Computing $\sqrt{2}$ with FRACTRAN

Khushi Kaushik; Tommy Murphy; David Weed

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arXiv · 2412.16185

Computing $\sqrt{2}$ with FRACTRAN

Khushi Kaushik·Tommy Murphy·David Weed

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Abstract

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.

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Khushi Kaushik, Tommy Murphy, David Weed. 2024-12-12. Computing $\sqrt{2}$ with FRACTRAN. https://arxiv.org/abs/2412.16185

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