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Universal Turing Machine In Penrose Tile Cellular Automata

Unknown Lamer posted about a year and a half ago | from the mine-bitcoins-using-xscreensaver dept.

Math 24

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."

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24 comments

Woosh (-1)

Anonymous Coward | about a year and a half ago | (#41193049)

...

Universal Turing Machines (2)

2.7182 (819680) | about a year and a half ago | (#41195091)

There is a reason there are 50 different definitions of computable function - they are not hard to come by. As a professional mathematician/theoretical computer scientist I find it totally unsurprising to find one in the Penrose tiles. If it is useful for something, that's different. But you build almost any sufficiently rich mathematical structure and you can interpret a subset of them as Turing machines.

Re:Universal Turing Machines (0)

Anonymous Coward | about a year and a half ago | (#41201877)

If you could characterize "sufficiently rich", that might be a more interesting observation.

Are there Penrose buckyballs? (1)

G3ckoG33k (647276) | about a year and a half ago | (#41193153)

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:Are there Penrose buckyballs? (0)

Anonymous Coward | about a year and a half ago | (#41193387)

Penrose tilings have negative curvature.
Balls have positive curvature.

They are opposites.

Re:Are there Penrose buckyballs? (0)

Anonymous Coward | about a year and a half ago | (#41193481)

Penrose tilings have negative curvature.
Balls have positive curvature.

They are opposites.

But, what if you turn the tiling upside down? ;)

correction (0)

Anonymous Coward | about a year and a half ago | (#41194085)

Um, I mean, Penrose tilings have zero curvature. I was thinking of thinking of the Poincare disc. Sorry.

Re:Are there Penrose buckyballs? (1)

Hentes (2461350) | about a year and a half ago | (#41193553)

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

Re:Are there Penrose buckyballs? (0)

Anonymous Coward | about a year and a half ago | (#41193739)

Hexagons are flat too...

Re:Are there Penrose buckyballs? (0)

Anonymous Coward | about a year and a half ago | (#41201909)

Buckyball surfaces are a mix of hexagons and pentagons. It's the pentagons that allow the ball to be non-flat.

Re:Are there Penrose buckyballs? (1)

Mikkeles (698461) | about a year and a half ago | (#41194847)

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

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

Anonymous Coward | about a year and a half ago | (#41193605)

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 (4, Interesting)

Shad0w99 (807661) | about a year and a half ago | (#41193407)

Somehow Greg Egan's book "Permutation City" came to my mind when reading this. With his Autoverse representation on cellular automats.

Re:Permutation City (1)

blackpaw (240313) | about a year and a half ago | (#41196869)

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

Turing Machines Everywhere (-1)

Anonymous Coward | about a year and a half ago | (#41193409)

Is this another Minecraft story?

8 states? (1)

Hentes (2461350) | about a year and a half ago | (#41193507)

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

There you go (1)

dargaud (518470) | about a year and a half ago | (#41194575)

Previous /. story [slashdot.org]: "Before we can totally discount the theory that space-time is comprised of Planck-scale pixels, [...]". There you go, you can have Penrose-tiled planck pixels and still move in straight lines. Where do I pick my Nobel ?

What's a Turing Machine? (-1)

Anonymous Coward | about a year and a half ago | (#41194859)

One that can buttfuck as well as a human?

Re:What's a Turing Machine? (-1)

Anonymous Coward | about a year and a half ago | (#41195831)

Awwww, me got downmodded....

Re:What's a Turing Machine? (-1)

Anonymous Coward | about a year and a half ago | (#41199907)

It wasn't funny. Alan Turing's suicide over his socially unaccepted homosexuality was a loss to us all.

Impressive (0)

Anonymous Coward | about a year and a half ago | (#41204661)

Wow !

Is this a New Kind of Science?
*irony*

Thanks for posting this story! (0)

EnergyScholar (801915) | about a year and a half ago | (#41206459)

I wish to offer a general apology for the terrible quality of comments on this story. Obviously, most readers failed to even understand what the story was about. I thought the best comment was the snarky 'Is this NKS?' at the end, as this story obviously does tie into NKS. Anyway, thanks, submeta, for posting a fine old skool slashdot story. Let's hope our readership is less ignorant and juvenile next time around.
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