The Following Is Called the Chaos Game

question 15

Short Answer

The following is called the Chaos Game. Start with rectangle ABCD in which A is located at (0, 0), B
is located at (0, 8), C is located at (3, 8), and D is located at (3, 0). Then, roll a fair die. We will say
that A is the winner if we roll a 1, B is the winner if we roll a 2, C is the winner if we roll a 3, and D is
the winner if we roll a 4. If we roll a 5 or 6, we disregard the roll and roll again. Each roll of the die generates a point inside or on the boundary of the square according to the following rules.
Start: Roll the die. Mark the winning vertex and call it P1.
Step 1: Roll the die again. From P1 move one-half of the way straight toward the next
winning vertex. Mark this point and call it P2. Steps 2, 3, etc.: Continue rolling the die, each time moving to a point one-half of the way
from the last position to the winning vertex.
The grid below shows rectangle ABCD.
.
What sequence of rolls would produce the following sequence of marked points?
P1: (0,8), P2 : (1.5,8), P3 : (0.75, 4)
(a) (2,3,1)
(b) (1,4,2)
(c) (2,1,4)
(d) (2,4,3)
(e) None of the above.

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Definitions:

Tertiary

Refers to the third level or stage in a sequence; in education, it commonly relates to post-secondary education such as universities and colleges.

Quaternary

Relating to the fourth stage or division, often used in context of geological periods or the sector of the economy that deals with knowledge-based activities.

Historiography

The study of the methods and principles through which history is written, including the different perspectives and interpretations.

Historical Research

The study of past events or conditions through the examination of relevant primary sources, secondary sources, and artifacts.