In heraldry

Heraldry

Heraldry is the profession, study, or art of creating, granting, and blazoning arms and ruling on questions of rank or protocol, as exercised by an officer of arms. Heraldry comes from Anglo-Norman herald, from the Germanic compound harja-waldaz, "army commander"...

 and architecture

Architecture

Architecture is both the process and product of planning, designing and construction. Architectural works, in the material form of buildings, are often perceived as cultural and political symbols and as works of art...

, a line which is drawn nebuly is made up of a series of bulbous protrusions, which are supposed to resemble clouds (Latin nebula: a mist, vapor, or cloud).(OED)

The title of the 1903 book The Nebuly Coat

The Nebuly Coat

The Nebuly Coat , by J. Meade Falkner, is a novel which tells of the experiences of a young architect, Edward Westray, who is sent to the remote Dorset town of Cullerne to supervise restoration work on Cullerne Minster...

refers to the coat of arms of one of the characters.
Its use in coats of arms can be seen in the cases of Jones and Munk, both Canada, FLEETWOOD BOROUGH COUNCIL, England and HYDE BOROUGH COUNCIL, England