The atoms of a surface in modern optics correspond one-to-one with the focus-points of an image, whereas the faces and facets of surfaces in ecological optics correspond to the nested forms of a structure. Change of an optic array can be thought of in quite different ways, as a set of motions of the elements of the array, or as a change in some or all of its parts. The motions of optical elements in an array can be compared to the motions of material bodies in space, and then the powerful mathematics developed for mechanics and kinetics is available for the analysis of an array. Gunnar Johansson’s analysis will work for what might be called a flat event seen from the front, or a transparent event, with the essential parts of the machine or the man always projected in the array.