## Universal Turing Machine In Penrose Tile Cellular Automata 24

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New submitter submeta writes

*"Katsunobu Imai at Hiroshima University has figured out a way to construct a universal Turing machine using cellular automata in a Penrose tile universe. 'Tiles in the first state act as wires that transmit signals between the logic gates, with the signal itself consisting of either a 'front' or 'back' state. Four other states manage the redirecting of the signal within the logic gates, while the final state is simply an unused background to keep the various states separate.' He was not aware of the recent development of the Penrose glider, so he developed this alternative approach."*
## Universal Turing Machines (Score:3)

## Are there Penrose buckyballs? (Score:2)

Are there Penrose "buckyballs", i.e. a version of the buckyball using the Penrose tiling?

I am not sure if they exist mathematically and have never seen them discussed anywhere.

## Re: (Score:2)

Penrose tilings are flat, hence they can't cover a ball. It's impossible [wikipedia.org].

## Re: (Score:2)

## Re: (Score:2)

True, but it be interesting to know if a sphere could be "triangulated" with Penrose tiles.

## Re:Are there Penrose buckyballs? (Score:4, Interesting)

No, you can't make a sphere with Penrose tiling. As has already been mentioned, a flat tile can't be used to cover a sphere. But more importantly, there isn't a generalization that will work either. The thing that makes Penrose tiling interesting is that it is aperiodic. No aperiodic pattern can work on a sphere since you necessarily are periodic when you make one complete revolution around any greater circle on a sphere.

## Permutation City (Score:4, Interesting)

## Re: (Score:2)

Or "diaspora" where I belive he had naturally occurring penrose tiles in an alien biology performing turing calculations

## Re: (Score:2)

## 8 states? (Score:2)

That's not very impressive, especially since he basically just copied the four-state WireWorld rule.

## There you go (Score:2)

## Thanks for posting this story! (Score:1)