5 ms·

Experiment with Penrose Tilings and other patterns

149 points by bibanez 4y ago

dvh 4y ago
Just mentioned in minute physics video: https://youtu.be/-eqdj63nEr4 https://youtu.be/-eqdj63nEr4
- bibanez 4y ago
  Yes that's where I got it from! For me it's one of those interesting corners of the internet I always like to check up upon
julienchastang 4y ago
Wonderful! My complements to Aatish for developing this project. I look forward to experimenting with it further.
deleted 4y ago
[deleted]
WithinReason 4y ago
Are any of these actual Penrose tilings?
- AceJohnny2 4y ago
  Yes, the default display is.
mdp2021 4y ago
And when you are done playing with the site, if you have spare time, you can "entail" some "Penrose's" in Simon Tatham's Portable Puzzle Collection's "Loopy".
diydsp 4y ago
Just in case you missed the subtle question mark of help in the top right corner, the author's explanation here is stunningly clear: https://github.com/aatishb/patterncollider#readme https://github.com/aatishb/patterncollider#readme Kudos to aatishb. I've been fascinated by this generations since approx 1995 when there was a webpage at a university with webcgi script to transmit the params to a server to render a .gif. I've read many explanations since then, but it's only this time around that I get it!
- bobbylarrybobby 4y ago
  Wow, that algorithm to generate tilings is so simple, it's beautiful. The kind of thing that after you've seen it you feel silly for not having thought of it yourself.
AceJohnny2 4y ago
Small bug: on Safari 16.1 (Ventura 13.0), clicking a single line in the line diagram highlights a bunch of lines in the line diagram (but a single line of tiles in the tile diagram)
dandelany 4y ago
Awesome! A few years ago I made some physical Penrose tiles out of wood & magnets, this will help me come up with some new designs to make with them :) https://twitter.com/dandelany/status/1313591497577570305 https://twitter.com/dandelany/status/1313591497577570305
- bibanez 4y ago
  These are beautiful!
pmarreck 4y ago
So I'm a person who loves this sort of thing. My favorite is probably aperiodic tilings such as the one featured at http://aperiodic.net/ http://aperiodic.net/. So, me, opening the OP link: "OH MY GOD!" Has anyone actually tiled any portion of their property with something like this? If so, you have my envy
- mhb 4y ago
  Lots. Search for, e.g., bathroom Penrose tiling.
psd1 4y ago
I love the "disorder" setting: https://aatishb.com/patterncollider/?pattern=0.29&disorder=0.58&zoom=1.1&showIntersections=false&contrast=8 https://aatishb.com/patterncollider/?pattern=0.29&disorder=0...
- rnhmjoj 4y ago
  It's very aptly named: if you keep the "pattern" close to 1 and slowly decrease the "disorder" you can even see a sort of second order phase transition.
spencerflem 4y ago
This is so lovely :)
yesenadam 4y ago
Amazing, very nicely done! I was hoping for some way of really getting disorder! But the parallel lines seem to stay parallel and evenly spaced no matter what. I wrote a program years ago to make tilings from any arrangement of lines, including random lines - they dont have to be in parallel groups; any arrangement of lines makes a tiling - and have still never seen the idea anywhere else. i.e. I'd love another slider or two that make the lines increasingly unparallel and unevenly spaced. Many pictures of what I mean on this page https://www.adamponting.com/de-bruijn-tilings/ https://www.adamponting.com/de-bruijn-tilings/
jhoechtl 4y ago
I am outing myself as a noob in this regard, but what can this tiling be used for? Eg. assigning computer generated icons from a random number to users which cannot be forged? If so, how?
- wolfram74 4y ago
  Many moons ago I was in an organic chemistry class of some sort, and aperiodic tilings were mentioned as being useful for thinking about liquid crystal displays. Sorry I can't provide more context than that, it was a long time ago.
- mkl 4y ago
  I'm not sure what you mean about forging, but there's nothing secure or one-way about this - you can go backwards from the image to the parameters. The primary purpose, which it's quite good at, is making pretty pictures.
Yuyudo_Comiketo 4y ago
Simply fascinating! Would be immensely cool to be able to export to SVG.
JKCalhoun 4y ago
The 3-Fold Symmetry grid lines are at 120 degrees to one another, the 4-Fold Symmetry grid lines at 90 degrees. Any way to rotate just one of the "plane" of grid lines relative to the others? Curious how the pattern would change.

