This photo is a good example of the rule of thirds since the center of the flower lies near the top right corner of the photo. The focus, the majority of the flower lies right on the one corner of the photo.
This image is a nice example of pattern because of the shape that is repeatedly created out of the fence. The way the white lines wrap around each other creates a rounded, yet sharp shape that is quite appealing to look at in my opinion.
Both are good examples of the compositional principles I asked you to look for. Both also nicely use the contrast of light and dark.