Fractal Curves

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

Cat curve fractals with polyhedra

The cat fractal curve is formed by 5 segments of equal size, generated in each iteration. Using a 13° slope of the first segment relative to the x-axis, we have the formation of this fractal that resembles a cat.

$Cat curve fractal$

This work shows cat fractal curve with polyhedra, modeled for visualization in Virtual Reality.

3D Models | Home

$RV de fractais$

3D models

1. Tetrahedron

$Tetrahedron Cat curve fractal$
Applying the construction principle of the cat curve fractal with the tetrahedron, we obtain an tetrahedron cat 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. Great dodecahedron

$great dodecahedron Cat curve fractal$
Cat curve fractal of great dodecahedron.

3. Cuboctahedron

$Cuboctahedron Cat curve fractal$
Cat curve fractal of cuboctahedron.

4. Truncated icosahedron

$Truncated icosahedron Cat curve fractal$
Cat curve fractal of truncated icosahedron.

5. Small dodecahemicosahedron

$Small Dodecahemicosahedron Cat curve fractal$
Cat curve fractal of small dodecahemicosahedron.

6. Stella octangula

$Stella Octangula Cat curve fractal$
Cat curve fractal of stella octangula.

7. Small ditrigonal dodecacronic hexecontahedron

$Small ditrigonal dodecacronic hexecontahedron Cat curve fractal$
Cat curve fractal of small ditrigonal dodecacronic hexecontahedron.

8. Rhombicosacron

$Rhombicosacron Cat curve fractal$
Cat curve fractal of rhombicosacron.

9. Great disdyakis dodecahedron

$Great disdyakis dodecahedron Cat curve fractal$
Cat curve fractal of great disdyakis dodecahedron.

10. Great stellapentakis dodecahedron

$Great stellapentakis dodecahedron Cat curve fractal$
Cat curve fractal of great stellapentakis dodecahedron.

11. Joined truncated cube

$Joined truncated cube Cat curve fractal$
Cat curve fractal of joined truncated cube.

12. Disdyakis dodecahedron

$Disdyakis dodecahedron Cat curve fractal$
Cat curve fractal of disdyakis dodecahedron.

13. Hendecagonal dodecahedron

$Hendecagonal dodecahedron Cat curve fractal$
Cat curve fractal of hendecagonal dodecahedron.

14. Biscribed orthotruncated propellor octahedron

$Biscribed orthotruncated propellor octahedron Cat curve fractal$
Cat curve fractal of biscribed orthotruncated propellor octahedron.

15. Heptagonal dodecahedron

$Heptagonal dodecahedron Cat curve fractal$
Cat curve fractal of heptagonal dodecahedron.

16. Dodecahedron

$dodecahedron Cat curve fractal$
Cat curve fractal of dodecahedron.

17. Regular map

$Regular map Cat curve fractal$
Cat curve fractal of regular map.

Cat 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., "Cat curve fractals with polyhedra: visualization with Virtual Reality". Available in: <https://paulohscwb.github.io/fractalcurves/cat/>, 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/