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
• Start. Roll the die. Mark the chosen vertex and call it
• Step 1. Roll the die again. From
• 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
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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