Cycle detection with Mathematica

Suppose we have cellular automaton on a network. For simplicity, we will use matrix notation.

ClearAll[adjMatrix, initStates, nodeStep, allStep]; (*Adjacency matrix*) adjMatrix = {{0, 1, 1, 0}, {0, 1, 0, 0}, {1, 0, 1, 1}, {0, 0, 1, 0}}; (*Initial states of nodes*) initStates ={0, 1, 1, 0}; nodeStep[adjMatrix_, states_, node_] := With[{inputs = Pick[states, adjMatrix[[All, node]], 1]}, (*Any suitable function here*) BitXor @@ inputs ]; allStep[adjMatrix_, states_] := nodeStep[adjMatrix, states, #] & /@ Range[Length@states]; 

Starting from some initial state, the function allStep is applied iteratively. It is known that sooner or later we will get a cycle.

For test example:
{0, 1, 1, 0} → {1, 1, 1, 1} → {1, 0, 1, 1} → {1, 1, 1, 1} → ...
(period 2)

But first, not necessarily straight from the initial state. Second, about the cycle length (period), it is only known that it is smaller than $2^{size}$

I have not been able to find a way to simultaneously detect the cycle and determine its length. For detection I use

data = NestWhileList[allStep[adjMatrix, #]&, initStates, Unequal, All]; 

and then we can find the length of the cycle.
Several ways have been suggested here.

• FindRepeat. It fails with period 1
• SequencePosition. I do not understand what should be M in my case: SequencePosition[data, Take[data, M]]?
• FindTransientRepeat. It works, but much slower than brutal force method
• First@Differences@Flatten@Position[data, Last@data]

Some timings:

data = ContinuedFraction[(Sqrt[12] + 2)/7, 100004]; Timing[Length@Last@FindTransientRepeat[data, 2]] {0.499203, 6} Timing[r = SequencePosition[data, Take[data, -10]]; r[[-1, 1]] - r[[-2, 1]]] {0.0156001, 6} Timing[First@Differences@Flatten@Position[data, Last@data]] {0.0468003, 6}