Final answer:
The design principle that influences the sense of unity and relatedness by rearranging objects to emphasize their similarities and differences is proximity, a Gestalt principle that groups elements based on their spatial closeness.
Step-by-step explanation:
The design principle that explains the simplest way to influence the sense of unity and relatedness in an image by rearranging objects to emphasize similarities and differences is proximity. The principle of proximity, one of the Gestalt principles, suggests that elements that are close to one another tend to be perceived as a group. This principle is clearly illustrated in Figure 5.26, where one block of dots is seen as a single unit on the left side (a) and the dots are perceived as three separate columns on the right side (b) because of their spatial arrangement. Employing the principle of proximity can simply and effectively create a sense of unity and cohesion within a composition.
In contrast, other design principles like the Rule of Thirds relate more to the placement of the subject matter to create balanced, interesting, and visually pleasing compositions, while balance involves arranging visual elements in a work of art equally or appropriately to create stability. However, it is proximity that directly addresses the closeness of elements to manipulate how they are collectively perceived within a design or artwork.