"EventLabeling"→Automatic uses ordinarily placed vertex labels; "EventLabeling"→True uses in-circle labeling for each vertex; "EventLabeling"→"Colors" uses a different color for each rule index.

Event vertices have the form {"Event", timeStep, ruleIndex, positions, eventIndex}.

Edges are tagged by list indices. Rules with associations produce tagged edges with keys as tags.

Examples

Basic Examples (2)

Make a token-event graph of a simple rule:

In[1]:=

$ResourceFunction["TokenEventGraph"][n_ :> {n + 1, n + 2}, {1, 2}, 2]$

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Multiple rules:

In[2]:=

$ResourceFunction["TokenEventGraph"][{n_ :> n + 1, n_ :> 2 n}, {1, 2}, 2]$

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Scope (3)

Make a WolframModel-like TokenEventGraph:

In[3]:=

$Module[{w = 0}, ResourceFunction["TokenEventGraph", ResourceVersion->"2.2.0"][{{{x_, y_}, {y_, z_}} :> {{w++, y}, {y, z}, {z, w}, {x, w}}}, {{0, 0}}, 3, AspectRatio -> 1/2]]$

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Edges are tagged by corresponding input or output list index:

In[4]:=

$ResourceFunction["TokenEventGraph", ResourceVersion->"2.2.0"][{n_, m_} :> {n - m, m - n}, {1, 2}, 2, EdgeLabels -> "EdgeTag"]$

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Tag edges with keys by having associations on both sides of a rule:

In[5]:=

$ResourceFunction["TokenEventGraph", ResourceVersion->"2.2.0"][<|"left" -> n_, "right" :> m_|> :> <|"-" -> n - m, "+" -> n + m|>, {1, 2}, 1, EdgeLabels -> "EdgeTag"]$

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Options (15)

Mode (1)

Mode of picking tokens can be one of: "Tuples" (default), "OrderedTuples", "Subsets":

In[6]:=

$ResourceFunction["TokenEventGraph", ResourceVersion->"2.2.0"][{n_, m_} :> n + m, {1, 2, 3, 4}, 1, "Mode" -> "Tuples"]$

Out[6]=

In[7]:=

$ResourceFunction["TokenEventGraph", ResourceVersion->"2.2.0"][{n_, m_} :> n + m, {1, 2, 3, 4}, 1, "Mode" -> "OrderedTuples"]$

Out[7]=

In[8]:=

$ResourceFunction["TokenEventGraph", ResourceVersion->"2.2.0"][{n_, m_} :> n + m, {1, 2, 3, 4}, 1, "Mode" -> "Subsets"]$

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TokenDeduplication (3)

Every token is deduplicated by default:

In[9]:=

$ResourceFunction["TokenEventGraph"][ f[n_] /; n > 2 :> {f[n - 1], f[n - 2]}, {f[7]}, 4, "TokenDeduplication" -> True]$

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"TokenDeduplication"→False turns off deduplication across time steps:

In[10]:=

$ResourceFunction["TokenEventGraph"][ f[n_] /; n > 2 :> {f[n - 1], f[n - 2]}, {f[7]}, 4, "TokenDeduplication" -> False]$

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"TokenDeduplication"→None turns off any deduplication:

In[11]:=

$ResourceFunction["TokenEventGraph"][ f[n_] /; n > 2 :> {f[n - 1], f[n - 2]}, {f[7]}, 4, "TokenDeduplication" -> None]$

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EdgeDeduplication (1)

Remove multiedges:

In[12]:=

$ResourceFunction["TokenEventGraph"][{n_, m_} :> n + m, {1, 2}, 2, "EdgeDeduplication" -> False]$

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In[13]:=

$ResourceFunction["TokenEventGraph"][{n_, m_} :> n + m, {1, 2}, 2, "EdgeDeduplication" -> True]$

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EventDeduplication (1)

Keep or remove duplicate events:

