5 ms·

The Aperiodic Table

94 points by jgrahamc 5mo ago

pohl 5mo ago
Don't miss that you can click through to aperiodictable.com to see it live. Also: when did everyone stop calling this quasiperiodic and start calling it aperiodic? I feel like the almost-but-not-quite translational symmetry was a useful distinction. Has it fallen out of favor?
- jerf 5mo ago
  I believe it is just "as of" the XKCD comic, for which "aperiodic table" seems more sensible than "quasiperiodic table" for how the comic was written. The exciting thing about using the Penrose tiling is that you get "aperiodic" without it just being completely arbitrary. For that it is natural to borrow XKCD's terminology for this particular project. I don't think mathematicians are going to change their term to "aperiodic". Almost everything is aperiodic. Quasiperiodic indicates something much more interesting is happening.
- argee 5mo ago
  Everyone's focused on the aperiodic part, meanwhile I'm wondering just what about this visual qualifies as a "table"...I suppose "aperiodic voronoi" doesn't quite have the same ring.
nilirl 5mo ago
Even after reading the Wikipedia entry I couldn't intuit what Aperiodicity means. Does it mean simply lack of pattern? But that doesn't seem to be the case, at least visually. Just last month I wrote a post about how Mendeleev's real genius was in how we went looking for periodicity [0] and how that helped predict elements. Does aperiodicity have any cool properties that help in specific domains? [0] https://www.nair.sh/guides-and-opinions/communicating-your-expertise/how-to-use-a-spreadsheet-for-creativity https://www.nair.sh/guides-and-opinions/communicating-your-e...
- keeganpoppen 5mo ago
  > Does aperiodicity have any cool properties that help in specific domains? well, it helps as the basis for all life on the planet as we know it (DNA, RNA, et al.). which is pithy, but i think actually has fairly deep implications (ie is not _just_ pithy).
  - TacticalCoder 5mo ago
    > well, it helps as the basis for all life on the planet as we know it (DNA, RNA, et al.) And how much of that would we have understood if not for Mendeleev allowing us to discover new elements thanks to the periodicity of its table? Elements in Mendeleev's table are at a lower level than DNA / RNA.
  - gilleain 5mo ago
    DNA is one-dimensional aperiodicity, which is ... fairly common. This sentence is one-dimensionally aperiodic! Most biological structures are amorphous in some way, rather than strictly aperiodic. There are structures (honeycombs, for example) that are extremely regular, and especially on smaller scales (like virus capsids). Other biological structures are loosely fractal (self-similar across a narrow range) - lungs, blood systems, and so on. I don't know of any biological structures that could accurately be described as aperiodic - like a quasicrystal - but given I'm just learning about Defense-associated reverse transcriptases, it would not surprise me if there is something out there.
- danbruc 5mo ago
  There exists no translation that leaves the tiling of the entire plane unchanged. The same local pattern [1] will of course occur repeatedly, there are only so many different patterns of any given size, but if you look at large enough scales, any translated copy will eventually diverge. Maybe someone can make a version of this - if it not already exists - where you can move a semitransparent copy of the tiling around, maybe with a score for the alignment achieved. [1] I am not sure if this is true, but as we have to tile an infinite plane, I could imagine that any pattern of finite but arbitrary size will occur infinitely often.
- 5mo ago
oersted 5mo ago
I would have found an aperiodic monotile (single shape) a bit more satisfying. https://momath.org/the-hat/ https://momath.org/the-hat/ But the simplicity of the shapes in the Penrose tiling has its own charm. And the way it rearranges itself when scrolling around the tiling is awesome!
pavel_lishin 5mo ago
This is very cool, but are the actual relationships between the elements represented as you drag the table around? Or does it just set the element in the "nearest neighbor" spot?
- jgrahamc 5mo ago
  The code attempts to retain the "shape" and "layout" of the periodic table.
  - Kotlopou 5mo ago
