Koch Snowflake-An Iterated Function System

Nicole Van Oort
04/04/16
George Mason University
Math 493-Mathematics Through 3D Printing
Shows the progression of an iterated function system from a hexagon to a Koch Snowflake.

The Koch Snowflake also known as the Koch curve is a fractal curve, and an iterated function system. Fractals are images, or mathematical sets that display a repeating pattern at every scale, also known as self-symmetry. In other words at any scale you look at the image, the image appears to copy or repeat itself. One can also describe a fractal as a shape made up of smaller images of itself. An iterated function system is a method of creating a fractal, repetition of a function creates a union of several copies of the same fractal varying in size, rotation and translation. The Koch Snowflake is based of iterations of the Koch curve, which was first described by Helge von Koch, a Swedish mathematician in 1904. This was one of the earliest fractal curves to be described and he described it in his pape