I believe one key principle of composition is: Repetition with variation.
Let’s take the painting Port Marly, gelée blanche (Port Marly, hoarfrost), an oil on canvas by Alfred Sisley, as an example.
Port Marly, gelée blanche - Port Marly, hoarfrost - Oil on canvas (1872) by Alfred Sisley (Paris, 1839 – Moret-sur-Loing, 1899)
An obvious application of this principle is to have a repetition of an element in the painting in different sizes. A group of several trees of similar shapes but different sizes will work well on this principle.
The trees on the left form a repeated round shape
Another form of repetition with variation is less obvious but also works well: The underlying geometry of the composition can be based on similar shapes repeated in different sizes.
The shape of the river bank forms two similar triangle rectangles
The shape of the sky and the shape of the water are almost two mirror shapes of different size.
The reason patterns are necessary for a pleasing composition is that we are addicted to them. As Marcus du Sautoys commented in his book The Number Mysteries: A Mathematical Odyssey through Everyday Life:
“But how do you come up with a sequence of choices which you can be certain is random and does not have some hidden pattern? It’s a real problem: we humans are notoriously bad at producing random sequences – we are so addicted to patterns that we tend to let structure seep into any random sequence we try to put together.”