The only thing missing from this is a reference to the mathematical theory of harmonic analysis, which provides a way to calculate the exact eigenvalues (or modes) of these systems (well at least a linear approximation to them). In particular, there is a lot that can be said about such systems (formally defined by a self-adjoint operator on a Hilbert space) beyond simply simulating them.
It is believed that the stone carvings in the Rosslyn Chapel show not only knowledge of these Chladni patterns, but also represent the first use of them to encode information. It's believed by some who study them that they encoded sacred melodies in the physical structure of the church in a way that only those with hidden knowledge (at the time) could decipher.
The most fascinating thing about the Rosslyn Chapel is that since it was built during the 1400s it predates Chladni by at least THREE CENTURIES! That's pretty fantastic in itself.
"Like many claims in the cymatics community, the hypothesis that the carvings represent Chladni patterns is not supported by scientific or historical evidence.[citation needed] One of the problems is that many of the 'box' carvings are not original, having been replaced in the 19th century following damage by erosion."
Citation needed indeed, but there's no academic research about this extravagant theory anyways, and with my foray into the subject, I just found the patterns to be decorative geometric shapes with a coincidental resemblance to Chladni patterns.
I know it's debated, but it wouldn't be the first time humanity rediscovered forgotten knowledge! What intrigues me about it is it still lines up with Occams Razor and the KISS principle, if mystics and academics of the day wanted to encode secret knowledge this would fit the bill perfectly at the time the original chapel was built.
I haven't looked I to the actual history as much, I ran across Rosslyn reading about art history and cathedral architecture and I spent a lot more time reading about Chladni patterns than I ever did about Rosslyn itself. Thought the link would be interesting in light of the original article.
Now what I am wondering is the shapes of these patterns on non-square and non-circular plates. I haven't seen many exotically shaped plates so it leads me to wonder if the patterns don't show up as well on other shapes. I'm curious from a visual perspective what 'patterns' occur in nature like some people obsess about relationships between made-up numbers ;)
I had heard about these a million times and understood laser resonance, but hadn't previously made the connection to atomic resonance! Not sure I fully grasp it yet, but it's great to have identified that area :-)
