Didumos69

LEGO Technic Chemistry Lab - The LEGO Molecular System

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EDIT: I just renamed this thread as it evolves into a wave of primitives and patterns that all take part of something I would like to refer to as The LEGO Molecular System, with LEGO parts being the 'elements', the primitive compounds being the 'molecules' and the generated (potentially) infinite patterns being 'matter'. Of course these LEGO molecules may represent real molecular counterparts, but they don't need to. It's The LEGO Molecular System :wink:!

I've been intrigued by infinite patterns for whole my life and was looking for the smallest Technic primitive to create an infinite recurring pattern that is the same in all 3 dimensions. This is the smallest I could come up with:

800x450.jpg?a=1

It generates this pattern:

800x450.jpg

What is the smallest primitive that can generate an infinite recurring pattern that is the same in all 3 dimensions?

LXF-file here.

Edited by Didumos69

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I saw a display in Chicago this past weekend, at the Museum of Science and Industry (working on photos and will create own thread). It is not the smallest 'primitive', but it is made with 2×4 bricks.  

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Never thought about this, but for some reason it reminds me for metal foams or even more for nanotubes.

0b3dd7f0d56e063a6a19075c86da4e39.png

AAAAnd as I am writing this... it popped into my mind: hexagon is one of the basic geometry to minimize surfaces in nature, so here is my version (but 2D only):

800x450.jpg

Edit: Is there any part in LEGO to make it 3 dimensional?

Edited by agrof

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2 minutes ago, agrof said:

800x450.jpg

I thought of that as well, but the OP mentioned it had to be 3D ... the above is rather 'flat'. :)

PS. I've been 'collecting' the above shapes for a while, they open up many possibilities in 'geometric' design.

Edited by DrJB

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Yes, it is flat - as mentioned it is to minimize the surfaces, looks it works in LEGO universum as well. :laugh:

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This is becoming very interesting. Let's look at the original 'design' from OP.

1. It uses the same parts', oriented along the 3 directions of an XYZ space

2. All combined together, the parts have In total, the parts have 12 pinholes and 12 pims. Some are already mated/connected but three of each are left not connected so they mate with the next 'module'.

The above says that whatever combination f parts we pick, the total number of male/female mating connections must match (can anyone prove the oposite?)

Perhaps the 'logical' candidates are to include these parts, though I have not figured out a way yet to interconnect them

Part No: 10197  Name: Technic, Axle and Pin Connector Hub with 2 Perpendicular AxlesPart No: 6536  Name: Technic, Axle and Pin Connector PerpendicularPart No: 44809  Name: Technic, Pin Connector Perpendicular 2 x 2 Bent and some parts with male pins Part No: 2780  Name: Technic, Pin with Friction Ridges Lengthwise WITH Center Slots

 

Whatever collection of parts we pick, one (at least) has to have 3 connection points. A part with 2 connection points can only lead to 'chains' (1-dimensional periodic structure). This rules out the secpnd part (by itself) but it could still be used in conjunction with other.

Yes I know, I do not have an answer ... yet.

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5 hours ago, agrof said:

800x450.jpg

Thinking a bit more about your proposal ... YES, you can use the above structure to create an infinite staggering. ALl you need is to build several 'sheets' like the above and then connect them with the pin-axle (below).

 Part No: 43093  Name: Technic, Axle Pin with Friction Ridges Lengthwise

If we then accept that the structure needs not be 'identical' in all 3 directions, then the smallest primitive consists of one each of these parts

Part No: 43093  Name: Technic, Axle Pin with Friction Ridges Lengthwise Part No: 57585  Name: Technic, Axle Connector Hub with 3 AxlesPart No: 10288  Name: Technic, Axle and Pin Connector Triple

 

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6 hours ago, Didumos69 said:

I've been intrigued by infinite patterns for whole my life and was looking for the smallest Technic primitive to create an infinite recurring pattern that is the same in all 3 dimensions. This is the smallest I could come up with

It generates this pattern

Woah - that looks awesome!  Here is something I came up with a while ago that fits the description - I have not computed which is smaller.

Actually, some of us were thinking along similar lines at the last convention I was at (Bricks Cascade).  We came up with a related question: design a similar 3D structure that is very strong but at the same time very low density (and preferably not too expensive).  Then the idea would be to make a huge slab of it (say a 1m x 1m x 1m cube for starters).

7 minutes ago, DrJB said:

Thinking a bit more about your proposal ... YES, you can use the above structure to create an infinite staggering. ALl you need is to build several 'sheets' like the above and then connect them with the pin-axle (below).

That is the structure of graphite.  I made a piece like this a while back...  Can we find a way to do the crystal structure of diamond?

Edited by aeh5040

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The structure of diamond is a cube inside an octahedron, inside another cube ...

