Rhombic Tilings

A look at how a regular polygon of n sides leads to a certain suite of rhombs which can tile the entire plane ...

Category:

Film & Animation

Tags:

• geometry
• Penrose
• rhomb
• polygon
• tiling
• tessellation
• animation

[tkluysk]

I'm looking into using the penrose tiles for modular architectural purposes.

What tools are you using to visualize the tilings (2D and 3D)?

[rufus16180339887]

I use the software Mathematica, which has its own programming language, to make the 2D and 3D tilings. In Mathematica I have implemented the "generalized dual method." This creates a given tiling. Sometimes I create a tiling in Mathematica and export it to other software, such as POV-Ray.

[bubsy1990]

would it be possible to put on this video again but without the music? it is such well explained info which i'd love to learn but find it difficult to concentrate with the music.

thanks :)

[bumgut]

Wow amazing. Wish i was good at maths!

[rufus16180339887]

Too briefly: the generalized dual method itself generalizes to n dimensions. In the plane, an "arrangement of lines" leads to a zonogonal tiling. For instance, a certain arrangement of lines leads to the Penrose tiling. Wherever two lines intersect, a rhomb arises in the tiling. But if three lines of the arrangement intersect at a single point, then a hexagon arises; if four lines intersect at one point, an octagon, and so on. Hmmm ... I will think about a movie illustrating the GDM ...

[dwyllie]

Very good. :-)