We have used color merely to indicate the proximity of the vertex with the given color. For example, the portion of the triangle closest to the green vertex is colored green, and so forth. There is some terminology associated with the chaos game that is important. The sequence of points generated by the chaos game is called the orbit of the seed. The process of repeating the rolls of the die and tracing the resulting orbit is called iteration .
Iteration is important in many areas of mathematics.
In fact, the branch of mathematics known as discrete dynamical systems theory is the study of such iterative processes. There are two remarkable facets of the chaos game. The first is the geometric intricacy of the resulting figure. The Sierpinski triangle is one of the most basic types of geometric images known as fractals . With probability one, the orbit of any seed eventually fills out S .