Mathematics includes arithmetic, algebra, geometry, and calculus. A guitar string can be tensiled to any vibratory pattern you wish. It can be in 'tune' or out. It is not arbitrary. The string struggles at different tensions to vibrate, but when it hits the exact tension of least resistence it forms a perfect wave that can be hamonized with the five other perfect pitch strings.
Few things sound as beautiful as a stringed insrument properly tuned.
Home meaning the most perfect wave fluctuation. The string is at home when there is zero disconsonance. Like a guitar in tune, so is a stream. But at the same time the chaotic motion of the the molecules in the smoke can only be chaotic under the stringent confines of their boundries. But at the same time it is confined to be chaotic within a disipline of ponderous proportions.