This object was created for Math 401 at George Mason University during the Fall 2021 semester.

This shape is the first few layers of a fractal produced by an iterated function system. It starts from a basic hexagon and gradually introduces more complexity from iteration to iteration. The resulting pattern is self-similar as it is formed only from copies of the original hexagon.

One of the more common methods of computing IFS fractals is the "chaos game" (Weisstein). This process involves picking a random point inside a polygon and then placing further points a set distance between the last point and a random polygon vertex. The method used to construct this IFS fractal was much more orderly. I chose points to create the pattern I wanted to see.

Iterative function systems are most often contractive, meaning points are brought closer closer and closer together. I achieved this effect by scaling each layer in OpenSCAD. I specifically scaled the width of the largest hexagons in each layer to be half that of the previous layer. This resulted in an appealing stair-step design. However, you can easily change this by altering the number of edges of the base polygon or the scaling of the layers.

Weisstein, Eric W. "Chaos Game." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ChaosGame.html