Is Bosco’s Rule Universal?

Abstract

The Game of Life (Life) is a two-state, two-dimensional, nearest neighbor cellular automaton (CA), which John Horton Conway proved is universal. The Larger than Life (LtL) family of CAs generalizes Life to large neighborhoods and general birth and survival thresholds. A specific threshold-range scaling of Life to LtL yields Bosco’s rule, which is a range 5 CA with dynamics similar to Life. In the 1990s Conway challenged us to prove that rules such as Bosco’s are, like Life, universal. Here we show that Bosco’s rule supports patterns such as those used in the proof that Life is universal. Specifically, we build a sliding block memory, similar to the auxiliary storage device Conway described and claimed could be built. Our construction is based on Life’s sliding block memory designed and built by Dean Hickerson in 1990. In a companion paper we explore various questions which have arisen since Conway posed his challenge, including whether the details given in his proof that Life is universal are sufficient and what necessary and sufficient conditions are required to prove that Bosco’s rule, or any two-dimensional CA, is universal.