The Following Is Called the Chaos Game

question 21

Short Answer

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 .

What would be the resulting coordinates of P3 if the sequence of (4,1,4) was rolled?

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