Liz Sattler, NDSU

Math Club, February 20^th, 2015.

TITLE: The Chaos Game

ABSTRACT:  Suppose there is an equilateral triangle in the plane and label the vertices. Consider the following sequence: start with a point x_0 in the plane. Randomly select one of the vertices and draw a line from x_0 to that vertex. Let x_1 be the midpoint of this line. Next, draw a line from x_1 to another randomly selected vertex. Let x_2 be the midpoint of this line. Continue this process (draw a line from x_n to a randomly selected vertex and let the midpoint of this line be x_{n+1}) to define an infinite sequence. If we plot many points of this infinite sequence, we start to notice a very familiar set, Sierpinski’s triangle, regardless of our initial choice of x_0. In this talk, we will introduce some terminology and tools from symbolic dynamics to sketch an idea about why this happens.