    I'm sorry, but... this is why I'm unhappy about AI-generated projects. The parent post asked a more-or-less specific question about how this works and offered their working hypothesis (that it works by taking the rectangular periodic table and mapping each element to its nearest Penrose tile). I would also be curious about this, because e.g. it seems non-obvious to me that the resulting table would have no holes inside. Does there have to be any extra step to ensure that? But your reply is not informative at all. If you wrote this yourself from scratch, you would be able to answer this kind of question (and report on anything interesting that came up while creating the program), but this way the post just hangs here to be forgotten, and I haven't learned a new thing about Penrose tilings. :(
    - jgrahamc 5mo ago
      The code includes an ELEMENTS array with the layout of elements on the standard periodic table with H at the (1, 1) position. The tiles are laid out on the page and the code attempts to place the elements as close to the "standard" position (rectilinear) by calculating the Euclidean distance from the centroid of rhombi to the centre of the square that would be drawn for the element in the standard table. So you've got 118 elements with ideal locations and a whole bunch of rhombi with known locations. The Euclidean distance (without bothering with the sqrt) is used as the "cost" function for the Hungarian algorithm (https://en.wikipedia.org/wiki/Hungarian_algorithm https://en.wikipedia.org/wiki/Hungarian_algorithm): the idea is to minimize the cost (distance from ideal) for each element. You will sometimes see some gaps in the periodic table as this layout isn't "perfect" (in the sense of without isolated rhombi inside the table) and I did work on having a post-layout pass where these islands were identified and filled by moving adjacent rhombus assignments, but I wasn't happy with how this tended to break the layout of the periodic table (I was going for some visual "looks similar to the classic U shaped periodic table) and so decided to accept them.
khhghuing 5mo ago
[dead]
sashank_1509 5mo ago
Aside and maybe controversial: If I didn’t know that the author used AI, then I would have liked this way more. But that is because I would assume the author did this on his own and that would feel like a cool quirky thing to do. I just don’t care for a cool quirky thing if an AI made it.
- RationPhantoms 5mo ago
  > I just don’t care for a cool quirky thing if an AI made it. While I understand the knee-jerk reaction, especially to writing, people make about AI, it's starting to have a counter-effect on me. A brush can destroy (sweep) or create (paint) but it's still a tool.
- HiroProtagonist 5mo ago
  I don't think it is necessarily controversial, but I subscribe to the opposite view. I try to judge a thing by whether or not it is good, not by its provenance. For example, if I read a book which I thought was written by a human and loved it, why should my opinion change if I learned after the fact that it was written by AI and not a human? I can't un-laugh those laughs, and un-enjoy the enjoyment I received from it, you know what I mean?
  - tiagod 5mo ago
    Imagine you really enjoyed your meal at a restaurant, and in the end the waiter tells you it's made of people. Is it still a good meal, and most importantly, would you recommend it to other people?
    - drugstorecowboy 5mo ago
      I really don't think this is the same thing. A closer analogy would be you enjoy your meal at a restaurant, and at the end the waiter tells you the chef was a robot. Why should the provenance of something make any difference at all? If the author of your favorite book was convicted of some terrible crime, would the book you loved so much before you heard the news suddenly lose all its value to you?
jerf 5mo ago
Tempted to 3D print something based on this. It's pretty neat. And now's the time, too, while the periodic table ends nicely at the last row.
- jgrahamc 5mo ago
  Do it! Make an aperiodic table jigsaw with tiles that are elements and a lot of blanks!
  - jerf 5mo ago
    I'm not a woodworker. (By which I mean I don't have any of those tools, not that I'm unwilling to learn. But I would need $1K+ of tools to get started.) I have a different idea I'm going for. The first test print is just finishing up as I type this, if it works it'll be a bit to print everything but hopefully it'll look cool when I'm done. I'm going more for a puzzle intended to hang on the wall.
bassrattle 5mo ago
Interesting! I just built aperiodicgenerator.com to do this with aperiodic monotiles. Would love some feedback!
latentframe 5mo ago
Nice to see that human intuition depends on periodicity when structures become unperiodic , classification becomes harder even if the rules under are deterministic

