one interesting feature of the chiral aperiodic monotile "spectre" is the line segments that make it up can be replaced with almost any shape. so I think it'd be cool to see the edges have a jigsaw puzzle shape to them so they can lock together.

@OskarPuzzle

10 ай бұрын

Nice idea. Please enter in the ongoing competition about spectre implementations!

@siddhantkumar6340

10 ай бұрын

The spectre is better known as the 'vampire'

@Autoskip

10 ай бұрын

@@siddhantkumar6340 Yeah, who says maths isn't funny - "We might call this the 'vampire einstein' problem, as we are seeking a shape that is not accompanied by its reflection". It's my favourite line from the paper for fairly obvious reasons.

This is on the level of an actual puzzle I'd buy in a store, very cool design

@OskarPuzzle

10 ай бұрын

Or 3D-print it yourself?

@ControlledWrinkles

10 ай бұрын

3D printing is an endeavor that some folks may not have time for, although it’s is by far the most practical way to produce this puzzle. The fact that all the pieces are different makes manufacturing this by conventional methods a nightmare, it would be really sexy if it was EDM cut from metal though.

Brilliant evolution of this tiling. Love it!

@LeoStaley

10 ай бұрын

I love that relatively big youtubers like you enjoy Oskar Van Deventer like I do.

The puzzle with magnets have one disadvantage. In its solved state, all the tiles have the same orientation regarding their filament color. So you instantly know whether a piece is in the wrong orientation/spot. On top pf the solved puzzle, you could stack another layer to solve.

@OskarPuzzle

10 ай бұрын

The multicolor filament is on purpose to help with the orientation. The magnets help to keep the pieces together.

What is the name of the improved version of this tiling pattern?

@1.4142

Жыл бұрын

spectres

@Zyugo

10 ай бұрын

Parkas

@Cr42yguy

10 ай бұрын

"The mad hatter" fitting for its dificulty

@j.vonhogen9650

10 ай бұрын

Is it "Ein Stein"-tiling perhaps? With "Ein Stein" meaning "one stone" in German? "Einstein tiling" sounds to me like a play on words, isn't it?

@OskarPuzzle - This is an amazing and absolutely beautiful puzzle! Well done, Oskar! I'm even more impressed by the concept and design of your puzzle than by the discovery of the "Ein Stein" aperiodic tiling itself. Very impressive!

I have to think the version Oskar made is incredibly hard to assemble. It's also gorgeous.

@OskarPuzzle

6 ай бұрын

Thank you. Placing the first two pieces is indeed incredibly hard (19x18 tries). But placing the next pieces get easier and easier: max 17 tries for the third, 16 for the fourth, ...

beautiful puzzle

@OskarPuzzle

10 ай бұрын

Thank you!

These hat types can be made into jigsaw puzzles with all tiles having the same shape, The twist at work can be that behind every tile is its mirror image, so the player has to identify which side to use

Oskar, I've watched a bunch of your videos and I always felt like something was missing. You almost always present your puzzles in the solved state, and rarely "scramble" them and solve them yourself. I'm sure you've done so, but seemingly never for a video? I think it would make great content. Perhaps it's not your style, but if you ever decide to make a video of you solving someone's puzzles (or your own), I think they'd be wildly popular.

@OskarPuzzle

10 ай бұрын

Alas, I am a bad puzzle solver. I hope you manage convince some other KZread puzzler to make solve videos for my puzzles.

Wow! Incredable!

Need to send one to Mr. puzzle, he’d have a blast, Chris Ramsey would literally go insane I think.

Best regards, excellent Puzzle

This is highly compelling while at the same time very intimidating 🤣😅

@OskarPuzzle

10 ай бұрын

Indeed, it is. There are 19x18 options to fit the fits two pieces. Then 17 options to fit the next one. Etcetera. So once you have fitted the fits two pieces, the remainder is not that difficult any more. I used oriented multi-color filament to tune down the difficulty level even further. Plus it looks nice.

This is a very impressive puzzle design! I would definitely buy one if it was released as a product. I don't know much about the mathematics involved other than a superficial interest. But I imagine it would be possible to create curved pieces such that they assemble into a 3-dimensional object. A sphere is the obvious choice but, given the nature of the tiles, I think maybe something less ordinary would be more appropriate, such as a Möbius loop or a Klein bottle. Although a Klein bottle may be impossible to implement!

Nice!

Aperiodic structure is even more interesting and confusing than ordinary crystal structure

The non-reflected monotile is called the "spectre". I'm very glad to see you exploring the topic and I bet there are some truly special puzzles to be found. One that could be interesting would be a variation of your interpolation idea but which extends from a monotile in both directions, up as well as down. This would completely hide the monotile from view and perhaps let you make a difficult puzzle with half the number of pieces. Searching now I found at least one person extending monotiles into 3D space filling tilings, which is perhaps where this sort of puzzle exploration will naturally go: kzread.info/dash/bejne/hqOEttiaidKtk8Y.html Edit: Another KZreadr, Jade from Up and Atom just published a video on monotiles which answers an open question in my suggestion above of how to extend your 3D puzzle so that it interpolates in both directions (up and down) into other tilings. She shows that just like how your hats interpolate to arrows, there is exactly one other tiling that it can interpolate into a periodic tiling, shaped a bit like the number 6. See kzread.info/dash/bejne/c2V2yrGPh5vXirg.html

@OskarPuzzle

10 ай бұрын

Thank for these references. Interesting!

@MelindaGreen

10 ай бұрын

@@OskarPuzzle Does my suggestion make sense and do you think you'll attempt it? I'm kind of excited about this one.

@OskarPuzzle

10 ай бұрын

@@MelindaGreen Please email me about this directly, detailing your suggestion. I am in a discussion with Eric Vergo and others about a similar idea. Good to patch you in.

Is 19 the complete selection of the pieces or were there any pieces unused?

@OskarPuzzle

10 ай бұрын

I thought 19 would be a nice number, sufficiently difficult (likely too difficult already ...). The pattern is infinite. Each of those countable-infinite pieces would be different.

looks like a really interesting and simple but impossible to solve puzzle

About "all tiles have different shapes". Even if we count mirror images and distinguish orientations, there are only a finite number of shapes, right?

@OskarPuzzle

10 ай бұрын

No. In my 19-tile version, all 19 tiles are different. If you would build a 10000-tile version, then all 10000 tiles would be different. It is impossible to make an infinite tiling of these with only a finite number of shapes. Obviously, the more tiles, the more similar the tiles are. As you know, there is an infinite number of rational numbers between 0 and 1. Each tile would be associated with a different rational number ...

@mananself

10 ай бұрын

I see. Thanks!@@OskarPuzzle

looks horrendously difficult....

@OskarPuzzle

10 ай бұрын

Indeed, it is. There are 19x18 options to fit the fits two pieces. Then 17 options to fit the next one. Etcetera. So once you have fitted the fits two pieces, the remainder is not that difficult any more. I used oriented multi-color filament to tune down the difficulty level even further. Plus it looks nice.

🐢