These are the properties used to extract states at a particular moment in the evolution. They always return lists, but in the examples below, we plot them for clarity.
"FinalState" (aka -1) yields the state obtained after all replacements of the evolution have been made:
In[] := HypergraphPlot @ WolframModel[{{1, 2, 3}, {4, 5, 6}, {1, 4}} ->
{{2, 7, 8}, {3, 9, 10}, {5, 11, 12}, {6, 13, 14}, {8, 12}, {11,
10}, {13, 7}, {14, 9}},
{{1, 1, 1}, {1, 1, 1}, {1, 1}, {1, 1}, {1, 1}}, 6, "FinalState"]"StatesList" yields the list of states at each generation:
In[] := HypergraphPlot /@ WolframModel[{{1, 2, 3}, {4, 5, 6}, {1, 4}} ->
{{2, 7, 8}, {3, 9, 10}, {5, 11, 12}, {6, 13, 14}, {8, 12}, {11,
10}, {13, 7}, {14, 9}},
{{1, 1, 1}, {1, 1, 1}, {1, 1}, {1, 1}, {1, 1}}, 6, "StatesList"]This is identical to using the "Generation" property mapped over all generations:
In[] := HypergraphPlot /@ (WolframModel[{{1, 2, 3}, {4, 5, 6}, {1, 4}} ->
{{2, 7, 8}, {3, 9, 10}, {5, 11, 12}, {6, 13, 14}, {8, 12}, {11,
10}, {13, 7}, {14, 9}},
{{1, 1, 1}, {1, 1, 1}, {1, 1}, {1, 1}, {1, 1}}, 6][
"Generation", #] &) /@ Range[0, 6]In fact, the "Generation" property can be omitted and the index of the generation can be used directly:
In[] := HypergraphPlot /@ WolframModel[{{1, 2, 3}, {4, 5, 6}, {1, 4}} ->
{{2, 7, 8}, {3, 9, 10}, {5, 11, 12}, {6, 13, 14}, {8, 12}, {11,
10}, {13, 7}, {14, 9}},
{{1, 1, 1}, {1, 1, 1}, {1, 1}, {1, 1}, {1, 1}}, 6] /@ Range[0, 6]"StatesList" shows a compressed version of the evolution. To see how the state changes with each applied replacement,
use "AllEventsStatesList":
In[] := HypergraphPlot /@ WolframModel[{{1, 2, 3}, {4, 5, 6}, {1, 4}} ->
{{2, 7, 8}, {3, 9, 10}, {5, 11, 12}, {6, 13, 14}, {8, 12}, {11,
10}, {13, 7}, {14, 9}},
{{1, 1, 1}, {1, 1, 1}, {1, 1}, {1, 1}, {1, 1}}, 3,
"AllEventsStatesList"]Finally, to see a state after a specific event, use "StateAfterEvent" (aka "SetAfterEvent"):
In[] := HypergraphPlot @ WolframModel[{{1, 2, 3}, {4, 5, 6}, {1, 4}} ->
{{2, 7, 8}, {3, 9, 10}, {5, 11, 12}, {6, 13, 14}, {8, 12}, {11,
10}, {13, 7}, {14, 9}},
{{1, 1, 1}, {1, 1, 1}, {1, 1}, {1, 1}, {1, 1}}, 6][
"StateAfterEvent", 42]"StateAfterEvent" is equivalent to taking a corresponding part in "AllEventsStatesList", but it is much faster to
compute than the entire list.