94 points by jgrahamc 5mo ago

pohl 5mo ago

Don't miss that you can click through to aperiodictable.com to see it live. Also: when did everyone stop calling this quasiperiodic and start calling it aperiodic? I feel like the almost-but-not-quite translational symmetry was a useful distinction. Has it fallen out of favor?

jerf 5mo ago
I believe it is just "as of" the XKCD comic, for which "aperiodic table" seems more sensible than "quasiperiodic table" for how the comic was written. The exciting thing about using the Penrose tiling is that you get "aperiodic" without it just being completely arbitrary. For that it is natural to borrow XKCD's terminology for this particular project. I don't think mathematicians are going to change their term to "aperiodic". Almost everything is aperiodic. Quasiperiodic indicates something much more interesting is happening.
argee 5mo ago
Everyone's focused on the aperiodic part, meanwhile I'm wondering just what about this visual qualifies as a "table"...I suppose "aperiodic voronoi" doesn't quite have the same ring.

nilirl 5mo ago

Even after reading the Wikipedia entry I couldn't intuit what Aperiodicity means. Does it mean simply lack of pattern? But that doesn't seem to be the case, at least visually. Just last month I wrote a post about how Mendeleev's real genius was in how we went looking for periodicity [0] and how that helped predict elements. Does aperiodicity have any cool properties that help in specific domains? [0] https://www.nair.sh/guides-and-opinions/communicating-your-expertise/how-to-use-a-spreadsheet-for-creativity https://www.nair.sh/guides-and-opinions/communicating-your-e...

keeganpoppen 5mo ago
> Does aperiodicity have any cool properties that help in specific domains? well, it helps as the basis for all life on the planet as we know it (DNA, RNA, et al.). which is pithy, but i think actually has fairly deep implications (ie is not _just_ pithy).
- TacticalCoder 5mo ago
  > well, it helps as the basis for all life on the planet as we know it (DNA, RNA, et al.) And how much of that would we have understood if not for Mendeleev allowing us to discover new elements thanks to the periodicity of its table? Elements in Mendeleev's table are at a lower level than DNA / RNA.
- gilleain 5mo ago
  DNA is one-dimensional aperiodicity, which is ... fairly common. This sentence is one-dimensionally aperiodic! Most biological structures are amorphous in some way, rather than strictly aperiodic. There are structures (honeycombs, for example) that are extremely regular, and especially on smaller scales (like virus capsids). Other biological structures are loosely fractal (self-similar across a narrow range) - lungs, blood systems, and so on. I don't know of any biological structures that could accurately be described as aperiodic - like a quasicrystal - but given I'm just learning about Defense-associated reverse transcriptases, it would not surprise me if there is something out there.
danbruc 5mo ago
There exists no translation that leaves the tiling of the entire plane unchanged. The same local pattern [1] will of course occur repeatedly, there are only so many different patterns of any given size, but if you look at large enough scales, any translated copy will eventually diverge. Maybe someone can make a version of this - if it not already exists - where you can move a semitransparent copy of the tiling around, maybe with a score for the alignment achieved. [1] I am not sure if this is true, but as we have to tile an infinite plane, I could imagine that any pattern of finite but arbitrary size will occur infinitely often.
5mo ago

oersted 5mo ago

I would have found an aperiodic monotile (single shape) a bit more satisfying. https://momath.org/the-hat/ https://momath.org/the-hat/ But the simplicity of the shapes in the Penrose tiling has its own charm. And the way it rearranges itself when scrolling around the tiling is awesome!

pavel_lishin 5mo ago

This is very cool, but are the actual relationships between the elements represented as you drag the table around? Or does it just set the element in the "nearest neighbor" spot?

