A theoretical computer built in a mixed-up
mathematical universe might not sound like the most practical invention.
But the discovery shows that computation can turn up in the most
unlikely places, which in turn might spur more realistic models of
physical and chemical processes.
The computer is what's known as a universal Turing machine,
a theoretical construct invented by mathematician Alan Turing that's
capable of simulating any computer algorithm. The computers we use today
are approximations of Turing's idealised machine.
Katsunobu Imai
at Hiroshima University in Japan and colleagues have found a way to
bring Turing's computational order to an irregular universe based on
Penrose tiles – a feat that was considered highly improbable until now.
Named after mathematician Roger
Penrose, the tiling is an arrangement of two four-sided shapes called a
kite and a dart, which covers a two-dimensional plane, without
repeating, to create a constantly shifting pattern.
The team used this mathematical
playing field to make a cellular automaton, a two-dimensional universe
in which patterns of cells evolve to create complex structures. The most
famous cellular automaton is the Game of Life, a grid of identical
square cells that can either be "alive" or "dead".
Players have created universal Turing
machines in the Game of Life's orderly, two-state universe. But making
one work in a more chaotic Penrose universe presented a greater
challenge to Imai's team.
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