The pictures in this directry are related to Chladni figures. They were made with the programs in the subdirectory Notebooks. staaf3.gif shows a snapshot of an oscillating thin bending bar with free ends. The solution has 3 nodes. The equations are u´´´´ = freq² u with boundary conditions u´´´(1) = u´´´(-1) = u´´(1) = u´´(-1) = 0. Here freq is proportional to the frequency of oscillation. The proportionality constant depends on things like the stiffness of the bar. min8-3.gif and plus8-3.gif show pretend snapshots for an oscillating thin square plate. They are built naively from the solutions in staaf3.gif and staaf8.gif. Thus min8-3.gif shows f(x)g(y)-f(y)g(x), where f is from staaf8.gif and g from staaf3.gif. Black is negative. The displayed frequency ignores the exponential terms in f and g. We could not solve the equations symbolically. Lord Rayleigh, Theory of Sound, page 372, calls this problem difficult. rond1-2.gif shows a snapshot for an oscillating thin round plate of radius one. We simplified the boundary conditions. If Delta denotes the Laplacian, then the equations are Delta Delta u = freq² u with our boundary conditions saying that both Delta u and its gradient vanish on the boundary. Black is negative and freq is as above.