# Wave Convergence generator, pretty patterns

## Main Question or Discussion Point

Hi everyone, here is a web browser program of a complicated wave-pattern generator:
https://dl.dropboxusercontent.com/u/114667999/Public.html [Broken]

i wished to have a formula that explains cymatics patterns, and patterns found in wave tanks, because they are fascinating. I wrote an program that can produce similar patterns to those found in square 2d plates wave tanks. it has some distant relation to wave interactions on the atomic scale perhaps?

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Bessel functions come to mind. But it depends on the shape of your vibrating drum head/cymatics plate. Different shapes can have different special functions for solutions.

What does your program do? Numerically solve some form of laplace's equation?

it is uber simple mathematics, so everything was written using multiplications and additions. rather than deriving an equation, the program is inspired by thinking of water ripples.

when a drop arrives in the middle of a water tank, it it rebounds simultaneously from the 4 borders towards the centre again and the waves combine by addition. so I coded 5 drops in different positions, one drop in the middle, and 4 drops around it in a cross pattern, each drop on water is a concentric ring of sine waves. the resulting 2-D patterns were amazing, so I figured that the waves would rebound again at the other end of the wave tank and so I should add another 4 drops further away, to make more the physical modelling even better. So what you see is basically 9 drops falling on an infinitely large pond in a cross pattern. varying the distances of the 1st and 2nd set of concentric rings, from the centre, as well as their amplitude and period, produces all the variation.

As a finishing touch, I added another concentric polar rose in the middle that should be similar to some of the radial patterns that would happen due to reflections that corners of the wave tank/two-dimensional metal plate, and it exponentially multiplies the variation of patterns from the original 9 drop model. What it is missing is real mathematics!

In a cymatics plate there are very strong standing waves relative to the length of the plate parallel and at 45'degrees, and the plate tends to form square and Diamond shaped cells of similar wave patterns. I don't know how you would rewrite it for a round pond! the result is an imaginary material mathematically completely inaccurate! It's because I learnt mathematics by designing synthesisers, and when you recreate sounds of violins and gongs, you have to kind of make up a physical model of the instrument with sine waves etc! sonically it's a not at all harmonious.

also note that combining round and square makes the mandelbox ;)

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