Examples for

Turing Machines

Alan Turing's "Turing machines" provide for a universal notion of computation. Wolfram|Alpha simulates, analyzes and gives information about the rule space of many Turing machines. It also creates interactive visualizations, including network visualizations, of the evolution of Turing machines. Specify a rule number or explicit rule or just give a number of states and colors for a random sample.

Turing Machines

Investigate this simple model of a computer with simulations, analysis and visualizations.

Specify a Turing machine by number or rule:

Include the number of colors and states in a query:

Choose a Turing machine at random:

Specify a famous Turing machine:


Dive deep into the time evolution of a Turing machine, view only every nth slice of time or view only the steps where the head reaches the far left, right or center of the tape.

Specify a number of steps:

Specify a range of steps:

Uniformly compress time:

Retain only "interesting" steps:

Initial Conditions

Specify the initial conditions of a Turing machine, both its state and tape. Set the width of the tape and seed it with random, constant and/or repeating initial values.

Specify randomly generated tape:

Specify tape of finite width:

Specify constant tape:

Specify an initial tape containing a repeating pattern:

Specify an initial head state: