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?
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.
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.
A couple of days ago there have been 2 HN threads about quasicrystals, one being about quasicrystals that are found in some very rare natural minerals, which form in special conditions, like meteorite impacts.
Some people before Mendeleev have thought about periodicity of the chemical properties with the atomic mass, but the genius of Mendeleev consisted mainly that he had much more trust in the idea that periodicity must exist.
So while his predecessors were discouraged by the discrepances between periodicity and the known chemical properties, Mendeleev assumed that periodicity is true and any facts that appear to contradict it must be caused either by earlier experimental mistakes that have produced wrong values for some chemical properties of the known elements or by the fact that some chemical elements have not been discovered yet, so empty spaces must be reserved for them in the periodic table.
Nonetheless, the periodic table that comes from Mendeleev has remained somewhat misleading until today, because it was based mainly on the periodicity of valence, which was indeed the most important chemical property for the chemical researchers of the 19th century, which were interested in laboratory experiments made for the discovery of new chemical substances and elements and for the investigation of their properties.
For practical applications, e.g. for the modern chemical industry or metallurgy, valence, which determines the ratios in which elements may combine to form substances, is only one of the properties of interest. The chemical behavior of elements is mainly determined by 3 characteristics, valence, i.e. the number of electrons on the outer layer, atomic size and electronegativity. All 3 properties are approximately periodic, but the quasi-periods vary slightly and a big cycle that goes between 2 noble gases is frequently segmented in 2 or more minor cycles within which properties vary monotonically, but they jump at boundaries. For example, the electronegativity grows from alkaline metals until Cu/Ag/Au, then it jumps down to Zn/Cd/Hg, then it grows again until the noble gases, after which it jumps downwards again.
The result is that for each of the 3 essential properties of a certain chemical element there may be different chemical elements in the next "period" that resemble best with it and only one of those is located in the same "group".
The classification of chemical elements in "groups" is only partially useful, because to really understand chemistry you must also understand the other kinds of similarities between elements, which group the elements in a different way than the periodic table of Mendeleev.
For instance, given the 3 elements carbon, oxygen and sulfur, it is impossible to say which pair of them contains more similar elements, so they can be grouped together. Oxygen and sulfur are in the same Mendeleev group, differing from carbon. However, carbon and sulfur have almost the same electronegativity, differing from oxygen, which causes a lot of similarity between many of their chemical compounds, e.g. between carbonates and sulfates. Moreover, carbon and oxygen have closer atomic sizes, differing from sulfur, which also explains many chemical properties, e.g. why the carbonate ion is CO3, while the sulfate ion is SO4.
A similar discussion can be done about almost any chemical elements, e.g. for some properties silicon resembles germanium and selenium resemble...
> Does aperiodicity have any cool properties that help in specific domains?
The proof of the aperiodic nature of the Wang tile set was showing that a Turing machine could be created out of Wang Tiles that tile the plane (periodic) if and only if the Turing machine does not halt. (I think I phrased that right)
> In 1966, Berger solved the domino problem in the negative. He proved that no algorithm for the problem can exist, by showing how to translate any Turing machine into a set of Wang tiles that tiles the plane if and only if the Turing machine does not halt. The undecidability of the halting problem (the problem of testing whether a Turing machine eventually halts) then implies the undecidability of Wang's tiling problem.
...
This means that you can create tiles that solve specific computations. Andrew Glassner's notebooks has a chapter on aperiodic tiles ( https://archive.org/details/andrewglassnersn0000glas/page/18... ) Page 216 has a tile set that finds the minimum of two numbers.
Crystals are a form of solid that in some sense have "long range regularity". One way (the obvious way) to have this is to have a (translational) symmetry. For a while, it was thought this was the only way. Aperiodicity (in the sense of this post) was then discovered, leading to the discovery of a new way to arrange matter that maintains this "long range regularity" without having translational symmetry, namely quasi-crystals. This was the basis of the 2011 Nobel Prize in Chemistry.
For a popular exposition on quasi-crystals you can see
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!
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?
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.
Nice to see that human intuition depends on periodicity when structures become unperiodic , classification becomes harder even if the rules under are deterministic
14 comments
[ 5.7 ms ] story [ 37.1 ms ] threadAlso: 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?
