Shrinking the bight(s) of the bowline on the bight.

[xarax]

   Starting from the bowline on the bight ( red, in the attached picture ), we can shrink the one bight ( while, at the same time, the other widens, because the two bights are "communicating" ) to get an interesting single TIB bowline ( yellow ), or we can shrink both bights, to get a stopper ( white ).
   There are numerous ways one can dress those knots. I have deliberately chosen to show the one which : 1, corresponds to the simplest "flat" loose knot, so it is easy to remember how to dress, and, 2, it is very compact.
   Ashley states that "There are only two well known Double loops, and both of them are tied in the bight. They are the Bowline on the bight and the Spanish bowline." This means that the bowline on the bight is well known, so it seems a reasonable choice to utilize it as a basis of a single TIB bowline, by shrinking the one bight and widening the other. We do not even have to reeve the whole knot through the one bight, as we did in the case of the Sheepshank bowline, because this has already been done during the tying of the bowline in the bight itself, as shown in ABoK#1080, #1081 and #1082.

[xarax]

   In my view, this is a simple secure bowline, easy to remember how to tie as end-of-line and as a midline TIB bowline ( so, a very versatile eyeknot ), with a very compact nub and nice, fluid lines. It should have been published somewhere, but I was not aware of it till last night - and that is why I had to wait a few hours to tale some decent pictures of it in the light of the day...

[Dan_Lehman]

I'm most impressed at how you can get 2800pixels resolution
in under 100kb !!?  (My 800px images in iPhoto's "medium"
JPEG quality will sometimes exceed the limit; yours look to
have suffered nothing of JPEG quality in their size!?)

 - - - - -

I'm less favorably impressed by the knot.  Collapsing an eye
is something that this knot is vulnerable to if the eyes are
loaded (and one not!) separately against a single end --the
end not feeding into the loaded eye but the unloaded one.
NB!

There are sharp (1 diameter) turns in the knot, which makes
it less attractive for firm cordage.

The orientation presented here is but one of the possible ones
that could arise from the simple guidance of "collapsing an eye",
as there isn't an agreed orientation for the old knot itself in exact
dressing (or in preference for which end to load if loaded singly).

.:.  So, I'd prefer to go about the sort of extension to gain security
directly, which we've seen in some other variations on the bowline.

--dl*
====

[xarax]

There are sharp (1 diameter) turns in the knot...

   
   In the particular dressing shown, there is one such turn ( singular ), indeed - although it is located deep into the collar structure, at a point after ( post ) the higher collar, where, presumably, the loading coming from the returning eye leg has been reduced already. This means that the line will be tensioned less, and it will not be forced to "fold" around one rope diameter - but it also means that it will have the tendency to remain slack a little bit.
    There is also this interesting theory by SS369, who claims that such a sharp U turn can impede the slippage of the Tail end more efficiently than a wider one :
 

The single u turn around the area in this example will provide more clamping and security, where as, if the area is rounder then it will have less clamping force to resist tail movement because the load/force is spread over two diameters.

   However, there are dozens of other, different dressings, which may be preferable regarding this. In fact, I believe that this shrank / collapsed bowline-on-the-bight can be dressed in more ways than a retraced fig.8 eyeknot ! To widen the curves followed by the lines inside the knot s nub, we can apply the same method shown in the case of the Water knot - which, after all, is the core on which we tie the bowline-on-the-bight : we can "twist' the pair of the ends inside the rim of the higher collar, and transport this twist inside the nub of the Water knot. I have seen that the best results are achieved when we twist the pair 720 degrees :
   
   http://igkt.net/sm/index.php?topic=2893.msg17422#msg17422
   
   In this thread I have chosen this particular dressing because the initial,"flat", loose knot is unique, in some sense - so it can be remembered and inspected more easily than the others - , and it generates a very compact final nub.

...there isn't an agreed orientation for the old knot itself in exact dressing (or in preference for which end to load if loaded singly).

 
   Once it is decided that the knot would be tied as end-of-line PET eyeknot, its Standing and Tail ends are determined - and once those ends are determined, the particular bight which we should shrink and the particular bight which we should widen and load are determined, too - and vice versa. So, there is no need or room for any "agreement".

--------------------------------------------------------------------------------------------------------------

how you can get 2800pixels resolution in under 100kb !!? 

