Field: square lattice, hexagonal lattice, freeform, 1-d
Moves: slide (15-puzzle style), rotate around lattice "great circle", rotate around interior point, swap, drop (singles or groups, with restricted placement at edges), place (arbitrary free location)
Matching result: promote/build (objects are combined to a next-tier object), clear
Minimum match size: 3, 4, 5+
|Slide||Lattice rotation||Point rotation||Swap||Drop||Place|
|Clear||Puzzle Pirates "Navigation" (cylindrical topology), PopCap Chuzzle||Puzzle Pirates "Foraging", KadoKado "Binary" (match-4)||PopCap Bejeweled, Puzzle Quest, Puzzle Pirates "Bilging"||PopCap Zuma (1-d, single unit), KadoKado "Paradice" (multiple units in parallel, match-4), KadoKado "Drakhan" (single unit, freeform), Puzzle Pirates "Sailing" (two-unit), Dr. Mario (two-unit, match-4)||PopCap Alchemy (match-6)|
|Promote||Alien Hive||Naturalchimie (2-unit drops)||Spryfox Triple Town|
I am sure I have seen a "clear"ing game with the slide-to-empty-space mechanic, but I cannot come up with it. "Alchemy" is something of a cheat.
I am less sure that the "promote" row can be filled in. So many games use the swap mechanic that I feel like there must be a "build+swap" game but I can't think of one.
One obvious variation is to perform rotations around the center on a square grid. I.e., the center rotation would move 4 squares, the one outside that would move 12 squares, the next ring has 22 squares.