As supercat pointed out to me, the three lowest bits of NUSIZx correspond to the different copies of a player:
bit 0 = the copy closest to the player
bit 1 = the copy in the middle
bit 2 = the copy farthest from the player
In other words:
aaaaaaaa bbbbbbbb cccccccc dddddddd eeeeeeee
where aaaaaaaa, bbbbbbbb, cccccccc, dddddddd, and eeeeeeee are 8 color clocks wide, with 8 color clocks between them.
aaaaaaaa is the player, which is always "on" (unless you set all of its bits to 0 in the GRPx register).
bbbbbbbb is the copy that's closest to the player, which can be turned on or off by setting bit 0 of NUSIZx to 1 or 0.
cccccccc is the middle copy, which can be turned on or off by setting bit 1 of NUSIZx to 1 or 0.
dddddddd isn't a copy-- I just put it there as a kind of "place holder," to help show the spacing between the copies.
eeeeeeee is the copy that's farthest from the player, which can be turned on or off by setting bit 2 of NUSIZx to 1 or 0.
This makes it easy to remember which values to use to get the results you want, as follows:
%00000000 = no copies, just the player by itself (aaaaaaaa).
%00000001 = 1 copy, placed closest to the player (aaaaaaaa and bbbbbbbb).
%00000010 = 1 copy, placed midway from the player (aaaaaaaa and cccccccc).
%00000100 = 1 copy, placed farthest from the player (aaaaaaaa and eeeeeeee).
%00000011 = 2 copies, at the "near" spacing from the player (aaaaaaaa, bbbbbbbb, and cccccccc).
%00000110 = 2 copies, at the "middle" spacing from the player (aaaaaaaa, cccccccc, and eeeeeeee).
These are the legal combinations that give you a normal-sized player, with or without any copies of the player. But there are 8 possible values for a 3-bit number. The other two values are as follows:
%00000101
%00000111
If %00000101 were "legal" for turning the copies on and off, it should turn on the bbbbbbbb and eeeeeeee copies. But the player and any copies need to be equally spaced. Since aaaaaaaa, bbbbbbbb, and eeeeeeee aren't equally spaced, that's an "illegal" value as far as getting multiple copies of a player are concerned.
Likewise, if %00000111 were "legal" for this purpose, it should turn on the bbbbbbbb, cccccccc, and eeeeeeee copies. But again, aaaaaaaa, bbbbbbbb, cccccccc, and eeeeeeee aren't equally spaced, so that's another "illegal" value for getting multiple copies of a player.
Fortunately, rather than "waste" these two "illegal" values, Atari gave them a different sort of meaning:
%00000101 = no copies, just the player by itself, but it's twice as wide as usual.
%00000111 = no copies, just the player by itself, but it's four times as wide as usual.
Michael