Colourful Windmill Patterns on All 6 Faces of the 4×4×4 Rubik's Cube

[FMLJohn]

Hello everyone!

Over the past few years, I’ve been exploring a class of patterns on the 4×4×4 Rubik’s Cube that I call "uniform windmill patterns".

By a uniform windmill pattern, I mean a pattern on the 4×4×4 Rubik’s Cube in which:

• each face of the cube displays a windmill figure with the same orientation, and​
• the four branches of any windmill are all different in colour, and​
• identical or visually similar colours are kept non-adjacent, so that no red-orange, blue-green, or white-yellow pair appears as a windmill branch and its background on the same face.​

Here is one example of such a pattern that I managed to achieve on my cube:

These patterns naturally led me to think about some underlying structural and mathematical questions, such as how many of them are realisable on a 4×4×4 cube, and when do the generating algorithms for such a pattern depend on the initial orientation of the solved cube.

I have written an article collecting these observations and ideas, along with some algorithms for achieving those patterns; it is available on Zenodo. I’m sharing the link here in case anyone is interested in a more detailed discussion:

https://zenodo.org/records/17737782​

I’d be very happy to hear your thoughts, and I’d love to learn if others have explored similar patterns or related questions.

Thanks for reading!

FMLJohn

 

[qwr]

Cool. Is that website like arXiv?

 

[FMLJohn]

Cool. Is that website like arXiv?

Yes Zenodo is like arXiv. Both of them host preprint papers, but arXiv has slightly stricter acceptance standards.

 

[Rosi]

I was a bit afraid of the forbidden windmill.
But yours looks super cool!!