Download the (free) GIMP "Image manipulation program" :
http://www.gimp.org/
File - Open - (Select the picture file in the computer) - Export as JPEG image - Replace - Check "Show preview in image window"- Check the " + " in front of "Advanced Options" - Uncheck everything except the "Optimize" option - At "Subsampling" box select the 4 : 2 : 0 (chroma quartered), and move the pointer in the "Quality" box left and right, until the "File size" becomes smaller than 100 kb - Close - Close without saving.

[xarax]

   (*)
   By the way, the dressings of the "front" and the "back" side    of the bowline-on-the-bight shown by Ashley in ABoK#1081 are different...

[Dan_Lehman]

...there isn't an agreed orientation for the old knot itself in exact dressing
(or in preference for which end to load if loaded singly).

Once it is decided that the knot would be tied as end-of-line
PET eyeknot,
its Standing and Tail ends are determined
--and once those ends are determined--,
the particular bight [that] we should shrink [is] determined, ... .
So, there is no need or room for any "agreement".

Perhaps I'm stumbling at what you mean by "determined";
or you are missing my qualification about a tying guided
merely by the prescription to "shrink one eye"!?

In tying the knot "PET" one is in essence coloring
(or filling in with material) the completed knot's schema;
and there is nothing to say that one has *begun* this
process on one vs. the other *end* --THAT is what
I'm pointing to.  (With the completed knot, TIB say,
one then might have chosen or have yet to choose
which end to load --the simple folding into a bight
to TIB the knot will place the tail into one or
the other position.)

So, if one has your presentation here (supplemented
with some step-wise and clearer guidance on the exact
structure --it's a challenge to deduce connections here,
even with both sides presented clearly, but set--),
then, yes, the orientation would presumably be well
presented and able to be followed.

--dl*
====

postscript :

Download the (free) GIMP "Image manipulation program" :
...

Thanks for this.  It is still surprising to see such difference
in sizes, no?!   --and noting that even at the optional (in
my browser) "+" (slight) enlargement the image quality
is GOOD (not that we need to examine fibres but we can)!

ps'  ::: >>> Perhaps there should be a thread begun by SS369
or you in Feedback (?) with such image-presenting tips as
we see requested from time to time --not only the basic
How-to-work-w/SimpleMachines-system-of-this-forum
but also some of the processing in preparation for that,
and other options (embedding URL'd imagery?).
Then we could refer to this as needed per request or
otherwise.
 

[xarax]

...a tying guided merely by the prescription to "shrink one eye"!?

   
   Not merely "shrinking one eye", shrinking THE particular eye ( shown in the first picture ), which, when the knot is in the initial loose, "flat" form ( or when it is "flattened" out in this form ), is the "inner" / "smaller"  eye.

...there is nothing to say that one has *begun* this process on one vs. the other *end*

 
   If one sees a finished knot in the middle of a line, and he does not know which of the two geometrically different knots is meant to be, of course he can not say which end can be considered the Standing and which the Tail end !    HOWEVER, if the knot is meant-to-be tied and loaded as shown in this thread, he can ! Notice that the loop which is formed by the continuation of the end which is meant-to-be the Standing end is noticeably wider than the other - the loop which is meant-to-be the continuation of the Tail end. The bulk of the part of the line that forms the meant-to-be Tail at this point works as an obstacle, over and around which the meant-to-be Standing part has to pass, in order to form what is meant-to-be the nipping loop. So, if one knows that the finished knot was tied as the knot that it was meant-to-be similar to the one presented in this thread, he can conclude how it is tied, so there was then, and there is now, no ambiguity whatsoever in which was and is meant-to-be the Standing end, and which was and is meant-to-be the Tail end.
   Of course, the fact that, if tied as a midline loop, this knot can also be loaded by the meant-to-be Tail end ( so, as a non-PET eyeknot ), without losing its integrity, is an advantage. I wouldn't recommend it a "span" loop, though.
   
   I will post a picture of the loose but not "flattened" knot, to show "step-wise and clearer guidance on the exact
structure" - even if it is not necessary - but first I have to wait the sunrise !

P.S. Here are some first pictures using a flash, which may be of some help. Notice that if he ties the knot in the end ( as an end-of-line loop ), all the knot tyer has to do with the line, after he has tied a right-hand bowline, is to the retrace the path of the Standing part.

