My grouping system isn't completely clean, of course, but what knot classification system could be? My little project may sound silly and full of holes to veteran knotters, but it still makes sense to me.
In grouping, I'm looking mostly at knot construction and also, but to a much lesser degree, the end result (appearance and function).
It will help to try to articulate your "family" criteria;
"silly" is a YMMV aspect, but there are many ways one might
group knots. The Bowline<=>Ashley's Stopper relation is one of
topology, not of function nor of tying -- dynamically, in use,
opposite parts are loaded (and the Bowline has an eye/loop/bight).
I'm particularly curious as to how the Butterfly came to be in some
"Prusik family"? (As well as how the Prusik avoided going to the
(Rolling) Hitch family reunion!)
To my amateur eye, they're strikingly similar, but we all look at knots differently. The Butterfly is a loop (ok, bight) that rolls around through another loop, creating a neat handhold, with no working or standing ends involved. The Prusik is a loop that rolls around through another loop, creating a neat handhold, with no working or standing ends involved. Asher's Bottle Sling is basically a Prusik with a twist. There is no comparing the Prusik to the Rolling Hitch or Clove or Constrictor, other than that they all go around fixed objects.
The Butterfly is an eye knot Tiable In-the Bight; the Prusik hitch is
a friction hitch to be tied around some object (usually rope). It is
primarily by function that one sees likeness to the Rolling Hitch;
but there are "Prusiks" (so-named, similarly structured, i.e.) that
are much like versions of the Rolling H. (where tail & SPart are
parallel, as in Prusik/Cow, not Clove), where one "half" is a single
turn, and is on the near (to loading/SParts) end of the knot).
But your "
amateur" fresh perspective on the Butterfly leads to interesting
explorations: e.g., tie it as though making a sort of Prusik hitch
to an object --
with a ring-sling--, bringing the eventual eye-bight
through the connected Butterfly SParts, which should be sized rather
small as a bight. (--have just done some simple, around-finger,
playing with this ...)
And the Highwayman's Hitch seems unrelated to the Rolling Hitch; that family is rather varied.
The Highwayman's Hitch is almost a Frustrator knot, with the addition of a draw-loop for quick release. These two that I'm putting in with "Rolling Hitches" are different from the Clove and Constrictor, etc., in that they contain bights. But still, you're wrapping cord around to create a post hitch and they start off the same way. The Buntline Hitch is a noose that with only one turn around a fixed object, so I'd say it does not qualify as a member of my "Rolling Hitch" family.
The Highwayman's H. is a treacherous knot; you'll do well to revise is
such that the SPart-loaded bight
surrounds the bight through which
the slip-/tail-bight is tucked as a toggle -- this is a surer variation.
In the original, the loading can collapse the slip-bight, possibly spilling
or else locking (i.e., unable to be slipped free) the knot!
The "Frustrator" is a
Constrictor with a twist, like you noted for
Asher's
Bottle Sling -- twist one of the loops.
Note that the "Double Fig.8 Hitch" in fact has not even a single "fig.8" !
Dan, the Double Fig.8 Hitch didn't get that name for no reason. When completed you don't see any figure eights, true, but again, it's the construction I'm (mostly) using for grouping. It's two overlayed figure eights, folded over and slid onto a post. You could almost say it's more "figure eightish" in construction than any other knot! Clearly, the Double Fig.8 Hitch is a member in good standing of both the Figure Eight and Rolling Hitch families. (I got no problem with duplication!) 
Whoa, we've been here before: by "fig.8" I mean
exactly a
Fig.8 -- not merely
something with an 8-ish figure (such as I think you can find in that Budworth
book for an
Overhand knot at the start of the
Tricorn (Ashley's #1029)).
In your referenced binder, there is no knotted structure at all, until
putting the ("8-ish"-laid) cordage around an object (as are
Clove &
Constrictornon-knots w/o an object).
On the other hand, if one accepted
topological equality (of the
base structure), say, there are some rather
Bowlinesque eye knots
that can come from a Fig.8 start, where the '8' is re-oriented into
the sort of turns of a Bowline.
...
So, there are families by all sorts of connections /perspectives !
Or knot.
Thanks,
--dl*
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