@Travis Hardiman pointed out that the code I have in the repository in the attiny10 branch is actually for attiny85, and the attiny10 code is missing, so I went ahead and re-created the attiny10 code (which I must have lost somehow), this time on attiny9 (which is the same as attiny10, only doesn't have ADC, which we don't need). It's in the attiny9 branch now. So to summarize:

• attiny85: https://bitbucket.org/thesheep/nyan/src/tiny10/main/
• attiny10 and attiny9: https://bitbucket.org/thesheep/nyan/src/tiny9/main/
• attiny13: https://bitbucket.org/thesheep/nyan/src/tiny13/main/

Sorry for the confusion.

Also, to program the attiny10, you need to use a programmer capable of programming with the TPI protocol — recent versions of USBASP support it, you just need to add a 1kΩ resistor...