Not sure there are lego elements suitable for this, but definitely worth a try.

This reminds me of a cuusoo proposal few years back where the author wanted 'basic' elements to do chemical molecules.

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46 minutes ago, DrJB said:

The structure of diamond is a cube inside an octahedron, inside another cube ...

Not sure there are lego elements suitable for this, but definitely worth a try.

This reminds me of a cuusoo proposal few years back where the author wanted 'basic' elements to do chemical molecules.

Unfortunately Lego lacks a part with tetrahedral structure of 109.5° I'm surprised lego hasn't done a molecular model kit. It could include a lot of interesting connectors, maybe they could make a 108° connector for making cyclopentanes and a 60° connector for cyclopropanes and epoxides. Those parts would be rather useful, as for making any sort of rigid geometric axle based shape is nearly impossible if you want to make any odd sided shape.

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2 hours ago, Tommy Styrvoky said:

Unfortunately Lego lacks a part with tetrahedral structure of 109.5° I'm surprised lego hasn't done a molecular model kit. It could include a lot of interesting connectors, maybe they could make a 108° connector for making cyclopentanes and a 60° connector for cyclopropanes and epoxides. Those parts would be rather useful, as for making any sort of rigid geometric axle based shape is nearly impossible if you want to make any odd sided shape.

Yes, it would be great to have such things.  However, the fact that we don't does not mean it cannot be done with existing parts.  In fact, it can - the question is how compactly and strongly.  To get started, here is a way to make an exact corner of a regular tetrahedron that is both strong and compact:

 

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7 hours ago, aeh5040 said:

Here is something I came up with a while ago that fits the description - I have not computed which is smaller.

Cool!

This is the primitive part to generate it. I certainly think it's more elegant than my find.

800x450.jpg

Btw, this gives me an idea for a non-existent part I would really like to have :wink:, if you get my point:

800x450.jpg

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56 minutes ago, mahjqa said:

infstack.gif

It's same only in 2 directions :P
Okay, I can't come up with anything, so you are still better.

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9 hours ago, aeh5040 said:

Here is something I came up with a while ago that fits the description - I have not computed which is smaller.

It would make a nice poster on the ceiling above a dentist chair...

800x450.jpg

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This would be the ideal case, although there is an issue with assembly order in some cases - marked with red.

800x478.jpg800x478.jpg

Here is the model in stp format - ATTENTION! it is way oversized (137x137x137 mm), and also no thickness tolerances are considered. In case anyone needs in other 3D format, just PM me.

Let's dig further with available LEGO parts.

 

Edited by agrof

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49 minutes ago, Didumos69 said:

It would make a nice poster on the ceiling above a dentist chair...

 

...if you need a vomiting or vertigo, or perhaps when dentist want to save expanses on anesthesia...:grin:

Edited by I_Igor

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1 hour ago, agrof said:

This would be the ideal case, although there is an issue with assembly order in some cases - marked with red.

Indeed it would. If you build row by row, then layer by layer, it would be buildable. 

1 hour ago, agrof said:

Let's dig further with available LEGO parts.

I will.

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11 hours ago, aeh5040 said:

That is the structure of graphite.  I made a piece like this a while back...  Can we find a way to do the crystal structure of diamond?

I thought that as well, but upon further examination, it is not. Graphite has 2 'distinct' layers. The lego structure has 3 distinct layers.

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M.C. Escher would be proud

8 hours ago, Didumos69 said:

800x450.jpg

 

Edited by JGW3000

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8 hours ago, agrof said:

Here is the model in stp format -

How do you export to STP? Do you model LEGO in some engineering 3D CAD to start with? Thanks.

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I work with 3D software, just threw it together in 5 mins to fulfill my curiosity, that's why it is not scaled and fine tuned. But shhhhhh, my boss might read this. :tongue:

Edited by agrof

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Not a 3D, but i like the process... It can be converted to 3D, but i need axles of infinte length for this task. And i don't sure how infinite axle will fit in 'smallest possible' bounds)

33458599440_3f05d77f38_c.jpg

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8 minutes ago, Victor Imaginator said:

Not a 3D, but i like the process... It can be converted to 3D, but i need axles of infinte length for this task. And i don't sure how infinite axle will fit in 'smallest possible' bounds)

Beautiful! What happens if you use longer axles (4L say)?  Can it slide around or is it still rigid?

7 hours ago, DrJB said:

I thought that as well, but upon further examination, it is not. Graphite has 2 'distinct' layers. The lego structure has 3 distinct layers.

I looked into this at the time, and I seem to remember finding that there are actually several forms of graphite, of which one was the "3 layer" type.  But I agree it is certainly not the usual form.

By the way, David Luders made some nice LDD versions of my "crystal":

https://www.flickr.com/photos/42988571@N08/13925365761

Edited by aeh5040

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