Iterated Function System

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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 n=1. Starting with n=1 instead of n=0 allowed me to make a bigger version of the more interesting shape of three octagons together instead of the original, boring, single octagon at n=0. This also allows for more iterations since the top pieces being too small is a limiting factor from choosing a large n. The printing was successfully done on the Monoprice Mini with 12% infill, a skirt, and about 1 hour 20 minutes print time.