What is the cordage we're seeing here -- looks like a kernmantle but I'll guess it's marine double braid, then, and supple/flexible.
Wrong guess. Read my words 
,
Oh, actually
read the answer !!
Well, looks like my looks-like
guessing is better than my reading.
It looks like esp. the white-ish rope shows the stiffness resistance
to snugness. And I think that the more roundish turning of this
version will see more opening than 1-diameter turns: in that if
the rounded turns surround just 2 diameters --which make a poor
approximation of a round
object to bind-- they will not so
well lock; but in some orientations the 1-diameter turns make for
a like-scissors-legs working where the rope wants to spring apart
rather than expand a circle, and just the presence of some wrap's
restraint of this then serves to keep the knot
as tightly set as
it was. -- at least, this seems to be a difference exposed when I
tried the End-Bound Dbl. Bowline (EBDB) in some slick soft-laid
3mm? polypropylene: even set firmly (in anger that it had dared
to loosen initially, ah, the nerve of it!) , after a brief holding the
end's wrap and the double-turn of the loop just relaxed all at
once. In contrast, a Janus was not so snug-tight on setting,
but this springy material with the sharper 1-dia. turns wanted
to open like scissor legs and simply couldn't, so pretty much
stayed in loose-but-workable state, not further loosening.
-- all of this pretty informal & limited in scope, but still IMO
worth considering.
Here's another variation, described in reference to your orange
rope's version: after the end enters the loop and then turns
around the opposite eye leg, and re-enters the loop, have it
cross OVER itself, and then go up to make a Bowline-like
collar turn around the S.Part, and exit through the center
of the nipping loop (and between its two passes there --the
exit is center of everything, thus). This looks pretty good,
and the revised crossing of itself I think gives better S.Part
curvature on loading, and a bit of give/spring, the re-entry
& final exit parts padding the S.Part from the end-side eye
leg (which will be firmer, having half the tension in it).
My conception of "bowline" is somewhat three-layered:
...
then it is the half of this big set that has the end entering the loop from the same side [ Xarax's emphasis ]
The end entering into the loop from the same side as in the common bowline,
is simply and plainly too restrictive a requirement ! As a bowline I think we have to
count any end-of-line loop, where we have one or more nipping loops, that encircle the rope strands, bight(s) or single strands, that go through it(them). What we must not characterize as bowlines, are end-of-line-loops that have overhand or double eight knots tied on them before the bights and the single rope strands pass through the nipping loop(s).
As of what exactly shape the nipping loop can have, I think that its function, and not its actual shape, ( more two dimensional, circular, or more three dimensional, spiral ) that offers to the bowline its "king of knots" status. If we have ore or more loops that, as they are more and more tensioned by the loading of the knot itself, are obstacles in the natural effort of the tail to escape from the knot, then we have bowline nipping loops.
Hmmm, I think that you've missed my point of "3-layered": that I use
"bowline" in different ways (for want of better terms, at the moment).
I.p., I do use "b." less restrictively --that is the first layer-- , by which
"anti-bowline" in a sense is implying the 2nd-layer "b.", but could be
paired with a "pro-bowline" term (say) as the subsets to "bowline"
set.
But consider what I see as essential: the nipping loop that feeds
into the eye -- that thus nips by active force in both directions
(unlike e.g. a Sheet bend where this corresponding loop is held at
one end, loaded from the other). When the bowline variants such
as the Eskimo (and one Ashley calls "Carrick") pull the S.Part-side
eye leg back around the loop and transform the essential "loop"
into a Crossing-knot form, you have significantly (IMO) now at
turn over the S.Part intervening to the path to the eye leg,
and enough of a changed mechanics to warrant it being considered
NOT in the "bowline" set. Mind, though, that between the paradigms
in this conception are the half-way situations, which beg to mess
up the distinction -- a sort of thing I try to avoid in some other
conceptions (i.e., where I choose to regard pure
apparentstructure over observed behavior).
--dl*
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