State, update rule, recursion

Three words carry the whole section:

Term	Plain meaning
State / Estado	the information we carry from one step to the next
Update rule / Regla de actualización	the recipe that converts the current state into the next one
Recursion / Recurrence / Recursión	applying that update repeatedly

The update rule usually looks like x[t+1] = A @ x[t]. Read it as:

next state = same matrix × current state

The word same is doing the work. One matrix, applied again and again.