A Powerful New 'QR Code' Untangles Math's Knottiest Knots

I think the comparison for the lay person is just fine. The author quoted the term and explains themselves.

A QR codes encode data to be scanned and converted for the convenience of the user.

These knot graphics encode data to be scanned and converted for the convenience of the user.

I mean... There is a 1-1 mapping, and they look kinda like QR codes. so technically, you can make an app that scan it and it will show you the corresponding polynomial.. It could even be useful for fast checking knots

The use of "qR cOdES®" appears to have developed from a previous system of colored "bar codes" algorithmically generated from the same types of invariant knots, but with less resolution. I suppose the "BAR coding" could be visually interpreted like resistor values in assembling or diagnosing circuit boards.

However, what they're doing is art. They are algorithmically generating beautiful artwork that can be admired for its colors, labyrinthine complexity, near-symmetry, shapes and analogy to real-world or theoretical knots.

https://en.wikipedia.org/wiki/Celtic_knot

https://en.wikipedia.org/wiki/Tartan#Legal_protection

https://en.wikipedia.org/wiki/Fractal_art

https://en.wikipedia.org/wiki/Moir%C3%A9_pattern

They have not proposed any way of scanning or processing the art back into data, and in fact they point out that printing, display, visual inspection or comparison may not produce mathematically accurate results, so this is representational art that they can emblazon on their mugs, sugar cookies, tee shirts, and sell on Etsy.

https://en.wikipedia.org/wiki/Psychedelic_art

In fact Dr. Bar-Natan has done a lot of work in perceptual art that looks like another thing: https://www.math.toronto.edu/drorbn/papers/PDI/

But he calls it "PDI" and not "Magic Eye™"

The fault of naming "qr codez®" doesn't rest solely on the latest researchers, but they are "standing on the shoulders of giants" who generated "bar c0des", which may have started with some colored pencils, a cocktail napkin, and 3 pints in a pub.

The text QR Code® itself is a registered trademark and wordmark of Denso Wave Incorporated.

The article notes near the end that the authors think the diameter of the hexagon is tied to another constant, so I would guess that they kept the full hexagon because studying a regular polygon has advantages that studying a wedge doesn’t — so, since they aren’t done studying this all yet, perhaps they have causes to consider a full hex rather than a wedge that are still WIP.

That trademark seems unlikely to survive reality. This sort of societal disregard is a specific argument to invalidate — knot a desirable outcome when suing a bunch of theoretical mathematicians.

This is the most non-sensical comment here. That’s not at all how trademarks work.

“Whoa! Some article said this mail app is an ‘Outlook’ for TempleOS! Better call the Microsoft lawyers.”

No, you’re allowed to compare products and ideas and mention their trademarked names without fear of legal issues.

Did the researchers name these “QR codes?”