http://www.newscientist.com/article/dn22134-first-gliders-navigate-everchang... Hopefully this will re-invigorate interest in cellular automata on Penrose tilings. I believe that the only pre-Ready research is that of Nick Owens and Susan Stepney, which was reported in their engaging chapter in Game of Life Cellular Automata (Andrew Adamatzky). I wouldn't be surprised if there exists a glider in a two-state Moore neighbourhood rule on the Penrose tiling. There's probably no small example akin to GoL's glider in the Owens-Stepney rule, since they would have already found it by now. However, we have a vast rule-space to explore, and who knows what lurks in this obscure corner of abstract Platonic reality? Sincerely, Adam P. Goucher