Everyone learned in their childhood the different geometric shapes and their visual properties. However, our everyday shapes (like triangles and circles, for instance) are not sufficient to represent more complex objects that exist in nature: snowflakes, lightning, the human lungs, coastlines, and the like. Those examples exhibit strange and fine structures at infinitely small scales and for this reason challenge standard human geometrical understanding. Those shapes are called fractals. Among the profusion of fractals, there is one of interest called the Sierpiński triangle. This specific “triangle” is related naturally to systems evolving with the time, one of them being the Chaos Game.

In this poster presentation, we invite all curious (scientific or nonscientific) to experiment with us, the Chaos Game, and to observe the appearance of the Sierpiński triangle. We will show how to construct this shape and will give some of its important properties. To study the systems represented by this shape, we will describe the construction of mathematical tools (like derivatives and integrals) that exist in traditional analysis. Finally, we will explain why the Chaos Game, given a long amount of time, describes the Sierpiński triangle.

Dr. Pozzi has been incredibly helpful in developing the presentation about a Mathematical Analysis on Sierpinski's Triangle. As the professor of the capstone course on the subject, she has demonstrated incredible knowledge on the topic, been clear and concise in her teaching, and patient, kind, and encouraging during office hours and when giving feedback on assignments.