The matrix for the Markov chain comprises the transition probablities. These numbers are the probabilities of changing from one colour to another at the end of an interval.
The high probabilities on the diagonal mean the colour is more likely to stay the same than it is to change. On these figures, it will take an average of five or six intervals before the colour changes, but there may be large deviations from this average.
Powers of the matrix represent longer-term transition probabilites. For example, the fifth power comprises the transition probablities after five intervals. These changing probabilities eventually settle down—if we wait long enough, any one of the four colours is equally likely to be displayed.