By law, faxes have to have the sender's phone number printed across the top. This is by law, not technical requirement, which means it's quite possible to not have that information, or at least not have it correct. Either way, you should have call records available from your phone company to help track the perpetrator.
Armed with that information, go file a police report (and assuming USA, an abuse report with the FCC), and then wait for the dream of justice that may or may not ever come.
You may also want to consider an electronic-only fax option. All-black TIFF files cost a lot less to produce, so the effect of such an attack is minimal. You could roll your own using the appropriate software and a fax modem, or you could subscribe to a commercial offering.