## Ginghoundstootham

01.23.2016 § 2 Comments

Here is Ginghoundstootham.

How did we get here?

**Introducing the Gingham-Herringbone Continuum**

Start out with good old Gingham:

Next, realize that there is a continuum connecting Gingham to Houndstooth by way of Shepherd’s check. Let’s look at Houndstooth:

Just imagine what would happen if you were to gradually increase the count of stripes in the diagonally striped squares of Houndstooth (or watch it here). As we approach infinity — an infinitely dense alternation of diagonal dark and light stripes — the stripes cease to appear distinct from one another and instead coalesce into a blended color: the color of the lighter squares in Gingham

(If we continue past Houndstooth, into two stripe, or even “one” stripe squares, you actually reach forms of Herringbone; hence the name of the continuum. Learn more about it on my other post here.)

**Tattersall**

So far, we have only dealt with one color against a background of white. A common variant (applicable to any member) of the Gingham-Herringbone Continuum (GHC) is Tattersall.

In Tattersall, each colored column alternates between two colors, A & B, and each row also alternates between those same two colors A & B. The result bears three types of intersection squares:

- A with A,
- B with B,
- and A with B.

Here’s Tattersall in Gingham form:

And here it is in Houndstooth form:

Now what if we were to change this pattern up a bit? Let’s not alternate purple and orange by column. And let’s not alternate purple and orange by row. Let’s just assign orange to columns, and purple to rows.

The result is something a step closer back toward the GHC, as we have returned to a simpler state where there is only a single type of intersection square. I’m not sure if this variation on Tattersall has a name, but it’s out there in the wild:

**Full Circle**

To finally achieve Ginghoundstootham, we add orange in between the purple stripes, and purple in between the orange stripes. Thus, columns once again boast both colors, and rows once again boast both colors. But instead of those colors alternating from column to column or row to row, they alternate within each column and row.

Perhaps even more importantly, compare the corner triangles of a column square with the corner triangles of a row square. They are opposites. The stripes between columns and rows are offset from each other. This way, whenever they intersect, orange blends with purple, and purple blends with orange. That is why the intersection squares no longer appear striped: they are striped, in a sense, but since the stripes are the same color (because they are combinations of the same two colors — A with B, or B with A) you can’t tell.

And so we’ve done it! We’ve made Ginghoundstootham.

**Blending Notes**

Note that I did not refer to orange and purple as “overlapping” each other. We cannot think of the means by which the orange and purple combine here as absorption of light in turns.

This is because if one color was on top of the other, it would take precedence in the final appearance. For example, if both orange and purple let 50% of light through, but orange was on top, then orange would be 50% of the final result, while purple would only be 50% of what was left, for a total of only 25%.

The reason this is a problem is that the disappearance of stripes in the intersection squares relies on the combination of purple with orange to come out the same as the combination of orange with purple. Order cannot matter.

Thus, we must think of the orange and purple as combining more like semi-transparent watercolor paint.

**Futher Transparency Note**

In traditional Gingham, transparency never comes up.

Note that as a consequence of the way transparency is used to create the fundamental effect of Ginghoundstootham, the ratio in darkness between the intersection squares and the connector squares is different than in traditional Gingham.

In traditional Gingham, the lighter squares are simply half the darkness of the darker squares.

In Ginghoundstootham, the lighter squares are fully two-thirds the darkness. Again, this is because the connector squares are letting 50% of light through, and two connector squares combined let 50% plus 50% of what’s left through, for a total of 75%, which is 3/2 of 50%.

**Name**

I call this pattern Ginghoundstootham because from a distance it most resembles Gingham, but were you to increase the diagonal stripe count along the GHC toward Gingham, what makes it distinct from Gingham would be lost.

That is, if the purple and orange stripes became hyper dense, the end result would be connector squares which looked like a lighter version of the pink in the solid intersection squares. The only way to distinguish the pattern from traditional Gingham at that point would be the ratio of darkness between the lighter and darker squares. A difference of 16.66% (that between 2/3 and 1/2) is not particularly striking.

So, since it is only by reducing the stripe count into Houndstooth territory that one may appreciate the fact that it is two colors combining in their transparency in two different ways to create a seemingly solid intersection square, I figured Houndstooth deserved some credit in the form of the name.

While I did draw inspiration from Tattersall, in the end this pattern has little to do with it other than being comprised of more than one non-background color.

See also:

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