The Following Is Called the Chaos Game

question 11

Multiple Choice

The following is called the Chaos Game. Start with a square ABCD in which A is located at (0, 0) , B is
located at (27, 0) , C is located at (27, 27) , and D is located at (0, 27) . 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 two-thirds of the way straight towards 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 two-thirds of the way
from the last position to the winning vertex.
The grid below show the square ABCD.

• A) (2,1,4)
• B) (1,3,3)
• C) (2,1,3)
• D) (2,3,1)
• E) None of the above.

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Definitions:

Outcomes

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