asymmetric (non repeating) tartans

[Rampant Lion]

Perhaps I don't understand what symmetry means, as applied to tartan, then? I was under the impression that, to be symmetrical, it would have to be ABA, or ABCBA or something like that. Am I mistaken in my understanding?

A symmetrical tartan, that has the same warp and weft, will look the same no matter how you rotate it. Basically it has a pivot point, actually 2 possible pivot points. In the Black Watch the pivot points are half-way through either of the blue squares.

Here's a picture of my Grant Hunting/Black Watch kilt at 0, 90, and 180 degrees. You can see the ABAC pattern in all 3 pictures look at the tartan left to right.



Now let's look at an asymmetrical tartan... the Buchanan tartan (The SP8's FC Buchanan).



You can see in each picture the tartan looks different.

[Barb T]

Excellent visual!!!

Here's another way of thinking about it. The pivots represent lines along which you could fold the tartan and have the two halves be exact mirror images of one another.

For the Black Watch, either the "B" or the "C" can be a pivot

ABACA B ACABA or ACABA C ABACA

The tartan is symmetrical because the sequence of letters is the same going either direction from the pivot. The fact that the "A" cannot be a pivot is immaterial.

A tartan with an ABCD pattern can't be symmetrical, because, no matter how many times you repeat the sequence, it's impossible to find a line across which the sett is a _mirror image_:

ABCDABC D ABCD nope; ABCDAB C DABCD nope; ABCDA B CDABCD nope; ABCD A BCDABCD nope

Cheers!

Barb

[Rampant Lion]

Excellent visual!!!

Here's another way of thinking about it. The pivots represent lines along which you could fold the tartan and have the two halves be exact mirror images of one another.

For the Black Watch, either the "B" or the "C" can be a pivot

ABACA B ACABA or ACABA C ABACA

The tartan is symmetrical because the sequence of letters is the same going either direction from the pivot. The fact that the "A" cannot be a pivot is immaterial.

A tartan with an ABCD pattern can't be symmetrical, because, no matter how many times you repeat the sequence, it's impossible to find a line across which the sett is a _mirror image_:

ABCDABC D ABCD nope; ABCDAB C DABCD nope; ABCDA B CDABCD nope; ABCD A BCDABCD nope

Cheers!

Barb

I was trying forever to figure out a way to type it like that that actually made sense... I couldn't so I resorted to pictures... The way you describe it, Barb, is the way my mind works it out.

[Mr. MacDougall]

Ah, thank you very much for the explanations and pictures. I believe I understand, now.

[gilmore]

I was trying forever to figure out a way to type it like that that actually made sense...

Yes, those articulate people, where would we be without them?