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:

Progesterone

A hormone produced in the ovaries, placenta, and adrenal glands that plays a key role in the menstrual cycle and pregnancy.

Fertilized Egg

The result of the fusion of a male sperm cell and a female ovum, marking the beginning of a new organism's development.

Zygote

The initial cell formed when a new organism is produced by means of sexual reproduction, resulting from the fusion of male and female gametes.

Implantation

The process by which a fertilized egg attaches to the lining of the uterus beginning pregnancy.