Re:A Game of Life on Penrose Tilings
by dandare on Thursday August 31, 2017 @02:34PM
(#15142643)
Once I seriously wanted to have Penrose Tiling tiles in my bathroom but after soon found out nobody manufactures such tiles and would have to produce them manually with a tile cutter.
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
> 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.
Re:A Game of Life on Penrose Tilings
by Karliss on Friday September 01, 2017 @01:25PM
(#15150521)
The paper describes a way of choosing a subset of tiles in penrose tiling that form a rectangularish grid and play the usual game of life there. Cells no not belonging to grid have little meaning in the cellular automaton. The paper suggest leaving them off or setting the same color as cells forming grid. It would probably look like game of life in slightly deformed grid.
Re:A Game of Life on Penrose Tilings
by fibo on Friday September 01, 2017 @04:43AM
(#15147018)
Thank you very much, I guess Conway wrote many articles about GoL. I am sorry I have no reference about them, maybe you can find some in the GoL wiki here http://conwaylife.com/w/index.php?title=Main_Page
https://www.youtube.com/watch?v=3DFi4FgzEeQ
http://www.tilexdesign.com/portfolio/detail.cfm/C/328/Carlet...
More info:
https://www.maths.ox.ac.uk/about-us/life-oxford-mathematics/... http://www.maths.ox.ac.uk/node/865
http://archive.aramcoworld.com/issue/200905/the.tiles.of.inf...
UC Davis Mathmetics Department Bathroom
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.
You might be able to relieve the edges by tumbling, but at the cost of changing the surface finish.
I mean, this seems straightforward enough
This is sorta my field. My goal is pretty pictures. Would this make pretty pictures? I dunno.
ok, here's a link : https://www.youtube.com/watch?v=3DFi4FgzEeQ
Game of life on triangle tiles: https://www.youtube.com/watch?v=IGNOP8aJlM8
generating Sierpinski's triangle: https://www.youtube.com/watch?v=4OSW6kfAnPI
Am I missing something?