This worksheet shows Chladni patterns using the trace-method with list and point coloring. Here is used wave equation of 3D standing waves.
It is a well known equation for the zeros of the standing wave on a square Chladni plate (side length L) is given by the following: cos(n pi x / L) cos(m pi y / L) - cos(m pi x/L)cos(n pi y / L) = 0, where n and m are integers ( http://paulbourke.net/geometry/chladni/).
I generalised this equation for the three-dimensional case:
cos(k*x π/L)[cos(l*y π /L) cos(m*z π /L) +s*cos(m*y π /L) cos(l*z π /L)]+
cos(l*x π /L )[cos(k*y π /L) cos(m*z π /L) +s*cos(m*y π/L) cos(k*z π /L)] +
cos(m*x π /L)[cos(k*y π /L) cos(l*z π /L)+s*cos(l*y π /L ) cos(k*z π /L)]=0 , where k, l and m are integers, s=∓ 1.
