"Don't underestimate this idea of mine...to pause sometimes to look into these stains on walls, the ashes from the fire, the clouds, the mud, or other similar places. If these are well contemplated, you will find fantastic inventions that awaken the genius of the painter to new inventions, such as compositions of battles, animals, and men, as well as diverse composition of landscapes, and monstrous things, as devils and the like. This will do you well because they will awaken genius with this jumble of things..." - Leonardo Da Vinci
Finding patterns is how we learn, how we make sense of the inflooding of sensory information, and how solve new problems. Pattern recognition can be conscious or subconscious, and finding the best pattern to match a particular problem is as important as synthesizing a patter in the first place.
Here's some interesting work that found that the right prefrontal cortex can't help noticing visual patterns: "We informed subjects that the stimuli were presented in a random sequence, that there was no need to make explicit predictions and that there was no benefit in doing so...they still noticed patterns in the sequence." The right hemisphere is the dreamy, intuitive, and less verbal side of the brain.
So maybe that's how it is. There are parts of our brains that are always noticing and remembering patterns, but then they get filed away. Perhaps Da Vinci's trick was just a clever way of bringing them to consciousness and finding novel matches. Maurits Escher had a similar practice. He doodled faces and intersecting animals in the wood grain of his bathroom wall.
Patterns Press Release