LikeLike

]]>LikeLike

]]>LikeLike

]]>However I think there is a small error in one of the figures. Ine third picture under the heading Wang Tiles ( The Second coloured tile picture) , the colouring on the top row, second from left tile should be only GREEN and Blue. One of the tiles is shown as red, I think it should be green,

LikeLike

]]>LikeLike

]]>Roger Vivier HongKong http://rogervivier.rogervivieronlineshoes.net

LikeLike

]]>LikeLike

]]>Thanks for your email, which requires some more thought on my part.

The two parallel situations that I have immediately in mind are the Game of Life acting as a computer and Jacquard looms and weaving in general.

The Game of Life can be initialised to provide a Glider Gun that fires out Gliders that can move and be destroyed by a Glider Eater

These can be configured to create a computer that can perform in the same way as any conventional computer in particular with the following logical operators.

My admittedly rather weak argument is that if the Game of Life can be configured to create an all purpose computer then it has the same functionality as a Turing Machine and can be considered to be one. It does not need to use any of the specific mechanisms specified by Turing.

LikeLike

]]>I can see how the above examples do computations, however I don’t believe they are still (simulating) Turing machines so was wondering if you could speak to that. If the top row is the initial state of the turing machine, and the machine evolves downward in time, it looks as though your turing machine is able to time travel and write values to the tape of previous points in time. For instance, note in your addition example that by the end of the execution, the answer is in the time = 0 row of data, even though it wasn’t present when the simulation really was at time = 0. Is this still somehow considered a Turing machine? If not, does this have any other names, as it obviously still does useful calculations?

And another question… are there any algorithms that you know of to place the tiles as you do the calculations? Doing it from top row to bottom row, left tile to right in each row, and only choose whatever tile fits the edge requirements, there are times when the tile to place is ambiguous (has more than one answer), however further down the line you will hit a situation where there is no valid tile placement so you will have to go back and try a different choice where the tile was ambiguous. It seems a bit like trial and error, and I’m wondering if you might ever have to go back quite a distance to rectify a situation, or if even you might ever have to go back to a previous row. If so, do you know of any better algorithms for making valid tiling? Or does this essentially come down to the halting problem so is unsolvable in general other than this systematic trial and error method.

Posted on behalf of Alan Wolfe

LikeLike

]]>LikeLike

]]>