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RulePlot—Wolfram Language Documentation

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• See Also
  • ArrayPlot
  • CellularAutomaton
  • TuringMachine
  • SubstitutionSystem
  • BooleanFunction
  • BooleanTable
• Related Guides
  • Boolean Computation
  • Computational Systems
  • Iterated Maps & Fractals
  • Discrete Mathematics

RulePlot[sys]

generates a plot representing the rule for the computational system sys.

RulePlot[sys,init,t]

generates a plot of the evolution of the system sys from initial condition init for t steps.

RulePlot[sys,evol]

generates a plot of the evolution evol assuming it is derived from a system of the form sys.

• Possible computational systems sys include:
• TuringMachine[{rule,s,k}] can be used to specify a Turing machine in which rule does not uniquely specify a transformation for each of the s k possible configurations, but that nevertheless will be rendered assuming s head states and k tape colors.
• RulePlot works with 1D and 2D systems.
• Options include:
• Possible appearance elements include:
• Possible plot legend forms include:
• "Icon" use an icon as the legend "Text" use text as the legend expr arbitrary plot legend
• In the form RulePlot[sys,evol], specific rules are typically ignored; only the implicit or explicit specification of number of colors, states, etc. is used.

Return the rule icon for elementary cellular automaton rule 30:

Plot the evolution of a cellular automaton for 10 steps:

Include the rule icon:

Plot the evolution of a Turing machine:

Return its rule icon:

Generate the evolution of a Turing machine:

Use RulePlot to display the history, using information on the rule to determine the form:

Show the rule icon for a substitution system:

Elementary cellular automaton rule 90:

Cellular automaton with more than two colors:

Cellular automaton with range greater than 1:

Cellular automaton with fractional range:

Totalistic 3-color cellular automaton:

Outer totalistic 3-color cellular automaton:

General two-dimensional cellular automaton:

Totalistic two-dimensional 5-neighbor rule:

Totalistic two-dimensional 9-neighbor rule:

Outer totalistic two-dimensional rule:

Rules specified using associations:

Turing machine rule 2506:

Turing machine with more than two states:

Turing machine with more than two colors:

Turing machines specified by rules:

Explicitly specify values of the number of states s and the number of colors k for the same transition rules:

Single-state Turing machine heads are represented with a dot:

Increase the number of states to change the representation:

An underspecified Turing machine does not have rules for all s k input configurations:

A nondeterministic Turing machine specifies different rules for the same input configuration:

String substitution system for two characters:

String substitution system for more than two characters:

String substitution system for length-2 strings:

String substitution system for strings of different lengths:

List substitution system for two integer values:

List substitution system for more than two integer values:

List substitution system with lists of different lengths:

Two-dimensional substitution systems:

Boolean function in two variables:

Boolean function in more than two variables:

Boolean function based on a vector of truth values:

Boolean function based on a table of truth rules:

Evolution of rule 30 for 10 steps:

Evolution for 50 steps from a single 1 on a background of 0s:

Evolution of a 3-color cellular automaton:

Evolution from a single 1 on a background of repeated 0110 blocks:

Evolution of a 3-color totalistic code:

Evolution of a 3-color outer totalistic code:

Evolution of rules specified by associations:

Evolution of a 2-state, 2-color Turing machine, starting with a tape of four 0s:

Evolution starting with an infinite tape of 0s:

Evolution of a 3-state, 2-color Turing machine:

Evolution starting with a tape of 1 on a background of 0s:

Evolution of a 2-state, 3-color Turing machine:

Evolution with the head initially in state 2:

Evolution of a Turing machine specified by rules, starting from a background of repeated 021 blocks:

A nondeterministic Turing machine can give different evolutions depending on the order of its rules:

An underspecified Turing machine does not have rules for all s k input configurations:

Specifying a complete set of rules eliminates the fixed point:

Use hexagons:

Use bricks:

Sometimes you can get a simplified result that shows cells whose value does not matter:

Shorten the display of the rule set:

Specify color rules for explicit values or patterns:

Make the frame blue:

Give a composite directive for the frame:

By default, a mesh is drawn around individual cells:

Do not use a mesh:

Make the mesh blue:

Give a composite directive for the mesh:

Give a plot legend describing the rule in text:

Give a plot legend describing the rule as an icon:

Give an arbitrary plot legend:

Make the marker of a Turing machine gray:

Draw the outline of the default markers:

Use the web plot theme:

Use this theme without a mesh:

Use the scientific plot theme:

Change the spacing inside the frame:

Change the spacing on each side of the icon:

Plot the evolution of a cellular automaton with ArrayPlot:

Use RulePlot to plot the evolution and the rule icon:

Plot the evolution of a Turing machine with ArrayPlot:

Use RulePlot to plot the evolution and the head of the machine:

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