# Universal Turing Machine In Penrose Tile Cellular Automata

#### Unknown Lamer posted more than 2 years ago | from the mine-bitcoins-using-xscreensaver dept.

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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."*

## Woosh (-1)

## Anonymous Coward | more than 2 years ago | (#41193049)

...

## Universal Turing Machines (2)

## 2.7182 (819680) | more than 2 years ago | (#41195091)

## Re:Universal Turing Machines (0)

## Anonymous Coward | more than 2 years ago | (#41201877)

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

## Are there Penrose buckyballs? (1)

## G3ckoG33k (647276) | more than 2 years 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 | more than 2 years ago | (#41193387)

Penrose tilings have negative curvature.

Balls have positive curvature.

They are opposites.

## Re:Are there Penrose buckyballs? (0)

## Anonymous Coward | more than 2 years 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 | more than 2 years 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) | more than 2 years 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 | more than 2 years ago | (#41193739)

Hexagons are flat too...

## Re:Are there Penrose buckyballs? (1)

## NoNonAlphaCharsHere (2201864) | more than 2 years ago | (#41193885)

## Re:Are there Penrose buckyballs? (0)

## Anonymous Coward | more than 2 years 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) | more than 2 years 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 | more than 2 years 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) | more than 2 years ago | (#41193407)

## Re:Permutation City (1)

## blackpaw (240313) | more than 2 years ago | (#41196869)

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

## Re:Permutation City (1)

## mrsurb (1484303) | more than 2 years ago | (#41222431)

## Turing Machines Everywhere (-1)

## Anonymous Coward | more than 2 years ago | (#41193409)

Is this another Minecraft story?

## 8 states? (1)

## Hentes (2461350) | more than 2 years ago | (#41193507)

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

## There you go (1)

## dargaud (518470) | more than 2 years ago | (#41194575)

## What's a Turing Machine? (-1)

## Anonymous Coward | more than 2 years ago | (#41194859)

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

## Anonymous Coward | more than 2 years ago | (#41195831)

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

## Anonymous Coward | more than 2 years 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 | more than 2 years ago | (#41204661)

Wow !

Is this a New Kind of Science?

*irony*

## Thanks for posting this story! (0)

## EnergyScholar (801915) | more than 2 years ago | (#41206459)