[xarax]

   As we all know, it is very difficult to describe verbally the dressing of a knot. I think that, after the knot tyer has formed the "flat" shrank bowline-on-the-bight ( first picture ) the one most important thing he has to do is to push the upper part of the rim of the nipping loop downwards, towards the tip of the bight, sliding it on the two adjacent and parallel ends (second picture). In other words, the upper part of the rim of the nipping loop should always remain located in between the upper part of the rim of the collar structure and the continuations of the two ends. To show this final position of the nipping loop, after it has been pushed downwards, it may be better to look at the back side of the bowline  .
   When we have placed the nipping loop in its proper place, all we have to do is to remove the slack of the collar structure, by pulling the returning eye leg. ( By pushing the nipping loop downwards and reducing the slack of the collar structure, the eye of the initial "flat" loop becomes a little larger, as shown in the pictures ).
   As I said again, this is the simplest dressing of the shrank bowline-on-the-bight which, 1.,  starts from an easily formed and inspected "flat" knot, and, 2., generates a very compact knot - while, at the same time, its nipping loop is not very narrow. We can dress the knot in numerous other ways, where the lines follow smoother, wider curves inside the knot s nub. However, all those dressings are much more complex, they start from more convoluted forms of the bowline-on-the-bight which are difficult to remember and to inspect, they require much more attention during dressing, and it is questionable if the supposedly greater strength is worth the trouble.
 

[xarax]

   If we tie the Standing part before (ante) the eye with a rope of the same diameter but of a different colour, or if we remove it altogether, we can easily distinguish the form of the collar structure. ( See the attached pictures ).

[xarax]

   As it was shown previously, it is very easy to remember how to tie, and to actually tie, the "flat" initial knot in-the-end : after we form a right-hand bowline, we just have to retrace the line of the Standing part with the line of the Tail end - keeping in mind that that, at this stage, we only form the "flat" knot, which does not involve any overlapping of those two lines. ( This reminds the way we dress a well-dressed retraced fig.8 knot ). I believe that this is a great advantage of this secure PET and TIB loop, in comparison to other such knots.
   The most interesting thing is that tying this knot in-the-bight  is even easier ! Just three steps : 
   
   1. Tie a simple overhand loop ( yellow ).
   2. The bight of this loop will become the collar of the final knot. So, reeve the whole nub through this bight ( red ).
   3. Pull out of the nub the one of the two "communicating" bights. Feed this second bight you have pulled out with the material of the first bight ( white) - until the first bight shrinks completely, and becomes the collar of the loop, and the second bight widens completely, and becomes the eye of the loop ( blue).
 
   That s all, folks ! Of course there are a few strings attached to this 1-2-3 , but in a verbal description of the tying and dressing of a knot we should nt expect anything else, should we ?    See the attached pictures which do not need footnotes, tie the knot a few times, and and then continue reading ;
   
   Note 1 : You should better tie the most compact overhand loop, and arrange the relative positions of the Standing end and the Tail end, as shown in the pictures. However, even if the two lines inside the nub of the overhand knot are "twisted" around each other in a different way, or if the Standing end and the Tail end are arranged differently, the resulting knot would be very similar to the one shown here - and you can re-dress it in the form shown here any time you wish.
   Note 2 : You should better reeve the nub of the overhand knot loop through the 'front" side of the ( yellow ) bight : "front", as shown in the pictures. However, even if you reeve the nub through the other, the "back" side of the ( yellow ) bight, the resulting knot would be also very similar to the one shown here - and you can again re-dress it in the form shown here.
   Note 3 : You should better pull the one of the two "communicating" bight which is closer to the end. However, even if you pull out the other "communicating" bight, the resulting knot would, again, be very similar to the one shown here - and you can, again, re-dress it in the form shown here.
 
   I have chosen to tie this particular overhand loop, and to reeve the nub of the initial overhand loop through this particular side, and to pull out this particular 'communicating" bight, so the final knot tied in-the-bight would immediately, without any further re-arranging of the lines inside its nub, be dressed in the same way with the knot tied in-the-end by this easy to remember ( I would say difficult, almost impossible to forget...  ) retracing method. 
  I suspect that a knot tyer would be able to tie the knot in-the-bight much faster than in-the-end, but, due to the "blind" retracing method, the in-the-end sequence of moves is conceptually simpler.