 'left-handed pinwheel':

. X . . .
. . . . X
. . * . .
X . . . .
. . . X .

And the 'right-handed pinwheel':

. . . X .
X . . . .
. . * . .
. . . . X
. X . . .

In other words, the 'left-handed pinwheel' can, from e4, go to d6, g5, f2, and c3. The 'right-handed pinwheel' can, from e4, go to f6, g3, d2, and c5.

Each 'pinwheel' piece is 5-way colorbound; you need 5 pinwheel pieces to cover every square on the board. However, its colorboundness is unusual and a pinwheel combined with any one of the other atoms (Ferz, Wazir, Dababa, Alfil, or even the other Pinwheel) becomes a non-colorbound piece.

Dividing up the knight in to the two pinwheels, we now have 64 possible short range pieces, 54 of which are not colorbound.

Other ways of dividing up the Knight

The pinwheel is a very unusual piece. It does not preserve left-right symmetry, which means it will not be as popular with chess variant inventors. The only widely known Chess Variant I know of with left-right asymmetrical pieces is Tori Shogi. However, it is far more common to have pieces that do not preserve forwards-backwards symmetry, including Chess' pawn, and Shogi's lance, silver and gold generals.

There is one way of breaking up a knight in to two moves-to-4-squares atoms that preserves both left-right and forwards-backwards symmetry, and two ways to break up the knight in to 4-square atoms that only preserve left-right symmetry.

All three ways of breaking up a knight have already been discussed by Betza. To summarize:

Sub-knight atoms #1: Narrow and wide knights.

Narrow knight:

. X . X .
. . . . .
. . * . .
. . . . .
. X . X .

Wide knight:

. . . . .
X . . . X
. . * . .
X . . . X
. . . . .

Both of these pieces are 4-way colorbound.

Sub-knight atoms #2: Crab and Barc

Crab:

. X . X .
. . . . .
. . * . .
X . . . X
. . . . .

Barc:

. . . . .
X . . . X
. . * . .
. . . . .
. X . X .

Betza liked these sub-Knight atoms the most; they are unique in that, unlike other symmetrical sub-Knight atoms, they are not colorbound. He preferred the Crab over the Barc, since it encourages one to attack the other player.

Sub-knight atoms #3: Forward knight and Backwards knight

Forward knight:

. X . X .
X . . . X
. . * . .
. . . . .
. . . . .

Backwards knight:

. . . . .
. . . . .
. . * . .
X . . . X
. X . X .

These pieces are not very useful by themselves until combined with other atoms; the forward knight is probably the more useful atom to add to other pieces.