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So they found the "Einstein"-Tile (as in "one stone")...


kweso

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Hi all.

Just found this article about a retired mathematician who found the so called "Einstein" tile. That would be a single tile that can be tiled gaplessly without producing a repeating pattern. 

https://arxiv.org/pdf/2303.10798.pdf

Now I wonder if this could be used in CGI to use a single texture that never shows repetitions.

 

I don't know if this is relevant in any way. I just love to see when  year old math problems are solved in my lifetime and I like observing how abstract science finds its way to applied technology...

And I had to tell somebody about this (but nobody in my immediate circles would care 😉 ).

Anyways. Have an awesome weekend!

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9 hours ago, kweso said:

And I had to tell somebody about this (but nobody in my immediate circles would care 😉 ).

 

Math as Art is always welcomed in this forum.

 

If you are into these things I recommend taking a look at papers from Bridges - Mathematical Connections in Art, Music and Science

 

You can use the MoSpline to create aperiodic patterns. So far the aperiodic monotile has no L-system. I tried the Penrose tiling here penrose tiling.c4d

 

A couple of years ago I had a small talk about new tiling features regarding the Cloner object with Rick Barrett, he found the ideas interesting and said he would consider a similar implementation on their new system (referring to the later released Neutron Project AKA SceneNodes).

 

image.png.e3a3eaec3585716a223e2177ce8ee535.pngimage.png.5bdf8dc41de8408a0cca5b67d63db1b4.png

 

Theoretically you can use the classical Cloner to create any pattern of mixed polygons if their center can be laid on a regular square grid. But non-repetitive tiling is trickier and each case is governed by it's own rules so I don't think there is a way to create such patterns natively in C4D. I would use other apps as helpers to export to C4D like InkScape or VisionsOfChaos (actually I take my Penrose tiles from Ready).

Edited by HappyPolygon (see edit history)
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Yeah. After I posted, I thought that in CG you won't need such a perfect shape to achieve non-representative textures. Will take a look at that video after cooking...

Laters..

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On 3/31/2023 at 7:27 AM, kweso said:

Now I wonder if this could be used in CGI to use a single texture that never shows repetitions.

 

 

 

I thought the same thing. It might be useful as a way to re-mix a standard seamless texture, so the artist doesn't need to create the texture in that specific shape. It would be crazy to paint a seamless texture in that shape. So the math should be used underneath (behind the scenes) to make the standard texture not appear to repeat. Basically, what the "seamless" option from C4D material tag attempts to do, I think. Not sure if that option is still in the newer versions, but I digress. This new shape would not be useful for anything that needs a repeated structure, like typical floor tiles. Random / Noise patterns may benefit from it though.

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On 3/31/2023 at 5:27 PM, kweso said:

Now I wonder if this could be used in CGI to use a single texture that never shows repetitions.

 

Νο.

 

In order to do that you'd need to fit your texture inside the einstein tile in a certain way that would repeat no matter how the einstein tile will be positioned next to  itself. In other words you'd need a second einstein tile to fit inside the first einstein tile. (if you want it to look seamless that is)

 

C4D already has a non-repetitive way to tile textures (probably faster than any polygonal tiling method) and it's called Scatter Node. Not many users know it because it can only be used in Material nodes and most users don't use those.

 

https://help.maxon.net/c4d/en-us/Default.htm#html/NET_MAXON_PATTERN_NODE_GENERATOR_SCATTER.html?TocPath=Node%20Editor%7CIndividual%20Assets%7CContext%7CScatter%7C_____0 

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7 minutes ago, keppn said:

Redshift-Users can also get a "No-Tile"-Shader on this OSL-Repository. It randomly scales, rotates and blends a single non-tiling texture; for simpler organic stuff like outdoor-ground, it works surprisingly well.

https://github.com/redshift3d/RedshiftOSLShaders

I use similar OSL shaders in Octane. Very cool.

But nice find this Einstein tile! Wonder if it has special features for engineering. 

 

Edited by zeden (see edit history)
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