Iterated Function System

Iterated Function System
Ryan Simmons
9/27/2021
George Mason University Math 401
Mathematics Through 3D Printing
This print is an iterated function system. An iterated function system is a shape transformed many times on top of itself by a function. The shape in my 3D printing has an octagon given some height with linear extrude. The transformation makes a layer of three smaller octagons connected in a row with the middle one rotated by 90 degrees. This creates a plus-like shape that continues for the smaller and smaller octagons.
The code works using a created module in OpenSCAD called “repeat(n)”. Inside the module is an if-else statement with n>0 being the if condition. Inside the if statement are three functions of modifiers that scale, translate, and rotate before calling the repeat function again with n-1. This causes n to go down stacking modifiers until n=0 and the shape is modified into multiple smaller shapes. This function is called five times in my code starting with