Sierpinski Triangles and the Chaos Game by Nick Stefanelli '24

Sierpinski Triangles and the Chaos Game by Nick Stefanelli ’24, Wednesday April 3, 1:00 – 1:50pm, North Science Building 113, Wachenheim, Mathematics Colloquium

Abstract: The Sierpinski triangle is a fractal named after Polish mathematician Wacław Sierpiński who was the first to rigorously define the shape in 1915. The pattern can be found in Roman art and architecture dating back to the 11th century, and there are a number of fascinating ways to generate the fractal including a coloring of Pascal’s triangle (mod 2). This presentation will explore another puzzling way of creating the Sierpinski triangle: Barnsley’s Chaos Game. After a brief discussion of metric spaces and Hausdorff distance, we will delve into the Contraction Mapping Theorem and Hutchinson operators to gain some insight into why the Sierpinski triangle results from a seemingly random and chaotic process.