Einstein Tile - How to Construct an Aperiodic Monotile Using Inkscape (The Hat Tile)

The Hat Tile or Einstein Tile (aperiodic monotile)
The discovery of an "Einstein Tile" was announced on 20th March 2023. This is a single tile that will completely tile the infinite plane but cannot do so in a periodic manner. Such a tile is called an aperiodic monotile. Previously it was not known if such a tile existed.
The video puts this discovery in context by describing how it develops from the work of Roger Penrose and his discovery in the 1970s of the Dart and Kite - a set of two tiles that had the same property.
The video then shows how the tile can be constructed using Inkscape which is a free open source vector graphics software. You are taken through each step in detail.
The video finishes by showing how you can attempt to create a tiling with the tiles you constructed. This is a fun activity.
Please like the video if you enjoyed watching and don't forget to subscribe to my channel: @mistercorzi

Chapters
0:00 Intro & Context
1:43 Inkscape preparation
3:38 Constructing the tile
10:14 Creating a set of 5 coloured tiles
12:19 How to start tiling
14:39 End links

Other videos in this series:

[waihekefish]

Just came across your video after seeing news reports of this new shape and was so curious to watch and it left me inspired as it speaks of a new breakthrough in our consciousness and understanding! what a fun breakthrough! So excited to see where this takes us!

[GenesisTruffle]

Thank you very for this video, you made it look very easy and I had a blast following and creating my own patterns. I'm fascinated by the Einstein Tile and this video only expanded my curiosity, thank you

[anthonyskellern]

Thank you for this fascinating deconstruction of the new Einstein tile. I must admit I was more interested in the incidental demonstration of Inkscape! I recently installed this powerful little vector drawing programme, but had not go very far with using it - I am a life-long Adobe Illustrator user (graphic designer) but my version will only work on my old backup machine now so I was looking for a budget version as I am now semi-retired... I am impressed!

[rameshks]

Thanks for visual presentation of Aperiodic Tile...
Really inspired by this.
Thanks to inkscape and all mathematicians

[nomadisation.h]

Thanks for this amazing video! It was really helpful and I succeeded on following you step by step. I just had one difficulty: when first making the hexagon I didn't know how to make sure that the upper edge is horizontal. I just rewatched and understood that I had to click on control while making the polygon. Thanks again! Looking forward to watch the rest of your videos.

[doctormo]

When selecting the border units, you can use the new size "hairline" which means "this will always show as 1px on the screen, no matter how zoomed in you are, and also it has an effective size of 0px" this is useful for this kind of geometric drawing as the path size is what you care about.

[annahitajasavala]

So looking at a manual geometric construction, would you start with an equilateral triangle, and then half equilateral triangles flipped and constructed on the sides? Will play with it. Thank you!

[oosmanbeekawoo]

The way you speak is like Mimir—the Smartest Man Alive! Now that I think Mimir is probably Scottish!

[NikBlackwell]

The Penrose tiles require that certain rules are followed to ensure a perfectly aperiodic tiling. Do you know what the rules are for these tiles? You clearly illustrated towards the end of the video how it's possible to make incompatible sequences. Hopefully there are such rules and they have also been discovered. Or even better, perhaps they might not be discoverable.

[ChristopherCampbell-rhhc]

I’m really surprised that the Moors and or Islamic decorative tile works that they accomplished over centuries didn’t use this “Einstein “ design. I’m thinking that possibly Because it Didn’t make any repetitions (?) Any thoughts on this would be appreciated.

[Jobby]

I tried this in Illustrator. Got so far, and was then slightly disappointed about having to flip...

[BillyLemonZest]

This is just a grid, but a very pretty one

[sillyproofs]

We have to learn things through first principles—although to design large images we'll need a more programmatic approach, cause this gets tedious real quick 🥵