Fractal Bloom

Recursive Triangle Blossom: A Study in Fractal Symmetry and Scaling
Name: Ahmed Elkartoum
Date: September 11, 2025
Course: George Mason University Math 401: Mathematics Through 3D Printing
Background & Mathematical Motivation
This project explores the creation of a recursive blossom structure using parametric geometry and radial symmetry, inspired by natural flower formations and based on scalable isosceles triangles. The object is generated in OpenSCAD, a script-based solid modeling language widely used in mathematical visualization and 3D printing workflows.
The underlying mathematical concept involves recursive layering, radial symmetry, and geometric scaling. Each "petal" is constructed from a triangular prism, arranged in a circular ring (with a user-defined number of petals n), and recursively stacked in diminishing layers. The transformation for each new layer involves two key operations:
• Scaling: A constant factor s (with 0 < s < 1) reduces the size of each subsequent layer.