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FinalElementCounts.md

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Symbols and Functions > WolframModel and WolframModelEvolutionObject > Properties >

Final Element Counts

FinalDistinctElementsCount (aka "AtomsCountFinal") and FinalEdgeCount (aka "ExpressionsCountFinal") are similar to corresponding *List properties, except we don't have "FinalVertexCount" (we should have it and also "DistinctElementsCountList", but they are not currently implemented).

The difference is that "VertexCountList" counts expressions on level 2 in the states whereas "FinalDistinctElementsCount" counts all expressions matching _ ? AtomQ (on any level). The difference becomes apparent for edges that contain non-trivially nested lists.

For example, consider a rule that performs non-trivial nesting:

In[] := WolframModel[<|
  "PatternRules" -> {{a_}} :> {{a + 1}, {a - 1}, {{a + 2, a - 2}}}|>,
 {{1}}, 7, "VertexCountList"]
Out[] = {1, 3, 6, 10, 15, 21, 28, 36}
In[] := WolframModel[<|"PatternRules" ->
     {{a_}} :> {{a + 1}, {a - 1}, {{a + 2, a - 2}}}|>,
   {{1}}, #, "FinalDistinctElementsCount"] & /@ Range[0, 7]
Out[] = {1, 4, 9, 13, 17, 21, 25, 29}

To understand why this is happening, consider the state after one step:

In[] := WolframModel[<|
  "PatternRules" -> {{a_}} :> {{a + 1}, {a - 1}, {{a + 2, a - 2}}}|>,
 {{1}}, 1, "FinalState"]
Out[] = {{2}, {0}, {{3, -1}}}

This state has 3 vertices (distinct level-2 expressions): 2, 0, and {3, -1}, but 4 atoms: 2, 0, 3, and -1. This distinction does not usually come up in our models since vertices and atoms are usually the same things, but it is significant in exotic cases like this.