ASCII permutations of a short range of square Chladni plates.
http://www.hevanet.com/solipsis/desktopcollage/chladni1an.gif here are some the original drawings Chladni did. http://www.hevanet.com/solipsis/desktopcollage/original.gif The basic experiment that is given the name "Chladni" consists of a plate or drum of some shape, possibly constrained at the edges or at a point in the center, and forced to vibrate historically with a violin bow or more recently with a speaker. A fine sand or powder is sprinkled on the surface and it is allowed to settle. It will do so at those parts of the surface that are not vibrating, namely at the nodes of vibration. The equation for the zeros of the standing wave on a square Chladni plate (side length L) constrained at the center 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. The Chladni patterns for n,m between 1 and 5 are shown in the ASCII animation. Some Further background: Ernest Florens Friedrich Chladni (1756 - 1827) performed many experiments to study the nodes of vibration of circular and square plates, generally fixed in the center and driven with a violin bow. The modes of vibration were identified by scattering salt or sand on the plate, these small particles end up in the places of zero vibration. Ernst Chladni first demonstrated this at the French Academy of Science in 1808, it caused such interest that the Emperor offered a kilogram of gold to the first person who could explain the patterns. The Wikipedia Entry: http://en.wikipedia.org/wiki/Ernst_Florens_Friedrich_Chladni
