I'm not proposing a new solution method -- I wish I were --, but it might help to simplify theory. I couldn't find it mentioned in any sudoku web site or forum I studied. Maybe I didn't try hard enough, but the amount of information is so incredibly large! Or maybe it's just so obvious or useless that nobody bothers to mention it. In that case: sorry for wasting your time, but don't fillet me! Actually, I would expect that programmers use this to try and find fishy objects.

The idea is, that for most 'normal' fishes (for instance where boxes do not come into play, as in 'franken' types, if I understand them correctly), if you administer them in a certain way, they are equivalent to naked or hidden pairs, triples, quads, etc. The administration is simple. Make a list of nine cells, like a Sudoku row. In cell n (1..9) write the (row-)numbers (1..9) of the cells in column n that contain the candidate.

An example (including solved singles). It might not be a viable configuration in real sudoku life, but that's not the point.

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`. . X . . . . . .`

. . . . . . . X X

. . . . . X . X .

. X . . X . X X .

X . . X . . X . .

. . . . X X . . .

X . . X . . . . .

. . . . . X . X X

. X . . X . X . .

Derived row:

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`(57)(49)(1)(57)(469)(368)(459)(2348)(28)`

An X-wing shows up as a naked pair of 5 and 7, pointing to a removable 5, and a sword fish as a hidden triple of 2, 3 and 8, where a 6 and a 4 can be removed.

You can also make a list of column numbers:

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`(3)(89)(68)(2578)(147)(56)(14)(689)(257)`

Here the X-wing shows up as a hidden pair and the swordfish as a naked triple.

As far as I can see finned fish are equivalent to almost locked sets (and can therefore be attacked analogously).

You can of course make an 'associated sudoku' with each row m (1..9) listing the row or column numbers for candidate m. Maybe this might help to find and solve '3d' configurations. In fact, each state of a sudoku being solved can be seen as a multivalued graph, i.e. a set of triples (row, column, candidate). The associated sudoku is the same set, but with a permutation of some coordinates: (candidate, column, row) or (candidate, row, column). The other permutations are pairwise equivalent.

I have tried to bring box-bound links into the picture (representing franken stuff?) but I didn't succeed. The boxnumber of a cell is not an independent coordinate. Also, I still know too little of the very advanced sudoku theory: I'm actually just a happy intermediate sudoku player.

Some people may find the whole idea a step back, as they prefer to look at diagrams instead of collections of numbers. They might try to look at (naked, hidden, almost) pairs, triples, etc. as fishes

I wonder if this is helpful.