If you haven't already, read the book "The Second Kind of Impossible" by Paul Steinhardt

https://www.goodreads.com/book/show/35297608-the-second-kind...

It's a riveting account of years of research to discover Quasicrytals from theory, to experiments, to literally hunting in a meteor field in eastern Russia!

Related, if you're interested in byproducts of nuclear explosions:

> researchers have identified a new material within trinitite called a clathrate—a cagelike chemical lattice that traps other atoms inside it.[0]

[0]https://www.scientificamerican.com/article/strange-crystals-...

There are also "natural" paracrystalline viruses that turn isopods blue and then kill them.

https://en.wikipedia.org/wiki/Invertebrate_iridescent_virus_...

There was a mathematician and a chemist arguing these structures had a pattern that had something to do with the distribution of prime numbers. https://www.quantamagazine.org/a-chemist-shines-light-on-a-s...

tl;dr Quasicrystals are aperiodic structures. The author notes that the conditions for creating them are rare, given the need for instantaneous high temperature. They recount that these can happen during space debris impact and when lightning hits sand. They close out by describing some of the chemical 'formulas' for these materials, given that characterizing a prototypical section is difficult without repeating elements.

I don't have anything to say about quasicrystals, other than it seems right up this blog's alley, as the other most recent articles are about math and materials (like feldspars [0]).

[0] https://www.explainxkcd.com/wiki/index.php/2501:_Average_Fam...