Charles Henry czhenry at gmail.com
Wed Mar 28 17:05:48 CEST 2007

```> The patterns probably depend on the stiffness of the plate/membrane as
> well as its shape, and the grain size and density of the sand.

It should depend on stiffness, density and shape.  The speed of sound
in a material is sqrt(stiffness/density).  The partial differential
equation for waves depends on these two constants, and the amplitude
of forcing. The units are a little tricky (and they are different
depending on the number of dimensions)
I have been engrossed by this idea, since I read it on the list :)
I'm sure you'll have a lot to research to make this work, and I really
hope you make something cool!

> By
> analogy with the Karplus-Strong vibrating string, which is a
> one-dimensional CA, usually the stiffness of the string is ignored.
> Also, the grain size would be the same as the pixel size and the density
> would be ignored. I see it as being like 2D version of the KS waveguide,
> with the superimposed grains moving in each time step towards the
> neighbour whose vertical acceleration is the lowest among 8 neighbours.
> Apart from the difficulty of doing a 2D KS, there is the further
> complication of an external frequency forcing (maybe introduced at the
> edges of the plate?).
>
> Martin

I see the edges as being different kinds of boundary conditions,
Dirichlet, Neumann, and Robin.
Dirichlet -> amplitude is zero at the boundary (reflected waves are
180 deg out of phase)
Neuman -> 1st deriviative is zero at the boundary (reflected waves are
in phase with incoming waves)
Robin -> 1st order differential equation (specifies a constant phase
difference between incoming/reflected waves)

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