149 points by bibanez 4y ago

dvh 4y ago

Just mentioned in minute physics video: https://youtu.be/-eqdj63nEr4 https://youtu.be/-eqdj63nEr4

bibanez 4y ago
Yes that's where I got it from! For me it's one of those interesting corners of the internet I always like to check up upon

julienchastang 4y ago

Wonderful! My complements to Aatish for developing this project. I look forward to experimenting with it further.

deleted 4y ago

[deleted]

WithinReason 4y ago

Are any of these actual Penrose tilings?

AceJohnny2 4y ago
Yes, the default display is.

mdp2021 4y ago

And when you are done playing with the site, if you have spare time, you can "entail" some "Penrose's" in Simon Tatham's Portable Puzzle Collection's "Loopy".

diydsp 4y ago

Just in case you missed the subtle question mark of help in the top right corner, the author's explanation here is stunningly clear: https://github.com/aatishb/patterncollider#readme https://github.com/aatishb/patterncollider#readme Kudos to aatishb. I've been fascinated by this generations since approx 1995 when there was a webpage at a university with webcgi script to transmit the params to a server to render a .gif. I've read many explanations since then, but it's only this time around that I get it!

bobbylarrybobby 4y ago
Wow, that algorithm to generate tilings is so simple, it's beautiful. The kind of thing that after you've seen it you feel silly for not having thought of it yourself.

AceJohnny2 4y ago

Small bug: on Safari 16.1 (Ventura 13.0), clicking a single line in the line diagram highlights a bunch of lines in the line diagram (but a single line of tiles in the tile diagram)

dandelany 4y ago

Awesome! A few years ago I made some physical Penrose tiles out of wood & magnets, this will help me come up with some new designs to make with them :) https://twitter.com/dandelany/status/1313591497577570305 https://twitter.com/dandelany/status/1313591497577570305

bibanez 4y ago
These are beautiful!

pmarreck 4y ago

So I'm a person who loves this sort of thing. My favorite is probably aperiodic tilings such as the one featured at http://aperiodic.net/ http://aperiodic.net/. So, me, opening the OP link: "OH MY GOD!" Has anyone actually tiled any portion of their property with something like this? If so, you have my envy

mhb 4y ago
Lots. Search for, e.g., bathroom Penrose tiling.

psd1 4y ago

I love the "disorder" setting: https://aatishb.com/patterncollider/?pattern=0.29&disorder=0.58&zoom=1.1&showIntersections=false&contrast=8 https://aatishb.com/patterncollider/?pattern=0.29&disorder=0...

rnhmjoj 4y ago
It's very aptly named: if you keep the "pattern" close to 1 and slowly decrease the "disorder" you can even see a sort of second order phase transition.

spencerflem 4y ago

This is so lovely :)

yesenadam 4y ago

Amazing, very nicely done! I was hoping for some way of really getting disorder! But the parallel lines seem to stay parallel and evenly spaced no matter what. I wrote a program years ago to make tilings from any arrangement of lines, including random lines - they dont have to be in parallel groups; any arrangement of lines makes a tiling - and have still never seen the idea anywhere else. i.e. I'd love another slider or two that make the lines increasingly unparallel and unevenly spaced. Many pictures of what I mean on this page https://www.adamponting.com/de-bruijn-tilings/ https://www.adamponting.com/de-bruijn-tilings/

jhoechtl 4y ago

I am outing myself as a noob in this regard, but what can this tiling be used for? Eg. assigning computer generated icons from a random number to users which cannot be forged? If so, how?

wolfram74 4y ago
Many moons ago I was in an organic chemistry class of some sort, and aperiodic tilings were mentioned as being useful for thinking about liquid crystal displays. Sorry I can't provide more context than that, it was a long time ago.
mkl 4y ago
I'm not sure what you mean about forging, but there's nothing secure or one-way about this - you can go backwards from the image to the parameters. The primary purpose, which it's quite good at, is making pretty pictures.

Yuyudo_Comiketo 4y ago

Simply fascinating! Would be immensely cool to be able to export to SVG.

JKCalhoun 4y ago

The 3-Fold Symmetry grid lines are at 120 degrees to one another, the 4-Fold Symmetry grid lines at 90 degrees. Any way to rotate just one of the "plane" of grid lines relative to the others? Curious how the pattern would change.