Turing Tumble Community

Functioning Boolean Computer Explanation?

I don’t understand the way boolean gates can be created with Turing Tumble.

Hi @s020031: I’m not sure I understand the question. Can you elaborate? There are probably many different ways of expressing logic gates. One done by @Florentin is AND Gate (standard size simulator) where he demonstrates an AND and a NAND gate (on a standard board). Another demo/design Binary Modular Division is based on use of XOR (using a larger board and more pieces). Is that the sort of thing you had in mind?

I don’t understand how the marbles can carry the value of a one or a zero. I am used to ball computers more like this:

If the balls fall through the circuit one at a time, how could you make a gate? Don’t they need 2 inputs, each of which have either a one or a zero?

In Turing Tumble, the information is typically represented via the orientation of bits (blue pieces) on the board, not by the location of the balls. While the balls are being used to power the computation, they can also carry information by their location on the board.

An AND gate can be constructed so that if two “input” blue bit pieces are initially pointed to the left (representing 0) or right (representing 1) at the start, then after the balls have run their course, a third bit piece is pointed to the right or left, depending on whether or not the two “input” blue bit pieces were both pointing to the right, respectively. Or, one can indicate the result of the computation by routing the last ball to a particular interceptor.

If you wanted the balls to carry the bit value, you could let a blue ball represent a 0, and a red ball represent at 1, and input the two one at a time. So a challenge to compute an AND gate might be the following: Create a TT layout with three interceptors. After the first (red or blue) ball is routed through it, that ball ends in the first interceptor. After the second ball (red or blue) is routed through it, that ball ends in the 2nd interceptor if both balls were red, and ends in the 3rd interceptor if one or both of the balls were blue. Which interceptor holds the second ball released indicates the value of the AND computation.

One can construct far more complicated things in which the position of the ball on the board is carrying information about the state of the computation, and such schemes have been used in constructions appearing in the conversation about whether Turing Tumble is Turing-Complete - see @jcross post on cellular automaton: or about how to use Turing Tumble to compute anything a finite computer can. In these constructions, which simulate a computation, at a given moment in time the current active ball is going down one of many possible paths, where the particular path represents information gathered by the computation at that time. When the next ball is released, its path will ultimately reflects the state of the computation at the next moment in time.

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