The Formation of a Sierpinski Triangle by the Chaos Game and its Proof using Iterative Function System (2019)

S. Yoon. 

Fractals, structures formed by iterations of identical shapes, can be found in numerous places including nature. The Chaos Game is an embodiment of this emergence of patterns from seemingly random actions. Using a dice and a piece of paper, one is able to generate the Sierpinski Triangle, a form of fractal structures. Within this report, I aim to empirically demonstrate the Chaos Game and explain why the Chaos game is able to produce such structures using the notion of iterative function systems.