Feeling a bit responsible for the "headless" and "franken" terms, I would like to add my 2 c.
I think the easiest way to describe these methods is thinking in terms of covering sets. A classic fish is either n rows or columns that can be "covered" by n columns or rows. (n rows covered by n columns and v.v)
Now for all these "fish" (that has been presented as "fish" on this forum so far) it holds true that the basis sets are always restricted to only columns or only rows. I think it was ronk who first introduced the idea that also using a box as part of the basis-sets could find a "smaller fish", but I don't think the idea of using boxes are yet concidered to be "fish" by the masses. This might change however.
Then the rest of the fish-names derives from using not only the opposite lines (row<->column) to cover the original fish, but to use boxes to do this as well, and also having "extra" candidates left in the fish after the number of covering sectors equals the number of basis-sectors.
A "finned" fish (in my opinion) is then a fish that, after you have been able to apply your n covering sectors, you are still left with some candidates. (the fins). These can then "see" some of the candidates within some of the covering sets(that are not part of the fish itself), and these can then be eliminated.
With that definition, you can actually divide ALL fish into finned and not-finned. However, there has been given some names to some of the special cases of covering. The "headless" variant was a result of getting exacly an "n-cover" (no fins) by using a box. I believe the first "headless" fish was a swordfish that had one box and two rows to cover three columns(a "classic" fish-illustration found many places since). In other words, a "headless" fish is also a "perfect fish" or a "non-finned-fish", but expanding the covering to include boxes as well.
Now by adding a "fin" to this, you got something that I think was just called a "finned swordfish", and that is also what I would argue it as. After expanding the fishworld to include boxes as covering sets, that falls nicely into place. (being "one extra" candidate outside the three covering sectors (row, row, box) and that candidate "seeing" some of the candidates inside one of those three sectors)
Now frankenfish was then introduced as the name of a fish using
more then one box for covering sets as well as being finned. The first frankenfish was a swordfish of three columns, that used two boxes and one row as covering sets, and had one "fin" that could see one of the two boxes. In other words a "finned-more-than-one-box-used-for-cover"-fish, but then again, if truly accepting boxes as cover, it would really only be a "finned" fish.
I guess the thing about this that differs most from "public opinion" is the definiton I use for a "fin". My definition is:
After you have covered a fish with N sectors with N other sectors, you are left with some candidates, these are concidered "fins" The rule that will always apply to fins are then that:
any candidates that are part of any of the covering sectors, but not part of the basis sectors, that can see all the fins, can be eliminated This POV will then be completly in line with what was concidered "fins" in the early fishes, but will IMO be more flexible to deal with the more complex sea-creatures that we are facing. (not having to talk about 16 fins when having to use a lot of boxes for covering sectors) Note also that this POV will limit most sea-creatures ( even of huge proportions) to just one fin. Two can also happen sometimes, but three is outright rare!
The exciting new ways for sealife to go is in my opinion the possiblity ronk has introduced to use a mixture of sectors to make the basis of the fish. If the saying goes "there is always a smaller fish", then can we look away when something thought to be a jellyfish can be shown to be a "swordfish" concisting of two rows and a box... ?
We'll just have to wait and see I guess!
Havard
, that is the logic behind it, the pattern above makes it easier to spot.
