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Love them knots! The sudoku of the universe :)
This is not a new QR code, nor is it powerful. It's worse in every way and is not really even a code.
Interesting article. I love it when maths gives us some beautiful visuals too.
Their use of “QR Code” is mighty confusing. QR (Quick Response) Codes are something specific that people are familiar with. These don’t share any characteristics apart from being images which represent something else. They’re not even the same colour or shape. Just call them “knot codes” or something.
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.

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.

this was so confusing at first not going to lie
https://en.wikipedia.org/wiki/QR_code#License

  The text QR Code itself is a registered trademark and wordmark of Denso Wave Incorporated.[107] 
Yeah these scientists need a legal team

https://www.qrcode.com/en/faq.html

https://greatreachinc.com/blog/one-thing-about-qr-codes-you-...

  Should “QR Code” be capitalized?

  Yes. “QR Code” must always be capitalized: both letters in “QR” and the “C” in “Code.” The registered trademark symbol (®) should follow the term in published materials. Using lowercase, adding an “s,” or other variations does not exempt you from the trademark.
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.
The knot codes are beautiful but the ones in the article all seem to be repeating patterns, so I wonder if you could take a 60° slice of each one and save space without losing information.
But I see all the "QR codes" have a hexagonal symmetry? So basically you can use only one corner (1/6) to represent a node? Why do they keep the entire hexagon?
Don't call it a 'QR Code' if it is not a QR Code.