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# Sierpiñski Fractal Brick

Eiffel tower like - nano material for constructing bricks
 (+2, -2) [vote for, against]

"Grow" bricks from nanosize up using the Sierpiñski Fractal paradigm. You'll get extremely robust but lightweight bricks.
 — pashute, Aug 25 2009

Steel tower http://img.alibaba....ion_Steel_Tower.jpg
Has a Siepinski-like structure, but only 2 levels deep. [spidermother, Aug 25 2009]

Like this? http://en.wikipedia.../wiki/Menger_sponge
The Menger Sponge - 3D (cubical) equivalent of the 2D Sierpinski Triangle (er, sort of...) [neutrinos_shadow, Aug 26 2009]

- if it did, it would be called a sponge. A *really* good one too.
 — zen_tom, Aug 25 2009

 Save for the gigantic hole in the center of it 1/4 of the brick's facial area.

Also, I'm thinking bricks are 3 dimensional, at least the last I checked. Is there a pyramidic equivalent?
 — RayfordSteele, Aug 25 2009

 There is a three dimensional equivalent - a tetrahedron with an inverted 1/3 length tetrahedron removed from the middle, and so on. Not readily stackable though.

  You must be referring to the Sierpinsky carpet. The 3D analog would be a cube with a square prism punched through each face, and the same done to each of the 20 remaining cubes, and so on. The faces would eventually be the same as a Sierpinsky carpet.

Some large steel towers have a structure that follows this principle to some extent (but using triangles, of course).
 — spidermother, Aug 25 2009

I thought that the point about a Sierpinski fractal was that, as it was iterated more times, it filled a higher and higher proportion of the available space? If so, then building a 3D equivalent with the smallest elements of "nano" size (which is what? nanometre?) would give you something denser than, say, sandstone.
 — MaxwellBuchanan, Aug 25 2009

Not necessarily. Atomic spacing in nanostructures, and their corresponding densities, is malleable. Think aerogels. Getting them into this arrangement, however, is crystallographic magic and probably warrants an MFD. I wonder if some crystalline structures already do it to some extent.
 — daseva, Aug 25 2009

 //Not necessarily// Yes, necessarily. Your smallest element is a single atom. The next largest will be a cluster of 4 atoms in a tetrahedron, then a 32-atom tetrahedron with twice the edge-lengths, etc. The spacing of the atoms will be determined by the relevant bond-lengths.

By building a 3D serpienski gasket (imagine starting with the big tetrahedrons and working downward - it's easier to imagine that way), you are starting with a very porous, open structure (large tetrahedra corner-to-corner; 50% empty). You then fill in 50% of each void with a half-sized tetrahedron, leaving smaller voids, which you then half-fill with smaller ones, etc etc. Eventually, you will have created a fully-dense material.
 — MaxwellBuchanan, Aug 25 2009

 You don't have to fill in any spacing and this is a ground-up paradigm, not the filling of a larger vessel that you describe. Besides, any material scientist will tell you that density is scale dependent. What's the density of an atom in the space of an atom? Very large. Carbon nanotubes are very dense if you only look at the volume of the tube, but when you have them loosely arranged in noncovalent networks they can take on a bulk density that is much much lower. I suspect you'll rebuke all this, though.

Consider that one wouldn't, and can't on physically terms, iterate the fractal pattern ad infinitum. This fact alone should convince you that lower densities are possible.
 — daseva, Aug 25 2009

 Yes yes, but you missed the point. The idea explicitly states that you "grow" bricks from nanosize (atom-size) up. So, if the smallest element is atom-sized, my argument holds. Just think about it a mo. The iteration is upwards from atom size, not downward. So, it can be iterated til you run out of stuff.

Also, any material scientist will not tell me that density is scale dependent. Apart from probably hyphenating "scale- dependent" (a moot point, granted), he/she would probably just say 'wha?'
 — MaxwellBuchanan, Aug 25 2009

Grow implies the structure has an intrinsic knowledge of it's eventual form. An example would be a snow flake. To make a block, say of snow flake, the block would have to have multiple starting centers. Each center wouldn't have knowledge of how to connect into another center. The total structure would have to be planned so therefore 'built' rather than grown.
 — wjt, Aug 26 2009

Sounds like a hideously expensive way of manufacturing something with the approximate performance characteristics of aerated concrete besser blocks [-]
 — BunsenHoneydew, Aug 26 2009

This isn't connected to that super simple reverse osmosis idea is it? A sponge-like membrane acting like solid salt so that only H20 can flow through. The big spaces would be used for collection.
 — wjt, Aug 26 2009

 //It has a density of (20/27) ^N of the construction material (where N is the number of iterations)// That can't be right. That equation says that the material density becomes lower with more iterations, whereas it will in fact become higher.

