As noted by BGrimley, the so-called "Algonquin Bowline" is
ABOK #1045;
#1043 is a similar, Fig.8-based knot.
The "Ontario Bowline" is also an Overhand-based loopknot.
It's structure is simple. Tie an Overhand knot oriented such that the SPart is on
the left, and the eye will be on the right--leave adequate material here.
The crossing of this Overhand is on top, its "belly" below; and the end exiting to
form the eye will thus go diagonally downwards & rightwards
[as in, e.g.:
www.knotingwork.com/Pages/basic_knots3.html ]
The end then forms an eye, arcing back anti-clockwise to re-enter
the knot at a complementary "diagonal" angle (acute) such that it crosses UNDER
only itself (over both other parts of Overhand, at crossing & belly).
The end then turns clockwise back around UNDER the SPart (just left of the knot),
and then back PARALLEL/tracing its initial exit from the Overhand
--i.e., what it made in forming the Overhand.
In the first "bowline", the legs of the eye enter the Overhand together;
in the Ontario Bwl, the re-entry of the end to the knot really doesn't much
go through the belly/center of the Overhand until the finishing tuck.
.:. NEITHER of these knots is a
bowline (except by someone's wanting to use
that name, presumably for legitimacy, promotion). And neither seems especially
well-suited to the rope problem they're intended to solve--getting a secure knot
in stiff/slick rope. Although the note about not being used by climbers shouldn't
itself be seen as evidence against them--climbers have some rather peculiar
(mis)understandings about knots, and esp. novelties!
Dave asks for information about strengths. I will again urge that such information
be given severe scrutiny if found, and prefer that it not be posted carelessly,
as bad information rapidly fills the void and it taken as gospel by preponderance,
quite possibly to ill effect. (E.g., the site cited by Dave has words to the effect that
the Bwl is not a very strong knot, at merely 60%; that is a figure for only some of
the material a Bwl might be tied in, and apparently this site is focused upon knots
for tying thin angling lines--where, yes, 60% is not much (though is about what the
ubiquitous Angler's Loop/Perfection Loop has tested at).)
*knudeNoggin*