In[14]:=

$ResourceFunction["TokenEventGraph", ResourceVersion->"2.2.0"][{n_ :> n + 1, n_ :> 2 n}, {1, 2}, 2, "EventDeduplication" -> False]$

Out[14]=

In[15]:=

$ResourceFunction["TokenEventGraph", ResourceVersion->"2.2.0"][{n_ :> n + 1, n_ :> 2 n}, {1, 2}, 2, "EventDeduplication" -> True]$

Out[15]=

StateVertices (1)

Include state vertices:

In[16]:=

$ResourceFunction["TokenEventGraph"][{n_, m_} :> {n m, n + m}, {3}, 2, "StateVertices" -> False]$

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In[17]:=

$ResourceFunction["TokenEventGraph"][{n_, m_} :> {n m, n + m}, {3}, 2, "StateVertices" -> True]$

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TokenDecompositionFunction (1)

Specify how states are decomposed into a list of tokens:

In[18]:=

$ResourceFunction["TokenEventGraph"][{n_, m_} :> {n m, n + m}, {3}, 2, "TokenDecompositionFunction" -> Select[OddQ]@*Echo, "StateVertices" -> True]$

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TokenRecombinationFunction (1)

Specify how tokens are recombined into states, default is a single state containing union of all output tokens. Here is an example of making a separate state from each token:

In[19]:=

$ResourceFunction["TokenEventGraph"][{n_, m_} :> {n m, n + m}, {3}, 3, "TokenRecombinationFunction" -> Map[List]@*Catenate@*Echo, "StateVertices" -> True]$

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MultiOutputEvents (1)

Split each event with multiple outputs into separate events:

In[20]:=

$ResourceFunction["TokenEventGraph"][n_ :> {n + 1, n + 2}, {1, 2}, 2, "MultiOutputEvents" -> True]$

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In[21]:=

$ResourceFunction["TokenEventGraph"][n_ :> {n + 1, n + 2}, {1, 2}, 2, "MultiOutputEvents" -> False]$

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TokenLabeling (1)

Disable custom token labeling:

In[22]:=

$ResourceFunction["TokenEventGraph", ResourceVersion->"2.2.0"][{n_ :> n + 1, n_ :> 2 n}, {1, 2}, 2, "TokenLabeling" -> None]$

Out[22]=

EventLabeling (1)

Label events by its rule index:

In[23]:=

$ResourceFunction["TokenEventGraph", ResourceVersion->"2.2.0"][{n_ :> n + 1, n_ :> 2 n}, {1, 2}, 2, "EventDeduplication" -> False, "EventLabeling" -> "Colors"]$

Out[23]=

TokenRenderingFunction (1)

Specify rendering for the token:

In[24]:=

$ResourceFunction["TokenEventGraph", ResourceVersion->"2.2.0"][{n_ :> n + 1, n_ :> 2 n}, {1, 2}, 2, "TokenRenderingFunction" -> (Style[#, 12, Bold, Red] &)]$

Out[24]=

TokenStyleOptions (1)

Provide style options for token boxes:

In[25]:=

$ResourceFunction["TokenEventGraph", ResourceVersion->"2.2.0"][{n_ :> n + 1, n_ :> 2 n}, {1, 2}, 2, "TokenStyleOptions" -> {FontFamily -> "Helvetica", FontColor -> Orange}]$

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TokenFrameOptions (1)

Provide frame options for token boxes:

In[26]:=

$ResourceFunction["TokenEventGraph", ResourceVersion->"2.2.0"][{n_ :> n + 1, n_ :> 2 n}, {1, 2}, 2, "TokenFrameOptions" -> {FrameMargins -> 0, Background -> Green}]$

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Version History

3.0.0 – 22 April 2024
2.2.0 – 14 March 2022
2.1.0 – 07 March 2022
2.0.0 – 23 February 2022
1.2.0 – 15 February 2022
1.1.2 – 19 January 2022

Related Resources

License Information

This work is licensed under a Creative Commons Attribution 4.0 International License

TokenEventGraph (2.2.0) current version: 3.0.0 »

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