As taken from Wikipedia
"Ukiyo or the Floating World is a term used to describe many aspects of life, including - but not limited to - the pleasure-seeking lifestyle and culture of Edo Period Japan.
This view of the Floating World is centered on Yoshiwara, the licensed red-light district of Edo (modern Tokyo). The area's brothels, teahouses and kabuki theatres were frequented by Japan's growing middle class. This particular Floating World culture also arose in other cities such as Osaka and Kyoto.
The famous Japanese woodblock prints known as ukiyo-e, or "pictures of the Floating World", depict scenes of the Floating World: geisha, kabuki actors, sumo wrestlers, samurai, and prostitutes."
Those are probably the most dreamy or sensual tattoos found on Yakuza members. The connection of the themes to the underworld is obvious. Coupled with the aesthetic value and the depiction of characters with similar personal traits to the Yakuza, makes this a no-brainer for any Yakuza to have as a tattoo.
I think the woodblock art style is more than obvious. Most illustrations are directly lifted off traditional illustrations of geishas and samurais, harkening back to the Yakuza's and Japan's past.
Check out the artist Horitaka's website HERE. He has written some really cool fully illustrated books on Tebori and Irezumi, including an excellent book on Floating World tattoos (the image above right is the cover to that book).