[Ubie] The voids become smaller and more numerous as you iterate (ie, if you start with a coarse pattern and add smaller elements in the usual way), with the total area (or volume) of void becoming less with each iteration. At infinite iterations, there are an infinite number of infintesimal voids, whose total area (or volume) is zero. Of course, you can only go as far as atom-size elements with a real material.
 — MaxwellBuchanan, Aug 27 2009

Of course [MaxwellBuchanan] is still working with maths. In the real world, the atoms still have to get to and be placed at, the right 3D positions to build the form wanted.
 — wjt, Aug 27 2009

 //I'm still no clearer whether the addition of smaller blocks is both outward and back inward into the central void/s. // Ah, point taken. I'd assumed that it was both out and in. But note also that the poster emphasizes starting with the small elements.

//In the real world,// Yes, yes. That's why I said //you can only go as far as atom-size elements with a real material.//
 — MaxwellBuchanan, Aug 28 2009

 I don't think you would get them to the atom size internally because to get the atoms to flow inside would block up and deform the holes you are trying to build. Placement, layer by layer, knowing the positions before hand would build your 3D wanted form but this is far from a crystal growth and fractal iterations.

Then again, it might be possible to giggle a set of atoms with a pattern that makes all the atoms sit in the 3D space where you want them to bond. It would be a pretty complex pattern of light, though.
 — wjt, Aug 29 2009

It would be interesting to compute how close an atom space-filling structure, say of diamond, would fill or fit to the Menger Sponge volume.
 — wjt, Aug 30 2009

 The voids created in each iteration remain, and further (smaller) voids are created in the remaining solid. The volume does indeed approach zero (while the surface area approaches infinity).

A real world example would obviously at best approximate the mathematical model for some finite number of iterations, and would have a small but non-zero density.
 — spidermother, Aug 30 2009

 //The voids created in each iteration remain, and further (smaller) voids are created in the remaining solid.// No, the voids don't remain. Imagine we start with Very Big tetrahedra, and iterate through successively smaller ones.

 First we take three tetrahedra and lay them on the floor, corner to corner. Suppose these first ones are of size 1. Then we balance a fourth one on top of them, resting on their points. You now have a tetrahedron of size 2, with a hole of size 1 in the middle.

 Now we take a tetrahedron of size 1/2* and we put it into the hole. It leaves four new voids around it, but some of the original void has been filled in, so the total amount of void decreases.

 We then take four tetrahedra of size 1/4*, and put them into the new smaller voids. Each newly added tetrahedron divides a void into four smaller voids, but also occupies part of the original void.

 Etsoforth.

 As you fill in the voids with smaller and smaller tetrahedra, the total number of voids increases, but the total volume of voids decreases.

[*it's not actually 1/2, 1/4 etc, more like 2/3, 4/9 or something; but the prinicipal is the same.]
 — MaxwellBuchanan, Aug 30 2009

[MaxwellBuchanan]; I think we're all talking at cross-purposes.
1: The idea - 'growing' a fractal solid with small particles. Volume increases faster than added mass (due to voids); density decreases.
2: Menger sponge (my fault...) - fixed volume, solid modified by removed mass; density decreases.
3: Your example - fixed volume, but with initial void, solid modified by adding mass into void; density increases.
All three are different; it took me a bit to get my head around why.
As to the idea itself, it would only be as strong as the material it was made of at a molecular/cellular level - ie: use carbon buckytubes to build a truss-like 'base unit', grow from there. Pretty much anything else will be too weak at the scale implied.

Ah, the old cross porpoises. Point prenée.
 — MaxwellBuchanan, Aug 30 2009

[neutinos shadow] Great thinking through, thanks. 1,2 and 3 should be the same given a set volume, scale and subunit size, whether you approach the construct from removing voids, adding varying sized groups or adding the tiniest subunits.
 — wjt, Aug 31 2009

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