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!
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.
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.
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 :)
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)
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.
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".
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?
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.
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.
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!