"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]:=

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

Out[1]=

Multiple rules:

In[2]:=

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

Out[2]=

Scope (3)

Make a WolframModel-like TokenEventGraph:

In[3]:=

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

Out[3]=

Edges are tagged by corresponding input or output list index:

In[4]:=

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

Out[4]=

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

In[5]:=

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

Out[5]=

Options (15)

Mode (1)

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

In[6]:=

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

Out[6]=

In[7]:=

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

Out[7]=

In[8]:=

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

Out[8]=

TokenDeduplication (3)

Every token is deduplicated by default:

In[9]:=

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

Out[9]=

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

In[10]:=

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

Out[10]=

"TokenDeduplication"→None turns off any deduplication:

In[11]:=

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

Out[11]=

EdgeDeduplication (1)

Remove multiedges:

In[12]:=

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

Out[12]=

In[13]:=

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

Out[13]=

EventDeduplication (1)

Keep or remove duplicate events:

In[14]:=

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

Out[14]=

In[15]:=

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

Out[15]=

StateVertices (1)

Include state vertices:

In[16]:=

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

Out[16]=

In[17]:=

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

Out[17]=

TokenDecompositionFunction (1)

Specify how states are decomposed into a list of tokens:

In[18]:=

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

Out[18]=

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]:=

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