Iterated Function System (IFS) – Flower

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Pantea Ferdosian George Mason University MATH 401; Mathematics Through 3D Printing December 2, 2019 Iterated Function System (IFS) - Flower What is an Iterated Function System? An iterated function system is a finite set of mappings on a complete metric space. Or perhaps more understandably, a set of transforms that make things smaller. If you start with an arbitrary point, and repeatedly iterate transforms selected at random, you can generate a fractal. In order to design a print that would represent an IFS, an original input or image is first transformed and/or translated into regions having similar characteristics. These copies (or maps) of the specific image would be generated and placed with respect to the original input until the entire region is covered and a particular "assortment" is formed. In other words, the IFS codes to an arbitrary starting image until the "attractor" emerges. For this print, I used OpenSCAD to design an illustration of Iterated Functions System. By using the "module" command, I designed a petal of the flower and also a base for the flower. This flower base was representative of the initial position of the function. I transformed and scaled each petal in order to obtain the flower look of the print. P.S. I used 2 different STL Files to have different colors for each layer. I will provide a picture of my actual print as soon as I have access to it. My print is still in progress.