Direct Rule Control for 3,3 Turing Machines

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

Turing machines are simple models of a computing machine invented by Alan Turing. They consist of a head that switches between states while reading from and writing on a tape. The symbols read or written are called colors. An additional symbol that cannot be read or written is called blank and marks the limits of the tape. Generalizations of such machines can have multiple heads or tapes.


The plot shows evolutions of 3-state, 3-color Turing machines. Each row of squares gives one step in the evolution of the tape. The squares correspond to bits on the tape: white squares represent 0-digits, yellow squares stand for 1-digits, orange squares for 2-digits. The angles of the small tears represent states.

One of the 198359290368 rules for a 3-state, 3-color Turing machine can be selected by setting the base 18 rule digits for each of the nine possible inputs. Combined icons for state and color on the left of these nine setterbars give the inputs which trigger their selected settings. Similar combined icons over the nine setterbars give the 18 possible right-hand sides of the rules. Another row of icons shows the resulting directions of movements for all possible results.

The initial position of the head is given in relation to the specified initial condition of the tape, which can be cyclic, padded by an infinite number of 0-, 1- or 2-digits, or padded by repetitions of the selected 8-digit initial tape specification.


Contributed by: Michael Schreiber (March 2011)
Open content licensed under CC BY-NC-SA




Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.