Fractal Tiling of Rhombic Dodecahedra

  • Thread starter Ventrella
  • Start date
  • Tags
    Fractal
In summary, the conversation is about the possibility of recursively tiling rhombic dodecahedra in a fractal manner, similar to the way hexagons can be tiled in the Gosper Island fractal. While the closest-packing method is the most common way to tile them, it is possible to create more complex patterns through recursive tiling.
  • #1
Ventrella
29
4
Hello!

Does anyone know if rhombic dodecahedra can be recursively tiled in a fractal manner? In other words, I am looking for the 3D equivalent of a Gosper Island, whose 7-segment generator can be inscribed within a 7 hexagon clump. 7 of those can be tiled. And 7 of those can be tiled again - and again. With each iteration of tiling, the perimeter becomes more fractalized.

As I understand it, rhombic dodecahedra can be packed together in a way that corresponds to the closest-packing of spheres. 13 of them create one "clump" with one rhomb nestled in the middle and 12 surrounding it.

Can this clump be tiled in 3D in the same way as the hexagon clumps of of the Gosper Island?

Thanks!
-Jeffrey

http://www.ventrella.com/Tweaks/index.html
 
Physics news on Phys.org
  • #2
This website has some information about fractal tiling of rhombic dodecahedra. It appears that the closest-packing method is the most common way to tile them. However, it is possible to tile them in a recursive manner to create more complex shapes and patterns, though it does not appear to be as easy or efficient as tiling hexagons.
 

Related to Fractal Tiling of Rhombic Dodecahedra

What is Fractal Tiling of Rhombic Dodecahedra?

Fractal Tiling of Rhombic Dodecahedra is a mathematical concept where rhombic dodecahedra, a polyhedron with 12 identical rhombic faces, are arranged in a repeating pattern to form a larger structure.

What is the significance of Fractal Tiling of Rhombic Dodecahedra?

Fractal Tiling of Rhombic Dodecahedra is significant because it is a perfect example of self-similarity, where the overall structure resembles its individual components. This concept has important applications in fields such as architecture, art, and computer graphics.

How is Fractal Tiling of Rhombic Dodecahedra created?

To create Fractal Tiling of Rhombic Dodecahedra, the rhombic dodecahedra are arranged in a specific pattern, starting with a single rhombic dodecahedron as the base. This base is then surrounded by six more rhombic dodecahedra, and the pattern continues to repeat on a larger scale.

What are the properties of Fractal Tiling of Rhombic Dodecahedra?

Fractal Tiling of Rhombic Dodecahedra has several unique properties, including self-similarity, infinite complexity, and a high level of symmetry. It also has a fractal dimension of 3, meaning it has a non-integer dimension between 2 and 3.

What are the real-world applications of Fractal Tiling of Rhombic Dodecahedra?

Fractal Tiling of Rhombic Dodecahedra has been used in the design of buildings, sculptures, and other structures. It also has applications in computer graphics, where it can be used to create visually appealing and complex patterns.

Similar threads

Recursive 3D Tiling of Rhombic Dodecahedra
    • Differential Geometry
Replies
1
Views
3K
Mathematica This Week's Finds in Mathematical Physics (Week 266)
    • MATLAB, Maple, Mathematica, LaTeX
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top