Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Turing Machine
This paclet provides tools for exploring and analyzing Turing machines, with an emphasis on the one-sided machines studied in A New Kind of Science. A machine is identified by its Wolfram enumeration number together with its state and color counts, written . From that compact specification the paclet runs a machine on integer inputs and reads off its halting value, step count, and tape width; visualizes its space-time evolution; tabulates the behavior of whole rule spaces (backed by a Rust implementation); searches for rules that reproduce a given behavior; and explores nondeterministic (multiway) machines.
{number,s,k}
One-sided Turing machines
— runs a one-sided machine on an integer input and returns its halting value, step count, or tape width
— visualizes the space-time evolution of a one-sided machine
— finds the rules that reproduce a given set of outputs
Rule enumeration
— the number of distinct rules for given state and color counts
— the transition table of a single deterministic rule
Behavior over rule spaces
— halted output values for every rule and input in a range
— step counts for halting machines
— maximum head widths for halting machines
Multiway (nondeterministic) machines
— the multivalued transition table of a multiway machine
— all tape values reachable from halted states
— how many states remain unexplored after a step bound
— tests whether a machine enters a cycle within a step bound
Visualization
— the output value as a function of the input
— the running time as a function of the input
— the runtime with a worst-case envelope across input sizes
— the values reachable by a multiway machine across inputs
— the named colors and plot styles shared by the visualizations
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