My impression is that there are two distinct general patterns, and not just one.
In the first, in the ordinary snell knots, the lines buried under the ( many, at least 7) snelling turns run parallel to each other, they do not cross. The many turns is their mode of securing the tail.
In the second, in the twisted eight knots, the lines buried under the ( few, mostly 4) snelling turns form a strangle knot, they cross. The strangle knot is reinforced by the overlapping riding turns. The crossed ends are their mode of securing the tail.
Let me try again --though I expected that "Strangle knot" alone
was sufficient (Ashley #<whatever>). In the square page of knot
images that you posted above,
the top-left knot is a (Double) Strangle knot; it's seemingly parallel
ends in fact cross, but not in this image -- they will do so in setting;
the 2nd-from-top-left is <who knows>; it you slide it off of the
object, it can be manipulated into a *Fig.12* knot (where this
nomenclature takes "Fig.8" and adds to it as one end turns
around the other before being tucked out through the loop
formed at the other (u-turn) end of the structure (the initial
member would be the Overhand, then Fig.8, Fig.9, Stevedore
(Fig.10) ... and so on.
In some thin, finely braided cord around a pencil, this knot
didn't even hint at holding; in the Fig.12 orientation, and set
firmly (given small size of material), it grudgingly imparted
some resistance, but slid pretty easily;
BUT, then loaded in the
opposite direction --as you have
suggested for the
Strangle-- , it held surely (this taken immediately
from the hard setting and loading of prior test) !? Interesting;
but I'd suspect though well gripping, it is not strong;
Left-center is a
Double Overhand knot which will tend to draw
up into a
Strangle (as depicted to its right). Note why I favor
"Strangle" as the base for the nomenclature and not "Overhand":
looking at the full overwraps, one matches their number to the
name, for "Strangle" (and for "Grapevine") --as the base knot
has one, in contrast to the
Overhand which has zero (and so
a "Double Fisherman's" = a "(single) Grapevine", the latter
having the easy wraps-count match, unlike the former).
...in fishing line, one sets knots at much higher relative loads; in rope, that potential is seldom realized, and the knots must tighten under load a good deal beyond what is set.
I agree. But there are some rope knots, like the constrictor, and in a lesser degree the strangle knot, where the riding turns keep the accumulated tension of the crossed ends constant, and, as a result, we have a highly tensioned, jammed, knot.

You completely miss the point: it has nothing to do with the
knot,
but with the
relative force vis-a-vis breaking strength in setting it!
Yes, the Strangle will hold those 50#-force you impart: now, in fishing line
of suitable strength not to have broken, that's rather close to the
maximum strain it can take; in rope, nowhere close. (Okay, it's not
the breaking strength per se -- snap a magic wand on any gripping
knot and raise it's material's strength by 100 and it doesn't then
slip; but you get the idea -- fishing knots get set to a pretty high
percentage of the force they are going to see,
and to have the same condition for rope you would need to
take some quite unusual setting method.
--dl*
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