The patterns are caused by papaya ringspot virus type-W, which
despite its name only infects plants such as watermelon, cucumber and
courgettes.
While it can stunt growth and reduce yield, the patterns
on the skin are, as you say, attractive, and in some parts of the world
they sell for higher prices. The virus is classified as a potyvirus and like most plant viruses has a single-stranded RNA genome.
Meriel Jones, Port Sunlight, Merseyside, UK