Visualization of Fractal curves with polyhedra in Virtual Reality (VR) with A-frame
author: Paulo Henrique Siqueira - Universidade Federal do Paraná
contact: paulohscwb@gmail.com
versão em português
Lévy curve fractals with polyhedra
The Lévy Curve, known as the C-curve, is a self-similar fractal described by the Italian mathematician Ernesto Cesàro. However, this curve is named after the French mathematician Paul Pierre Lévy, who was responsible for the representation and definition of the model for constructing this curve. This curve is formed by 4 segments of equal size, generated in each iteration.
This work shows Lévy curve fractals with polyhedra, modeled for visualization in Virtual Reality.
3D models
1. Tetrahedron
Applying the construction principle of the Lévy curve fractal with the tetrahedron, we obtain an tetrahedron Lévy curve fractal. In the first order of construction of the fractal, we construct four new tetrahedra corresponding to one original polyhedron. In this example, we have solid representations in orders from 0 to 5.
2. Icosahedron
Lévy curve fractal of icosahedron.
3. Great dodecahedron
Lévy curve fractal of great dodecahedron.
4. Snub cube
Lévy curve fractal of snub cube.
5. Tetrahemihexahedron
Lévy curve fractal of tetrahemihexahedron.
6. Small dodecahemicosahedron
Lévy curve fractal of small dodecahemicosahedron.
7. Concave dodecahedron
Lévy curve fractal of concave dodecahedron.
8. Great triambic icosahedron
Lévy curve fractal of great triambic icosahedron.
9. Cubitruncated cuboctahedron
Lévy curve fractal of cubitruncated cuboctahedron.
10. Medial disdyakis triacontahedron
Lévy curve fractal of medial disdyakis triacontahedron.
11. Joined truncated cube
Lévy curve fractal of joined truncated cube.
12. Disdyakis dodecahedron
Lévy curve fractal of disdyakis dodecahedron.
13. Icosidodecahedron
Lévy curve fractal of icosidodecahedron.
14. Triakis tetrahedron
Lévy curve fractal of triakis tetrahedron.
15. Szilassi toroid
Lévy curve fractal of Szilassi toroid.
16. Regular map
Lévy curve fractal of regular map.
Lévy curve fractals with polyhedra: visualization with Virtual Reality by Paulo Henrique Siqueira is licensed with a license Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International.
How to cite this work:
Siqueira, P.H., "Lévy curve fractals with polyhedra: visualization with Virtual Reality". Available in: <https://paulohscwb.github.io/fractalcurves/levy/>, May 2026.
References:
Ventrella, Jeffrey. “Fractal curves”. http://fractalcurves.com/
Weisstein, Eric W. “Uniform Polyhedron.” From MathWorld–A Wolfram Web Resource. https://mathworld.wolfram.com/UniformPolyhedron.html
McCooey, D. I. “Visual Polyhedra”. http://dmccooey.com/polyhedra/