The image on the left is NOT utilizing the "rule of thirds"
Notice how much more interesting this arrangement is because of the "rule of thirds
More examples of the use of the "rule of thirds"
The graphic to the left offers a comparison of two different compositions of the same sunset, shot within a few moments of each other.
The top composition has the sun centered vertically in the image, while the bottom composition has aligned the sun and the silhouette of the Capitol builing at the lower two points, according to the "rule of thirds".
This version provides a more balanced composition, placing the two main gocal points equally within the frame.
The following is taken from a phenomenal article and I've provided the link for it here:
Images taken from an Internet Google search of "Rule of Thirds"