There is no doubt that Henri Carier-Bresson knew his stuff and was very well acquainted with compositional theory. I have no doubt that he knew all about dynamic symmetry as well, I do an I'm nowhere near as good a photographer as he was.

Did he actively apply this to his images? I'm very sure that the answer is no. Photography does not lend itself to such precision, and it is not possible to capture dynamic scenes with that precision. But if you do study composition you become far more aware of the patterns and possibilities suggested by the frame, (yes it is the frame that contains these patterns and not the image, in the following I will re-create these patterns entirely from the frame and never from an image in a frame. It must follow then that the patterns are entirely a function of the frame and never the image. It thus follows that composition is ALL about where you put the frame).

As you become more aware of more complex patterns, including ones that are formed from points outside of the frame, you become more instinctively aware of them. Many times when you photograph the patterns and symmetries are more instinctive, you shoot first and analyse later.

One reason thirds is mis-understood is because if you never go beyond it and see the myriad of other patterns and symmetries available you will only ever see in "thirds" and so only ever compose in them.

The same is true of HCB, I do not doubt that he never limited himself to a single pattern or theory but researched and made himself familiar with many. He then "shot from the hip" and tightened it later with a crop when he had time to analyse what was at first instinctive.

What I do object to is those who think that in knowing a label, a word to attach to something, we understand composition. That we can compress all composition into one idea and somehow by knowing what to call it we have a complete knowledge. This is nothing more than just finding a cleverer sounding version of the rule of thirds, shoehorning a logical framework around it, making it fit into an idea rather than understanding the ideas and principles that drive things like dynamic symmetry.

Composition can be distilled into a simple principle that's best understood with the following example:

On a completely blank wall with no measuring device mark out a horizontal line that's exactly on meter in length, in short guess a meter.

Next, whatever your length of line is mark the spot in the exact centre of it.

If you repeated this with a hundred people a pattern would emerge and that is that although you will get a lot of variations in the length of the line just about everybody will be far more accurate in marking the centre point. The principle is simple, we do not see in absolutes, vision is relative. We do not see in meters and centimetres, we see by division and proportion. Our whole understanding of the 3D world is based on this, "small or far away" is simply an understanding of an object and experience of it's size when close compared to it's size in the landscape. A cow in a field, for example, we know how big they are and in comparison we know a small one is further away.

It is exactly the same when you place a frame around a subject, we can judge the centre of the frame, or divide it into thirds. There are symmetries that we also find pleasing without ever understanding their roots or construction. Dynamic symmetry is one of many, and it is a specific symmetry that applies to specific rectangles only.

The very special case of dynamic symmetry

Pythagoras gives us a very simple equation that links the sides of a right angled triangle with it's hypotenuse. The same is also true of a square that's liked to it's diagonal. If you take the diagonal of a square and use it to make up the long side of a rectangle then the proportion of the sides is 1: square root of 2. Basically called a root 2 rectangle. It is very important because there is an intrinsic relationship between the rectangle, the square it was formed from and the diagonals contained within.

The simple patterns that can be used in any rectangle are contained in the Photoshop Crop tool:

These are shown on a "golden ratio" rectangle that's derived from a root 2 rectangle and is a dynamic rectangle. If I combine them using both diagonals for the first grid continuing the truncated line to the corner you get this:

Yes, it's the grid for dynamic symmetry with all the silly names given to the diagonals. But how can one diagonal be different from another if the symmetry is dynamic? This mis-conception really masks what the special case of dynamic symmetry is about.

So what if we check that symmetry by rotating the rectangle by 90 degrees and superimposing it on the first?

Whoa symmetry!! Now if I continue to rotate, displace and superimpose the rectangles what happens?

Whoa, more symmetry!! I could continue this ad-infinitum and I would continue to get the same symmetrical pattern. Notice how the middle rectangle, (I've put the original lines in red back in there), is a perfect scale copy of the original grid in the original rectangle. Also note that the whole grid is made of perfect squares and exact scale copies of the original rectangle. I could carry on sub-dividing and get ever smaller exact copies, the symmetry repeats itself.

This is dynamic symmetry, it is the strange case of how dividing dynamic rectangles produces replicas of exactly the same in both dimensions, yep if you drew a few more lines then the patterns in the middle become independent of orientation, it is the same in portrait or landscape.

On why you can't apply dynamic symmetry to all rectangles

Very easy really, because there is no symmetry. It simply does not exist except in dynamic rectangles. Here is a standard static rectangle with the same pattern:

Here it is with the same pattern rotated and superimposed:

Zilch, nada. There is no symmetry. Why is it important? It is important because we see by recognising division. In the dynamic rectangle there is an exact square and an exact copy of the rectangle, in the static one there is no square and what's left is not a copy of the original rectangle. In short there is no proportion to compare, they simply do not line up.

If we go back to the original principle:

Take a static rectangle and mark a point that's exactly the golden ratio along it's bottom edge. I bet you can't do it, because it's not a proportion you are able to recognise or gauge. The import of this is that if it's not something you can gauge or see then it has no relevance to composition of symmetry. And neither will you be able to see or recognise it in an image, "oh look it's dynamic symmetry transposed to a static rectangle, and therefore not symmetrical anymore but you can still clearly see it and use it to analyse all photos." utter rubbish!

Now take a dynamic rectangle, say a golden ratio one, and divide it so one part is a square like so:

There you have golden ratio and you are able to both see and understand it without ever knowing anything about golden ratio, it's important not because it's 1:1.618 but because it's formed by making a square, a simple shape you can estimate and draw by eye. It is a shape you can imagine and see easily, something thats basic and often seen without recognising it, almost instinctive. Completely unlike golden ratio in a static rectangle.

This is why dynamic symmetry only applies to dynamic rectangles, something HCB well understood.