A class of Turing machines: Some turmite pair simulations

2012 is the Alan Turing year. One of his innovations is the Turing machine. My tribute to him is this online publication of papers related to my work og turmites. Turmites belong to a class of Turing machines acting on an infinite board divided into equal size squares.  The turmite concept was popularized by A. K. Dewdney  in Scientific American, Sept. 1989.

A snapshot of a running simulation

A running simulation started at x=1 and y=9

As the turmites move they change the colour of the squares they hit. Moves are controlled by their program (transition rules) combined with the colour of the square they land on. So the board acts as a read/write memory. Usually only one turmite operates on the board. I introduced the idea of a couple of turmites on the same board in 1990. Perhaps analogous to two processes unintentionally sharing  memory in an ordinary computer. This leads to interesting effects of interaction.

The algorithms and results are documented in the following files:
Normat (in Norwegian),
Scientific American
The Tinkertoy Computer.

The original program for simulating the turmite pairs was written in Basic for a MSDOS computer with EGA graphics. I have now reimplemented the program using HTML5, CSS3 and Javascript. You will need a modern browser for this. You may download, use, change and publish the simulator as you wish.

The two turmites starts out with a board where all squares are grey. When a turmite arrives at a new square it paints the square and moves in a new direction to the neighbour square. If the square is grey it will paint it with its own colour, if it’s painted, it will be painted grey. The direction of the next move is also dependent on the colour of the square. The turmite’s own colour is green for one and red for the other. My algorithm is stated in some of the above publications, but the number of possible algorithms is unlimited, so you may play a lot with this on your own computer and see if intriguing patterns arise.


0 Responses to “A class of Turing machines: Some turmite pair simulations”

  • No Comments

Leave a Reply