3D Mobius - Boy's Surface (Apéry & Bryant-Kusner) in Geometry Nodes
codesignprojects
Why are both Apéry and Bryant–Kusner included?
They represent the two premier mathematical formulations of Boy’s surface. Apéry’s algebraic formulation uses trigonometric polynomials and highlights family ellipses, whereas Bryant–Kusner is derived from minimal surface inversion, minimizing Willmore bending energy and exhibiting pronounced 3-fold spiral tunnels.
Can I use this setup in Cycles?
Yes. The Geometry Nodes trees output standard manifold mesh geometry. In Cycles, ensure Render Properties → Light Paths → Max Bounces → Transparent is set to 24 or higher so overlapping internal layers do not clip to black.
How do I change the proportions of the tunnels and lobes?
In the Bryant–Kusner tree, adjust Math.079 (Z scale/offset) to open or constrict the central tunnels, and adjust Math.064/Math.043 (X/Y scale) together to thicken or thin the 3 outer underbranching lobes.
Can I freeze the animation and treat it as a static asset?
Yes. Set the Anim_Speed Value node in Frame Anim_Speed to 0.0. The node tree will evaluate statically at phase zero. You can then rotate or transform the object directly in the 3D viewport.
Is any Python scripting or third-party add-on required?
No. Everything is built entirely using native, standard Blender Geometry Nodes and Shader Nodes. No scripts, external libraries, or add-ons are needed.
Have questions about this product?
Login to message
| Published | 1 day ago |
| Blender Version | 4.2 - 5.2 |
| Render Engine Used | Cycles, Eevee |
| License | Creative Commons |
Discover more products like this
procedural eevee next geometry_nodes animation moebius math visualization Shader mobius strip abstract boys surface topology educational