If your answer to any of these questions is "yes" or "possibly, I've never really thought about it but it sounds interesting", then give a listen to Budapest's derTANZ. The band consists of Árpád Gulyás on bass, Ákos Tornyos on drums, and Gábor Kovács on vocals, and their album is called Kaktusz (Cactus).
Here's "A Statue" - which STARTS OUT with a drum solo:
Here's "The Trap", which gets into a bit of a motorik rhythm, surrounded by wild punk abandon:
I couldn't subsist on a steady diet of this - generally, I need a bit more rhythm - but it's compelling and very enjoyable in spots. Follow either of the tracks above to their Bandcamp site to download it for "name your price".