A Game of Life on Penrose Tilings

Re:A Game of Life on Penrose Tilings by cpsempek on Thursday August 31, 2017 @04:13PM (#15143513)

Not Penrose tilings, but my math professor's bathroom floors are pretty cool https://www.math.ucdavis.edu/~greg/floors.html

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Re:A Game of Life on Penrose Tilings by clusmore on Friday September 01, 2017 @01:40AM (#15146392)

Don Knuth has a dragon curve in the entrance hall to his house: https://www.youtube.com/watch?v=v678Em6qyzk

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Re:A Game of Life on Penrose Tilings by SubiculumCode on Thursday August 31, 2017 @08:13PM (#15145136)

oh holy hell it is going to be hot in Davis tomorrow.

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Re:A Game of Life on Penrose Tilings by RandomInteger4 on Thursday August 31, 2017 @03:06PM (#15142885)

Would probably be easier to rent or buy a kiln and then make your own ceramic tiles. Cutting them after the fact is a frustrating experience.

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Re:A Game of Life on Penrose Tilings by pbhjpbhj on Thursday August 31, 2017 @06:47PM (#15144634)

You'd want a slab roller too so as to get consistent thickness, unless you want a hand-made look.

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Re:A Game of Life on Penrose Tilings by alejohausner on Thursday August 31, 2017 @04:38PM (#15143718)

The CS building in Carleton College has them in the lobby:

http://www.tilexdesign.com/portfolio/detail.cfm/C/328/Carlet...

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Re:A Game of Life on Penrose Tilings by qurashee on Friday September 01, 2017 @06:25AM (#15147323)

The Oxford Mathematical Institute has one just outside the entrance. We also have Penrose himself though :P

More info:

https://www.maths.ox.ac.uk/about-us/life-oxford-mathematics/... http://www.maths.ox.ac.uk/node/865

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Re:A Game of Life on Penrose Tilings by kuschku on Thursday August 31, 2017 @02:46PM (#15142752)

You could buy mosaic tiles in the forms (they exist), and put those then together.

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Re:A Game of Life on Penrose Tilings by lovemenot on Friday September 01, 2017 @08:03PM (#15153288)

This was done in Uzbekistan in the 15th Century CE. As well as at other Arab locations.

http://archive.aramcoworld.com/issue/200905/the.tiles.of.inf...

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Re:A Game of Life on Penrose Tilings by ghostbrainalpha on Thursday August 31, 2017 @04:19PM (#15143556)

https://www.math.ucdavis.edu/~greg/images/floor3.jpg

UC Davis Mathmetics Department Bathroom

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Re:A Game of Life on Penrose Tilings by sp332 on Thursday August 31, 2017 @04:43PM (#15143760)

That's not a Penrose tiling. The pieces are the wrong shape. See the description at the bottom of https://www.math.ucdavis.edu/~greg/floors.html

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Re:A Game of Life on Penrose Tilings by cpsempek on Thursday August 31, 2017 @05:03PM (#15143896)

Also not the math dept's bathroom, it's a faculty member's personal bathroom floor.

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Re:A Game of Life on Penrose Tilings by shagie on Friday September 01, 2017 @09:38AM (#15148201)

While not quite as "oh, that's neat" - a set of Wang dominoes might be interesting to people who know what it is (incidentally, Wang is the logician that had a conjecture that proved false and lead to the aperiodic set that Penrose came up with).

One aspect of the "this is undecidable" was that it to prove it is equivalent to solving the Halting Problem.

> In 1966, Wang's student Robert Berger solved the domino problem in the negative. He proved that no algorithm for the problem can exist, by showing how to translate any Turing machine into a set of Wang tiles that tiles the plane if and only if the Turing machine does not halt. The undecidability of the halting problem (the problem of testing whether a Turing machine eventually halts) then implies the undecidability of Wang's tiling problem

https://en.wikipedia.org/wiki/Wang_tile

In one of the books I've found - Andrew Glassner's Notebook: Recreational Computer Graphics - they have a set of tiles that implement some program. https://books.google.com/books?id=_4ZMC_QBAC4C&lpg=PP1&dq=An... (some other Turing machine Wang tile sets - https://grahamshawcross.com/2012/10/12/wang-tiles-and-turing... )

All that said - if you're willing to go with printed square tiles that implement an aperiodic tiling with edge rules, that might be an option.

And all that said... http://www.tessellations.org/real-materials-tessellations-16... is the story of making a Penrose kitchen floor.

> A potter friend, Jim Morrison of Cold Mountain Pottery (dot com), made several molds from my cardboard patterns for the two tile shapes. Over a period of several months I made about 1,300 tiles one at a time with the molds.

Another option to consider... instead of tile, wood. It might be a bit easier to cut to the right specification, and then use the clear epoxy penny floor approach to protect it.

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Re:A Game of Life on Penrose Tilings by chromaton on Thursday August 31, 2017 @03:16PM (#15142996)

Waterjet cut them from a bigger slab.

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Re:A Game of Life on Penrose Tilings by huhtenberg on Thursday August 31, 2017 @03:36PM (#15143198)

Wouldn't this leave sharp-ish edges?

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Re:A Game of Life on Penrose Tilings by chromaton on Thursday August 31, 2017 @04:01PM (#15143404)

That's probably not great for flooring, but might be fine for walls or a backsplash.

You might be able to relieve the edges by tumbling, but at the cost of changing the surface finish.

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Re:A Game of Life on Penrose Tilings by pavel_lishin on Thursday August 31, 2017 @03:37PM (#15143212)

Sand 'em down?

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Re:A Game of Life on Penrose Tilings by fibo on Friday September 01, 2017 @02:50AM (#15146655)

I read that Penrose was planning to create a kid game with his tilings.

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