Concept explainers
Exercises 31 through 34 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. 12-41 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 |elip| inside or on the boundary of the square according to the following rules.
• Start. Roll the die. Mark the chosen vertex and call it P1
• Step 1. Roll the die again. From P1 move two-thirds of the way toward the new chosen vertex. Mark this point and call it P2.
• Steps 2, 3, etc. Each time you roll the die, mark the point two-thirds of the way between the previous point and the chosen vertex.
Figure 12-41
Using graph paper, find the points P1, P2, P3 and P4 corresponding to
a. the sequence of rolls 2, 2, 4, 4.
b. the sequence of rolls 2, 3, 4, 1.
c. the sequence of rolls 1, 3, 4, 1.
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Excursions in Modern Mathematics (9th Edition)
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