If you wish to learn about photographic composition, I would go to this web site, and check out the free articles the author offers. He has an
#abolishROT hashtag there. The "rule of thirds" is really NOT a fundamental of design, nor of composition, but more of a modern-era urban legend, a bit of folk wisdom, something easily passed along in a sentence or two, and honestly, it's NOT, in any way, part of design,nor compositional theory.
Canon of Design Table of Contents
Don't worry about the rule of thirds, because honestly, it is not important. It's NOT the key to composition. The
elements and principles of design are what one wants to understand. The actual, real, academic principles of the field of design, not the misinformed folk wisdom from Popular Mechanics magazine.
Your flower photo for example, has a serious problem with repetition of
lines; extremely patterned background; and a strong figure/ground problem. Those fundamental issues are something that the "rule of thirds" cannot overcome. The issue is that the brickwork has an exceptionally strong pattern; THAT is what dominates the image--the strong, repeating pattern, with very strong, numerous lines. The background in your photo is very,very strong, but the foreground subject, is very small. The background is a mass of
shapes, in
repetition. With a very strong horizontal
direction. Of uniform size. And a hard, masonry
texture. The
dominance is all in the background.
If you look here, you will see what is meant by the elements and principles of design.
Elements and principles of design