See art composition books, especially "The Painter's Secret Geometry". Or else Google "The armature of the rectangle" or "Harmonic Symmetry".
IDK. What irks me with approaches like these that try to capture why a composition works, is that they suggest a logic by drawing basically every shape onto the image that they can think of and then argue something is happening in parallel with the lines, on crosspoints, in certain sections etc. The problem with this is that it's evident that if you criss-cross the entire image with a sufficient number of lines (as happens in particular in the armature trick), there's
always something happening in relation to those lines. And if the armature doesn't work, we can always throw the golden ratio at it.
The way I see it:
* There are no rules to composition. I think we all agree on this when it comes to making an image, but oddly, it doesn't apply once we try to understand why an image 'works'. Worse yet, maybe there are rules to making effective images, maybe there are rules to understanding effectiveness, and maybe effective images are effective because they break the rules - or yet again, maybe there are no rules. Truth is: "anything goes" (in the meaning of Feyerabend! Read the quote in its context, don't take it at face value - the context is essential.)
* Whatever works well, compositon-wise, is difficult to disentangle from other aspects of the image, like subject matter, contrast and color. The visual and emotional impact is always the combined effect of the total image.
* What 'works' in terms of composition is inherently culturally programmed. We like what we see if we've seen a lot along similar lines before. So it's debatable in the first place how universal 'rules' for composition are. It's an interesting question to what extent there's anything inherently human (or even reptile brain) about how we view images - or that it's basically all programming. Nature/nurture, if you will. The relevance of this is that the nurture argument would make all attempts to understand effective composition tautological - it's effective because we've always done it that way, and that's in turn what makes it work. The argument becomes void of meaning.
* I think there's something like 'visual logic' and it's debatable whether it can be captured into something as simple as a mesh of lines overlayed on top of an image. It's debatable even whether it can be captured in words (and I've had a pretty heated argument on that one with a good friend of mine - I'm still on the fence about it). It's a bit like trying to smash an effective poem into a rhyme pattern (many poems work despite/because they don't have one, to begin with!), or a classic movie into an archetypical storyline. The pattern is discernable, but it's at best only part of the essence underlying the question 'why it works'.
When it comes to the image in this thread, I really wouldn't be able to see whether it 'works' from a universal viewpoint. Apparently not. I still like it, personally. Why? Maybe it's because of a winter scene in a landscape that's familiar to me. It has something to do with the rhythm of the trees. The elusiveness of the foreground that tries to escape definition (something that reflections often do). The contrast relations. And yes, the ratios between lines, and dark and light surface area also does something. I couldn't pinpoint one particular aspect that "does it", let alone that I think it's meaningful to try and flatten it into a system of lines that you could put on top of the image. I don't think (in general, and especially in this case) that such an approach could ever capture the visual logic of an image like this. It may (will, does) work for illustrations and patterns used in e.g. wallpapers and also in geometric Islamic art. But that's a whole different ballgame (see also 'cultural programming' above).
