| An = | | which tends to B = | |
as n tends to infinity.
The colours of the three cells after n generations, when the initial colour indices are represented by the (3-dimensional) vector v0, are then given by the three components of the vector vn = Tnv0.
It is therefore evident that the asymptotic colours that result from the same initial distribution are given by the vector V = Bv0.
From the form of B it follows that V[1] = V[2] = V[3] = v0[2] which means that the two outer cells of the blinker asymptotically get the colour of the middle cell, which remains constant during the process.
Back to the Mathematical Aspects.