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?
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 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
Hexagonal, with shaded colors? QR Codes are, by definition, square and binary and traditionally use black and white. They're also used for a different purpose typically. They could easily have made them look more like QR Codes if they had wanted to, but they made their own artistic choices. Which I love btw, but they could have maybe chosen better wording. Something like 'fingerprint' or 'mugshot' would have conveyed the idea of it being useful for identification, if not perfect, much better.
Which I not only mentioned in my comment, it is not even slightly unique to QR codes.
> they look kinda like QR codes
In what way? QR Codes are black and white, square, and asymmetrical. These are colourful, hexagonal, and symmetrical. By that token, a 16th century tile also “looks kinda like a QR Code”.
I very much doubt you could show one of these to someone, ask them what they are, and that they would answer “QR Code”. They don’t look alike at all.
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 30° slice of each one and save space without losing information.
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.
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?
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.
> data to be scanned and converted
These appear to be write-only. Where have they documented the method of scanning and conversion? Is it patented?
The publication on arxiv only mentions visual inspection, in the context of being a bad idea.
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
> they look kinda like QR codes
Hexagonal, with shaded colors? QR Codes are, by definition, square and binary and traditionally use black and white. They're also used for a different purpose typically. They could easily have made them look more like QR Codes if they had wanted to, but they made their own artistic choices. Which I love btw, but they could have maybe chosen better wording. Something like 'fingerprint' or 'mugshot' would have conveyed the idea of it being useful for identification, if not perfect, much better.
> There is a 1-1 mapping
It is strong, but not 1 to 1:
> Tubbenhauer computed, for instance, that the invariant uniquely identifies more than 97% of the knots with 18 crossings.
Since they said "the corresponding polynomial", they must mean the mapping between the colored hexagons and the knot polynomials.
> mapping
Which I not only mentioned in my comment, it is not even slightly unique to QR codes.
> they look kinda like QR codes
In what way? QR Codes are black and white, square, and asymmetrical. These are colourful, hexagonal, and symmetrical. By that token, a 16th century tile also “looks kinda like a QR Code”.
I very much doubt you could show one of these to someone, ask them what they are, and that they would answer “QR Code”. They don’t look alike at all.
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 30° slice of each one and save space without losing information.
Interesting article. I love it when maths gives us some beautiful visuals too.
this was so confusing at first not going to lie
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.
https://en.wikipedia.org/wiki/QR_code#License
Yeah these scientists need a legal teamhttps://www.qrcode.com/en/faq.html
https://greatreachinc.com/blog/one-thing-about-qr-codes-you-...
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?”
> Did the researchers name these “QR codes?”
Yes.