Some ideas regarding Chladni. Untested code in Nim (sorry) as it has to 
fit into my pattern and audio synthesis stuff, but it should not be to 
complex to convert to POV-Ray (I'm tempted).

for a rectangulare plate:

proc chladniRect*(ampA, ampB, m, n, Lx, Ly: float): Pattern =
   proc fn(x, y, z: float): float =
     ampA * sin(PI * m * x / Lx) * sin(PI * n * y / Ly) +
     ampB * sin(PI * n * x / Lx) * sin(PI * m * y / Ly)
   initPattern(fn)


proc chladniRectFreq*(m, n, Lx, Ly, waveSpeed: float): float =
   (waveSpeed / 2.0) * sqrt((m/Lx)*(m/Lx) + (n/Ly)*(n/Ly))

type
   PlateMaterial* = object
     E:   float    # Young's modulus (Pa) - stiffness
     rho: float    # density (kg/m³)
     nu:  float    # Poisson's ratio - lateral contraction
     h:   float    # thickness (m)

const
   Steel* = PlateMaterial(
     E: 200e9, rho: 7800.0, nu: 0.28, h: 0.001
   )

   Aluminium* = PlateMaterial(
     E: 70e9, rho: 2700.0, nu: 0.33, h: 0.001
   )

   Glass* = PlateMaterial(
     E: 70e9, rho: 2500.0, nu: 0.23, h: 0.001
   )

   Wood* = PlateMaterial(          # spruce, along grain
     E: 12e9, rho: 450.0,  nu: 0.35, h: 0.003
   )

   Brass* = PlateMaterial(
     E: 100e9, rho: 8500.0, nu: 0.35, h: 0.001
   )


proc waveSpeed*(mat: PlateMaterial): float =
   ## Flexural wave speed in thin plate
   let B = mat.E * mat.h * mat.h * mat.h /
           (12.0 * (1.0 - mat.nu * mat.nu))    # bending stiffness
   let rhoH = mat.rho * mat.h                  # mass per unit area
   sqrt(B / rhoH)                              # simplified phase velocity


now the other way around:
f_mn = (c / 2) * sqrt((m/Lx)^2 + (n/Ly)^2)
invert
(2f/c)² = (m/Lx)^ + (n/Ly)^

now finde modes at frequency
loop over modes, get chladni and sum
this should then be convered to a spectrogram and create the sound from 
that.

It can be extended to 3d room modes so one can simulate small room 
acoustics (below Schroeder freq) and walk trough a .df3 media room that 
show the soundfield.

ingo

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