I’m looking for instances of complex inversions of design elements. To give you an idea of what I mean, here’s a few examples:
The colors red and blue are inverted between the flags of Cuba and Puerto Rico. This was deliberate on the part of Puerto Rican revolutionaries who modified the Cuban revolutionary flag to come up with their flag. Another inversion, this one not intentional, is those of Norway and Iceland:
The exact shades of blue are different, but in the past, the blue on Iceland’s flag used to be darker.
Note that these inversions are a bit more complex than a simple swapping of two stripes of a tricolor or bicolor. There are some of those out there, but I’m not interest in them.
Another example of complex inversion is the vowels in the words cacao and cocoa. Cacao is a plant, cocoa is the product of that plant. This was also not deliberate, but a result of confusion under the influence of the word coco, a different tropical plant.
Note that this is a more complex inversion than just swapping two letters. There are hundreds, if not thousands, of pairs of words that just a letter swap away from each other. But I’m not interested in those, or at least not for this thread.
Also note this question is not restricted to just flags and words. If there’s some other complex inversion, feel free to contribute it.
I’m still not clear what you mean by “complex” inversion.
Why would two colors being swapped in a cross pattern count as complex but not if they are in stripes? What’s the criteria for two words counting as a complex inversion?
Because stripes are the about simplest design element around.
Anything involving more than two letters. Also, it’d be best if there are some letters in common between the two words that are unchanged from one to the other.
OK, but given that there are probably not many flag inversions anyway, you may as well collect them all and ignore the ones that you don’t like.
So swapping only vowels, and at least 3? I think with that requirement, there are relatively few examples. From this PDF the best one was RAPIER and REPAIR, many of the others involve uncommon words.
Actually, those three (Palestine, Sudan, and Kuwait) make up a three-way inversion, or rather rotation. Well except for the truncated triangle, of course. The colors are not swapped, but rather rotated among three locations. The top color moves to the bottom, the bottom color to the triangle, and the triangle color to the top. I was wondering if something like that could be out there.
Every polyhedron has what’s called a dual. The dual is what you get when you swap the faces with the vertices. For instance, the dual of the cube is the octahedron. A cube has 6 faces and 8 vertices; an octahedron has 8 faces and 6 vertices. The two are true inverses; if the dual of X is Y, then the dual of Y is X.
That’s right. There are many other “duals” in mathematics, but polyhedra are perhaps the most concrete example. But they mostly arise because graphs (in math, a graph is a collection of points and connections between them) also always have a dual, and many things can be described in some way as a graph.
Another example is in electronic circuits, where you can always make a dual circuit where voltage and current are swapped. Swapping again gets you the original circuit.