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.
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-e...
https://en.wikipedia.org/wiki/Aperiodic_tiling
https://en.wikipedia.org/wiki/Quasicrystal
https://en.wikipedia.org/wiki/Aperiodic_crystal
A couple of days ago there have been 2 HN threads about quasicrystals, one being about quasicrystals that are found in some very rare natural minerals, which form in special conditions, like meteorite impacts.
Some people before Mendeleev have thought about periodicity of the chemical properties with the atomic mass, but the genius of Mendeleev consisted mainly that he had much more trust in the idea that periodicity must exist.
So while his predecessors were discouraged by the discrepances between periodicity and the known chemical properties, Mendeleev assumed that periodicity is true and any facts that appear to contradict it must be caused either by earlier experimental mistakes that have produced wrong values for some chemical properties of the known elements or by the fact that some chemical elements have not been discovered yet, so empty spaces must be reserved for them in the periodic table.
Nonetheless, the periodic table that comes from Mendeleev has remained somewhat misleading until today, because it was based mainly on the periodicity of valence, which was indeed the most important chemical property for the chemical researchers of the 19th century, which were interested in laboratory experiments made for the discovery of new chemical substances and elements and for the investigation of their properties.
For practical applications, e.g. for the modern chemical industry or metallurgy, valence, which determines the ratios in which elements may combine to form substances, is only one of the properties of interest. The chemical behavior of elements is mainly determined by 3 characteristics, valence, i.e. the number of electrons on the outer layer, atomic size and electronegativity. All 3 properties are approximately periodic, but the quasi-periods vary slightly and a big cycle that goes between 2 noble gases is frequently segmented in 2 or more minor cycles within which properties vary monotonically, but they jump at boundaries. For example, the electronegativity grows from alkaline metals until Cu/Ag/Au, then it jumps down to Zn/Cd/Hg, then it grows again until the noble gases, after which it jumps downwards again.
The result is that for each of the 3 essential properties of a certain chemical element there may be different chemical elements in the next "period" that resemble best with it and only one of those is located in the same "group".
The classification of chemical elements in "groups" is only partially useful, because to really understand chemistry you must also understand the other kinds of similarities between elements, which group the elements in a different way than the periodic table of Mendeleev.
For instance, given the 3 elements carbon, oxygen and sulfur, it is impossible to say which pair of them contains more similar elements, so they can be grouped together. Oxygen and sulfur are in the same Mendeleev group, differing from carbon. However, carbon and sulfur have almost the same electronegativity, differing from oxygen, which causes a lot of similarity between many of their chemical compounds, e.g. between carbonates and sulfates. Moreover, carbon and oxygen have closer atomic sizes, differing from sulfur, which also explains many chemical properties, e.g. why the carbonate ion is CO3, while the sulfate ion is SO4.
A similar discussion can be done about almost any chemical elements, e.g. for some properties silicon resembles germanium and selenium resemble...
The proof of the aperiodic nature of the Wang tile set was showing that a Turing machine could be created out of Wang Tiles that tile the plane (periodic) if and only if the Turing machine does not halt. (I think I phrased that right)
https://en.wikipedia.org/wiki/Wang_tile
> In 1966, Berger solved the domino problem in the negative. He proved that no algorithm for the problem can exist, by showing how to translate any Turing machine into a set of Wang tiles that tiles the plane if and only if the Turing machine does not halt. The undecidability of the halting problem (the problem of testing whether a Turing machine eventually halts) then implies the undecidability of Wang's tiling problem.
...
This means that you can create tiles that solve specific computations. Andrew Glassner's notebooks has a chapter on aperiodic tiles ( https://archive.org/details/andrewglassnersn0000glas/page/18... ) Page 216 has a tile set that finds the minimum of two numbers.
There's also some "if you use Wang Tiles you can pattern textures without repeating groups" - https://www.researchgate.net/publication/2864579_Wang_Tiles_...
For a popular exposition on quasi-crystals you can see
https://www.quantamagazine.org/quasicrystals-spill-secrets-o...
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!
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.