(Part 2 of huge reply for Jodina. Pardon its length)
... It would be great if it could be tested by whoever would feel like it. I recognize with slight excitement patterns on vibrating squares uploaded here, from when I worked on those.
I am open to criticism or concerns by the way. I could re-upload if you would be more comfortable with a different presentation of them. Or if the images are not fit for the website, seeing as they have been pending approval for a while now, I would accept that too. Slightly confused by lack of communication. Perhaps you have been confused too. I don't know.
I hope this reply was of any help! Best wishes to you too. -Une
Hi Jodina. I have been experiencing limitations on the website, being unable to reply to your wall comment or verify that any of my messages were received. I have felt troubled by it.
The friend request a while back was merely another attempt of replying. You are free to decline it.
I have some time on my hands again and will reply here. This is my response to your comment on my wall, asking about my uploaded images of vibrating hexagons.
I am very fascinated by nature, its hidden patterns and connections and seek to understand how it all works. I believe true understanding comes from a combination of spirituality/inner knowing/awareness/art/big picture as well as math/physics/logic/detail/small picture. I have been seeking out and discovering cymatic patterns from a mathematical standpoint using laws that govern vibrations, and I am hoping my discoveries can be applied to greater contexts to further the understanding of myself and others.
I say this just in case: Don't be scared off by my terminology or use of the word wave. Although many associate a wave with something that travels in a straight line, I use the terms wave and vibration interchangably, because I see them as the same thing. I see a wave as something that can take on many forms: Extending ripples, fluctuations and oscillations, expanding and contracting bubbles, etc.
The precise form of the vibration would be governed by stuff like the initial state, how the tiny parts relate to their neighbors, any external forces/sources, and any obstacles/boundaries to the environment. I used some of these concepts to generate my images, which I will attempt to describe.
How the tiny parts relate to their neighbors: I used the wave equation for this. The wave equation doesn't necessarily imply a linear, traveling wave, and could as well be called the vibration equation. It says that each tiny point will attempt to reach the average pressure/stretchiness/etc of its immediate neighbors. Since I am not interested in chaotic vibrations that are all over the place without resonation, I gave the wave equation the additional requirement that each part would vibrate the same way (resonating), only at different amplitudes/strengths, some of which may be 0 and not vibrate at all. Salt/sand would gather here when on such a vibrating membrane or plate. The name of this modified wave equation with added conditions, is the Helmholtz equation.
(The wave equation applies to sound in a medium and to vibrating membranes, but not to vibrating plates, because plates have to do with bending rather than pressure or stretching. The modified version, the Helmholtz equation, also applies to freely vibrating plates, however.)
Boundary conditions: Different shapes produce different patterns due to the effect of the boundaries. I used boundary conditions in order to only get vibrations relevant to the shape I'm working with. For the images you asked about, I used the hexagon shape, where the boundary/edges would vibrate freely.
With the Helmholtz equation and the boundary conditions set, the only remaining vibrations I'd get, would be those that resonate at resonant frequencies of the hexagon. It should be possible to produce them on a vibrating plate as well, but for plates where the center is fixed and horizontal, only the patterns with at least two lines through the center can be produced.
I made my own computer program to find the patterns and to produce the images that I uploaded. I very much enjoy doing stuff like this and hope it can be used by others to further research on cymatics. I believe different ways of looking at something, together can enrich the overall understanding of it (so here I come with my logical background), and I seek to learn and understand more.
I have not yet produced any patterns on an actual/physical hexagonal surface. It would be great if it