Geometrically (or fractally) speaking, the classic representation (seen above) is mathematically "mal-formed" (or "false"). My reasoning is based on the following construction analogy from the realm of fractals.
Consider first the "triangular" fractal whose first several iterations appear below:
Iteration 0:
/A
AV\A
/7 \A
AV \A
/7AVAVAV\A
Iteration 1:
/A
AV\A
/7 \A
AV \A
/7AVAVAV\A
AV
/7
AV
/7
Iteration 2:
/A
AV\A
/7 \A ,oO'`
AV \A ,oO'`
/7AVAVAV\A'`
AV ,oO'`
/7 ,oO'`
AVoO'`
/7'`
Iteration 3:
`''OOoo..,
`/AOoo..,
AV\A `''OOoo..,
/7 \A ,oO'`
AV \A ,oO'`
/7AVAVAV\A'`
AV ,oO'`
/7 ,oO'`
AVoO'`
/7'`
.
.
.
Iteration 10:
,,..oooOOO/`
,,..oooOOO''`` ,/`
,,,...oooOOO''`` /`
,,..oooOOO______,,,...ooooooOOOOOO/,/`
..oooOO*|''```''OOoo.., ,/,/`
\ |, | `/AOoo.., ,/`/`
\ '| | AV\A `''OOoo..,/`,/`
\ | | /7 \A ,oO'/`,/`
\ |, | AV \A ,oO'`/` /`
\ '| | /7AVAVAV\A'`,/` ,/`
| | | AV ,oO'` ,/` ,/`
\ |, | /7 ,oO'` ,/` /`
\ '| |AVoO'` ,/` ,/`
\ | /7'` ,/` ,/`
\ |,| ,/` /`
\ '|| ,/` ,/`
| || ,/` ,/`
\ ||/` /`
\ '| ,/`
\ | ,/`
\|,/`
'|
|
\
\
\
(and so on).
So, this is an analogy. What does the analogous "yin yang" style geometrical shape look like? This takes some imagination.
In geometry, there are regular planar shapes (regular polygons). The one with the least number of sides is the triangle. Does it even make sense to speak of a two-sided polygon? Suppose there were such a polygon and that it enclosed some area. But then one 'side' or the other (or both) would be curved rather than straight, and curvature implies an 'infinite' number of sides. So let's make a "two-sided" figure, knowing full well that it has more than two sides:
Iteration 0:
__,,..--**''``''**--..,,__
------------------------------
Now, the analogy is to imagine that the curved sides get more curved.
In other words, the small extension simply follows the existing curvature,
and each new curve is angled a little bit more than the last.
Iteration 1:
__,,..--**''``''**--..,,__
------------------------------__
`'-._
Iteration 2:
_ __,,..--**''``''**--..,,__
'-.,_------------------------------__
`''***----.....,,,,,,__________`'-.
Iteration 3:
__,,,.....,,,__
..--**''__,,..--**''``''**--..,,__
'-.,_------------------------------__
`''***----.....,,,,,,__________`'-.
`'-._
`'
Iteration 4:
*_ __,,,.....,,,__
`-,..--**''__,,..--**''``''**--..,,__
'-.,_------------------------------__
`''***----.....,,,,,,__________`'-.
`''**--..,,,____ `'-._
``````''''''
Okay, so the idea is probably becoming clear. The rule is "start parallel, curve to meet the endpoint then follow that path beyond a short distance". But what is the end result? (This is in the sense of a "geometrical limit".)
,.d88888888b.,
.d8P 888888888b.
.dP d888888888888b.
.dP d8888888888888888b.
.dP d8888888888888888888b.
.dP 888888888888888888888b.
8P 88888888888888888888888
dP Y8888888888888888888888b
,88 Y8888888888888888888888,
88` Y888888888888888888888
88 `Y888888888888888888
88, Y8888888888888888
'88 Y8888888888888'
9b 888888888888P
Vb 888888888888
`Vb 8888888888P'
`Vb 888888888P'
`Vb d8888888P'
`Vb d8888888P'
`V8b d88888888P'
`'988888888P'`
And there it is. No holes, no extras. The mathematical version of the yin yang.