Linux on Nexys2?

All the search results for [linux nexys2] discuss how the heck you run that djtgtgtgjdsasdfghjkcfg Digilent tool on Linux. In other words, how do you program the Nexys2 on Linux?

But what would it take to run Linux on the Nexys2, or a similar medium- sized FPGA? Can you just download an¬†¬†processor that has a gcc toolchain for it, throw in some I/O controllers, and get the kernel booted up? I am so new to FPGA that I can’t even do a back-of-the-envelope calculation whether a Linux-capable core, plus glue, would fit. But it would be a fun project to find out!