The phrase is not mine. I first saw it in print as the title of an article in Science magazine, written by Lynn Steen in the late 1980s, but Steen says it did not originate with him either. The Science of Patterns. I think it's a good slogan. That's why I took it for the title of my book.
Geometry studies the patterns of shape.
Calculus allows us to handle patterns of motion. Logic studies patterns of reasoning. Probability theory deals with patterns of chance. Topology studies patterns of closeness and position. And so forth.