In this question we consider a simplified two-dimensional cellular automaton model for the growth of a tumour in healthy tissue. The alphabet is (H, A,Q, N) where I denotes a healthy cell, A denotes an active tumour cell, Q denotes a quiescent tumour cell (alive, but not capable of spreading) and N denotes a necrotic (dead) tumour cell. HHHHHHH N if (r,y) = N or c(x, y) = Q HHHHHHH Q if (r,y) = A 9+1(x,y) = HHHHHHH A if ((x,y) =H and NA(z,y) = 1) HHHAHHH H otherwise HHHHHHH HHHHHHH HHHHHHH Time t=0 A starting state for this CA on a 7 x7 grid is shown above right. There is a single active tumour cell in c(3,3) in an area of healthy cells. (a) Calculate the following (i) N(2, 2) (ii) N(2,3) (iii) N (0,0) (iv) No (5, 2). (b) Use the grids below to calculate the states of the automaton at times t = 1,2,3,4,5,6,7 and 8. Be careful to apply the rules exactly as they are written. (Don't forget to staple the question sheet page to the rest of your assignment.) Time t=1 Time t=2 Time t=3 Time t=4 Time t=5 Time t=6 Time t=7 Time t=8