Universal computer

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A universal computer in a cellular automaton is a system that can compute anything that a Turing machine can compute. A cellular automaton in which such a system exists is called universal. A universal computer may be either infinite or finite, but when combined with a universal constructor, it is assumed to be finite.

Universal computers in Life

In 1982, John Conway proved in Winning Ways that the Game of Life has a (finite) universal computer, as well as a universal constructor. Proving the universality of a cellular automaton with simple rules was in fact Conway's aim in Life right from the start. The universal computer uses glider logic and a sliding block memory, and the proof of its existence is also outlined in The Recursive Universe.

In April 2000, Paul Rendell constructed a direct implementation of a Turing machine.[1] This computer is infinite, as it requires an infinite length of tape for the Turing Machine.

In 2002, using Dean Hickerson's sliding block memory, Paul Chapman constructed an implementation of a Minsky Register Machine (a machine of the same capability as a Turing Machine), which he extended to a Universal Register Machine, a finite universal computer.[2]

In 2009, Adam P. Goucher built a Spartan universal computer-constructor, which has three infinite binary memory tapes (program tape, data tape and marker tape). This allows data to be stored in linear space, rather than the exponential space that a Register Machine uses.

In 2010, Paul Rendell completed a universal version of his Turing machine pattern, followed in 2011 by a fully universal version, removing the previous requirement (needed for true universality) that the initial Life pattern must have unbounded size and infinite population.

In 2016, Nicolas Loizeau created an 8-bit programmable computer pattern, using only four basic parts: a period 60 glider gun, a 90° glider reflector, a p30 glider duplicator, and a glider eater.[3]

Universal computers in other cellular automata

David Eppstein and Dean Hickerson proved that the totalistic Life-like cellular automaton B35/S236 has a universal computer and universal constructor, using the same method of proof that Conway used to prove that Life is universal.[4]

Tim Hutton has implemented Codd's design for a universal computer in Codd's 8-state cellular automaton.[5]


  1. Paul Rendell (April 2, 2000). "A Turing Machine in Conway's Game of Life".
  2. Paul Chapman (November 11, 2002). "Life Universal Computer".
  3. Nicolas Loizeau (March 10, 2017). "Building a computer in Conway's Game of Life".
  4. D. Eppstein. "B35/S236".
  5. Tim Hutton. "Rule Table Repository".

External links