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:

Transmission

The act or process of sending or conveying something from one place, person, or thing to another, whether it be information, disease, or energy.

Social Reproduction

The necessary activities that guarantee the day-to-day reproduction and survival of the population.

Societal Norms

Shared guidelines or rules within a society that inform behavior and expectations.

Formal Education

A structured system of learning based on a curriculum, typically provided by schools, colleges, and universities, leading to recognized qualifications.