These shapes are in fact well known by the geologists: they are "Liesegang rings" or "bandings", rings or bands made by diffusion and precipitation of various metallic elements (usually iron, but it can also be manganese, aluminium...), transported by water diffusing accross a porous stone. One of the most reknown instance of these "Liesegang bandings" are the famous colored sandstones of Petra in Jordania:

but they are found quite frequently in other sandstones all over the world: