Animated Penrose Tiling
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- čas přidán 5. 09. 2024
- See also the second part: • Animated Penrose Tilin... . This is an animation of the celebrated Penrose non periodic tiling made with Povray, created at the Department of Mathematics and Physics, Catholic University, Brescia (Italy). By Maurizio Paolini and Alessandro Musesti. On the same subject you can see the new video "Decapodi" at • Decapodi
Another related video: • Rep-Tiles (Part 1)
deep zoom...fly by... absolutely beautiful graphics.. 😻
when I first started playing with Penrose tiles, I found them in the popular science of Scientific American magazine... in the math games at the back of the magazine... oh boy... so I started out with kites and darts.. quickly realized that a periodic structure was much easier than the aperiodic with pseudo pentagonal symmetry... 🤔
took me a couple of tries, but I worked out a couple of dots on either tile that had to be aligned correctly... a sort of north south and east west system that gave.. aperiodic pentagonal symmetry ... I later read the more detailed explanations of Roger Penrose.. prior to his becoming Sir Roger...
awesome mind... these guys have provided me.. my lovely wife and our son hundreds of hours of fun 😊... a little bit more beauty in our lovely Universe..
🙏 mil gracias 🙏
Absolutely beautiful. Very well explained and animated. I downloaded the version with the voiceover and that is even better.
Thank you for clarifying something that was confusing me. Now I understand that Penrose tiles are NOT automatically Aperiodic. The adjacency constraints make them Aperiodic. (I had thought that the adjacency constraints were only to ensure that the pieces continue to fit together on into infinity, without leaving gaps)
The quantity R is the celebrated Golden ratio (see Wikipedia). Maybe you can find some explanation in the subtitles.
Thank you for the comment.
freaking awesome
Hi, please explain the equation at the beginning (1:39)
I love povray, great animation!
I do not understand the R:L = L:(R-L) part.
How can they both be equal ratios when they are clearly showing a different length for R?
It's the usual definition of Golden Ratio: (a+b):a=a:b
Is the number of possibilities 2^N for N tiles, as each dart/kite can be in two orientations? It seems it's more complicated than that. Maybe that's only true when the kite/darts are assembled as rhomboids?
no comment.......