+ 1.2 Discrete Time Simulation [10 points] Wolfram's Rule 90 defines the following transition function for a 1D cellular automaton which shows the possible state transitions for state q; (the center cell) as a function of its neighbors qi-1 and qi+1. rule 90 0 1 0 1 1 0 1 0 For example, the left-most case states that if q-1 (left), qi (center), and qi+1 (right) are all 1, then q; (the center cell) should transition to 0 at the next time step. (a) 5 PTS Write the state transition function as a logical expression of the neighboring states qi-1 and qi+1- if 8(ai) = 0 if d (b) 5 PTS Complete a manual simulation using the transition rule above to propagate the initial state of the cells below (black = 1, white = 0) forward by 4 steps. 90 91 91 92 93 94 95 96 95 96 97 97 98 98 99 910 911 912 t = 0: t = 1: t = 2: t = 3: t = 4: