Recursive Star Spire

Recursive Star Spire
Prashiddha Subedi
10 September 2025
George Mason University Math 401: Mathematics Through 3D Printing


This project, called the Recursive Star Spire, explores mathematical recursion and affine transformations through 3D printing. The object begins with a large star base and extends upward with spires made from smaller stars that shrink and twist at each recursive step. This recursive design showcases concepts from fractal geometry, where self-similar patterns recur at varying scales. The construction demonstrates how mathematics, coding, and 3D printing can intersect to turn abstract formulas into tangible objects.

The star spire was created in OpenSCAD using iterative code that places scaled and rotated star prisms in layers. Instead of directly computing coordinates with trigonometric functions, rotations and translations were applied to replicate placement around a circle. Parameters such as the number of points on the star, shrink factor, height scaling, and