The code attempts to retain the "shape" and "layout" of the periodic table.
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. :(
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): 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.
I still find it curious how few holes there are (took a while to find one!), and finally figured out why: imagine a large square grid. It would probably have a different density than the rhombus grid, and it seems nontrivial to match it up. It seems that in the code this is done by each rhombus having edge length 50 while the periodic table elements are 38 x 42 pixels in size.
This, if I understand it correctly, means that this tiling is not just aperiodic but (in this regard) also anisotropic -- it's denser in one direction than another. And thus I have learned a new thing about Penrose tilings. :)
The other thing was the title. The code originally could have had two letters (e.g. P and E in APERIODIC) joined at a vertex and it looked odd (it looked like the word was broken) so there's specific code to make sure that doesn't happen.