Fractal Cylinder Pen Holder - Fully Customizable

Create your own unique fractal pen holders, tealight holders, key rings, and more using this highly customizable generator.

This model is based on a geometric circle‑packing algorithm (an Apollonian gasket), extended into 3D as a network of hollow cylinders with smooth filleted edges. The result is a beautiful, functional, mathematically inspired design that you can shape to your needs.

✨ What you can make?

With just a few parameters you can generate:

• Pen holders
• Tealight holders
• Key rings & small accessories
• Decorative desk organizers
• Mathematical art objects 

Your imagination is the limit!

🔧 What can you customize?

You can control:

• Cylinder diameters
• Cylinder heights
• Wall thickness
• Bottom thickness (or completely open base)
• Edge rounding
• Overall scale and proportions

Every object you generate will be unique, yet structurally consistent thanks to the algorithm.

📐 About the geometry 

This generator constructs a recursive packing of tangent circles using Descartes’ Circle Theorem. Each circle becomes a hollow cylinder with matching height, and the gaps between the cylinders are filled with recursively smaller cylinders until the minimum thickness is reached. Smooth filleted edges give the model a refined, print‑friendly finish.

The OpenSCAD script computes the circumscribing circle (the enclosing “outer” circle in the Descartes framework) to form a clean boundary. If an outer circle exists for the chosen parameters, the model adds arc segments along this perimeter and fills the adjacent triangles against the boundary, producing a tidy circular edge. If no valid outer circle is formed, the generator still produces the internal fractal cylinders without a circular boundary.

📦 Included example prints

To demonstrate the generator’s versatility, we added the following print profiles:

• Pen holder
• Tealight holder
• Key ring

🖨️ Print recommendations

• 0.2 mm layer height works well
• PLA or PETG recommended for everyday use
• For tealights: use LED tealights only!

🐛 Known issues and bug reports

The Parametric Model Maker (PMM) appears to have some memory limitations. If you encounter such issues with big models, scale them down in the PMM and then scale them up again in Bambu studio.

If you encounter anything unexpected (geometry artifacts, missing perimeter, odd recursion, etc.), please help improve the algorithm by leaving a comment mentioning the buggy parameter set and a screenshot of the PMM. We actively monitor comments and will iterate based on your reports. 

Thank you!

❤️ If you enjoy this model…