The reason behind zzz and how it got about is because comic strip artists had a tough time depicting slumber. They came up with a sound-word (onomatopoeia) instead because there is no actual way to express sleeping.

Snoring is represented onomatopoeically by Zzz. It was often employed in mediums when sound effects were unavailable, like as comic comics. Even though it wasn’t the only gadget used to represent snoring, this is where it earned its relationship with sleeping.