Solved: Exercises 37 through 40 refer to a variation of the chaos game. In this game you

QUESTION:

Exercises 37 through 40 refer to a variation of the chaos game. In this game you start with a square ABCD with sides of length 27 as shown in Fig. 39 and a fair die that you will roll many times. When you roll a 1, choose vertex A; when you roll a 2, choose vertex B; when you roll a 3, choose vertex C; and when you roll a 4 choose vertex D. (When you roll a 5 or a 6, disregard the roll and roll again.) A sequence of rolls will generate a sequence of points P1, P2, P3,c inside or on the boundary of the square according to the following rules.Using a rectangular coordinate system with A at (0, 0), Bat (27, 0), C at (27, 27), and D at (0, 27), find the sequenceof rolls that would produce the given sequence of markedpoints. (a) P1: (27, 0), P2: (27, 18), P3: (9, 24), P4: (3, 8) (b) P1: (0, 27), P2: (18, 9), P3: (24, 3), P4: (8, 19) (c) P1: (27, 27), P2: (9, 9), P3: (21, 3), P4: (7, 19)