The FRACTRAN programs $\sqrt{ 2}$GAME and NR$\sqrt{ 2}$GAME are presented, both of which compute the decimal expansion of $\sqrt{ 2}$. Our $\sqrt{ 2}$GAME is analogous to Conway's PIGAME program. In fact, our proof carries over to PIGAME to produce a simpler proof of Conway's theorem as well as highlight how the efficiency of the program can be improved. NR$\sqrt{ 2}$GAME encodes the canonical example of the Newton--Raphson method in FRACTRAN.
Categories: cs.PL