jgrahamc 5mo ago
The code attempts to retain the "shape" and "layout" of the periodic table.
- Kotlopou 5mo ago
  I'm sorry, but... this is why I'm unhappy about AI-generated projects. The parent post asked a more-or-less specific question about how this works and offered their working hypothesis (that it works by taking the rectangular periodic table and mapping each element to its nearest Penrose tile). I would also be curious about this, because e.g. it seems non-obvious to me that the resulting table would have no holes inside. Does there have to be any extra step to ensure that? But your reply is not informative at all. If you wrote this yourself from scratch, you would be able to answer this kind of question (and report on anything interesting that came up while creating the program), but this way the post just hangs here to be forgotten, and I haven't learned a new thing about Penrose tilings. :(
  - jgrahamc 5mo ago
    The code includes an ELEMENTS array with the layout of elements on the standard periodic table with H at the (1, 1) position. The tiles are laid out on the page and the code attempts to place the elements as close to the "standard" position (rectilinear) by calculating the Euclidean distance from the centroid of rhombi to the centre of the square that would be drawn for the element in the standard table. So you've got 118 elements with ideal locations and a whole bunch of rhombi with known locations. The Euclidean distance (without bothering with the sqrt) is used as the "cost" function for the Hungarian algorithm (https://en.wikipedia.org/wiki/Hungarian_algorithm https://en.wikipedia.org/wiki/Hungarian_algorithm): the idea is to minimize the cost (distance from ideal) for each element. You will sometimes see some gaps in the periodic table as this layout isn't "perfect" (in the sense of without isolated rhombi inside the table) and I did work on having a post-layout pass where these islands were identified and filled by moving adjacent rhombus assignments, but I wasn't happy with how this tended to break the layout of the periodic table (I was going for some visual "looks similar to the classic U shaped periodic table) and so decided to accept them.

khhghuing 5mo ago

[dead]

sashank_1509 5mo ago

Aside and maybe controversial: If I didn’t know that the author used AI, then I would have liked this way more. But that is because I would assume the author did this on his own and that would feel like a cool quirky thing to do. I just don’t care for a cool quirky thing if an AI made it.

RationPhantoms 5mo ago
> I just don’t care for a cool quirky thing if an AI made it. While I understand the knee-jerk reaction, especially to writing, people make about AI, it's starting to have a counter-effect on me. A brush can destroy (sweep) or create (paint) but it's still a tool.
HiroProtagonist 5mo ago
I don't think it is necessarily controversial, but I subscribe to the opposite view. I try to judge a thing by whether or not it is good, not by its provenance. For example, if I read a book which I thought was written by a human and loved it, why should my opinion change if I learned after the fact that it was written by AI and not a human? I can't un-laugh those laughs, and un-enjoy the enjoyment I received from it, you know what I mean?
- tiagod 5mo ago
  Imagine you really enjoyed your meal at a restaurant, and in the end the waiter tells you it's made of people. Is it still a good meal, and most importantly, would you recommend it to other people?
  - drugstorecowboy 5mo ago
    I really don't think this is the same thing. A closer analogy would be you enjoy your meal at a restaurant, and at the end the waiter tells you the chef was a robot. Why should the provenance of something make any difference at all? If the author of your favorite book was convicted of some terrible crime, would the book you loved so much before you heard the news suddenly lose all its value to you?

jerf 5mo ago

Tempted to 3D print something based on this. It's pretty neat. And now's the time, too, while the periodic table ends nicely at the last row.

jgrahamc 5mo ago
Do it! Make an aperiodic table jigsaw with tiles that are elements and a lot of blanks!
- jerf 5mo ago
  I'm not a woodworker. (By which I mean I don't have any of those tools, not that I'm unwilling to learn. But I would need $1K+ of tools to get started.) I have a different idea I'm going for. The first test print is just finishing up as I type this, if it works it'll be a bit to print everything but hopefully it'll look cool when I'm done. I'm going more for a puzzle intended to hang on the wall.

bassrattle 5mo ago

Interesting! I just built aperiodicgenerator.com to do this with aperiodic monotiles. Would love some feedback!

latentframe 5mo ago

Nice to see that human intuition depends on periodicity when structures become unperiodic , classification becomes harder even if the rules under are deterministic