How do we perceive patterns in the shapes and colors around us, and why is it human nature to crave order—with a healthy dose of disorder—in our surroundings? Science writer Philip Ball has penned numerous books on the symbiotic relationship between the mind, the eye and the patterns in our built and natural world. Here, he explains how our minds recognize patterns and why we seek order amid chaos.

How many times does a motif have to repeat for the eye to recognize it as a pattern?

This is a fundamental question for science: How many times does something have to recur before we suspect that we’re seeing a law of nature and not just a coincidence? There’s no definitive answer to the question because it has to do with our intuition about what we see—the impression that there’s...