Strange routing error in production logs

I just changed info-level logging to warn level in my production log
and it was quite enlightening! I found there were a lot of weirdly
formed requests and in particular a lot of requests like this:

ActionController::RoutingError (No route matches "/undefined/
with :subdomain=>"www", :method=>:get, :domain=>"", :host=>""}):

(domain name changed to protect the innocent)

Anyone seen this or something similar?