It is apparently easy to distinguish between geometric order and chaos.
The geometric order is represented by ideal mathematical forms (e.g. line, circle, square, plane, sphere, cube) and ideal relationships (e.g. perpendicularity, parallelism, symmetry, rhythm/regularity). Chaos is supposed to be the opposite of geometric order; it is represented by forms and relationships that are complex and hard to describe with the language of classic mathematics.
But things are not that simple. According to the theory of chaos, order is a special coincidence of a wider chaotic arrangement. This means that geometry exists inside chaos, and chaos undermines geometry all the time in a wide variety of ways. Reflection, refraction, surface texture and time dependent decay stand between us and ideal geometric forms.
Photography itself adds complexity to the subject. Even a chaotic stone wall when it is captured by the camera, is limited by the geometric rectangle chosen by the photographer.
The world famous site of Petra, in Jordan, is both an outstanding human realization and a staggering natural phenomenon.
The geometric monuments men carved in the narrow valley are a wonder to our spirit but, as a photographer, I could not resist the chaotic abstractions time has “painted” on natural rock all around.