A natural carnation
Image source: en.wikipedia.org
Reference: en.wikipedia.org Dianthus caryophyllus: wild ancestor of the garden Carnation.
Florigene genetically modified carnations
Carnations do not naturally produce the pigment delphinidin,thus a blue carnation cannot occur by natural selection or be created by traditional plant breeding.
Around 1996 a company (Florigene) used genetic manipulation to extract certain genes from petunia and snapdragon flowers to produce a blue-mauve carnation, which was commercialized as Moondust.
In 1998 a violet carnation called Moonshadow was commercialized. As of 2004 three additional blue-violet/purple varieties have been commercialized.