Recursive Gear Fractal

Yousef Alhuraibi
September 11, 2025
George Mason University Math 401: Mathematics Through 3D Printing

For this project, I started out with a simple gear shape that was created in openSCAD. My original design for the gear had included a hole in the middle, however after completing and computing the recursive steps and process, it became clear that the central hole reduced available surface area in regards to base space for the smaller iterations. To make room for recursion, I commented out the hole in the code which allowed me to place multiple smaller gears recursively on top of the base gear. This adjustment transformed the design from a simple gear into a fractal like structure.

The geometry for the gear was defined using circular and tooth like structures. Then the recursion process of this was handled by a separate module called "iterateonce". In this module there are 3 main process and functions, 'translate' which moves the iterated object across the plane [(x,y,z)], then ther