Just bringing up this thread again, in my post higher up I showed how someone got about 50% more 1x2 bricks with careful stacking. I suggested that you might be able to do even better with plates than with bricks, since there is more void volume in a stack of bricks than a stack of plates. For a demonstration of this, see these two stacks of trans clear elements (yes, sitting on my dashboard outside of my workplace):
You can see through the stack of 1x2 bricks much more easily, since the space of one brick isn't all filled up with the stud of the brick below. Anyway, yesterday I was by my closes LEGO store, and on the PaB wall they had a lot of 1x1 round plates, including trans dark blue, trans light blue, and trans clear. I filled up a small cup with these, thinking they'll be useful as water or maybe do one of those mosaics where the color variation is all based on the height of stacks of trans elements. A few other bits got in the mix, as the bin of trans clear 1x1 rounds also had some other trans clear elements and was just scooping things into the cup. Anyway, we'll see what sort of MOCs these result in, but this morning I sorted and stacked the plates. Then, just to test my hypothesis about efficiently filling, I put them all back in the cup. As you can see, there is an empty volume of about a third of the cup.
I was surprised that it does not seem like there is a big difference between bricks and plates in how much extra you can get between loosely filling cups and carefully stacking. In both of these cases it seems like the gain is about an extra fifty percent worth of elements. One possible consideration is that, even with the void volume inside the plate, 1x1 rounds just randomly mixed together do a pretty good job of doing efficient stacking on their own. An interesting experiment would be to make stacks of 2 1x1 round plates, and then randomly mix those. That way you'd still have very small, almost spherical objects that would shuffle together pretty well, but you'd also be using up some portion of the void volume.
A few caveats:
-This is all by eyeball. I didn't go back and fill in the resulting empty space with extra parts, and then count them to see the actual difference.
-There is a liability to stacks of 1x1 round plates - they don't easily slide past each other due to the lip and groove. So there may be gaps in the way I piled these stacks of plates together that would not happen with, say 1x1 square plates, or 1x1 bricks or round bricks.
-The indentation in the bottom of the cup is kind of problematic in trying to come up with efficient filling, as you need different size stacks around the outside than you need in the middle. With the bigger cups the indentation is a smaller percentage of the whole, so this effect is lessened.
-OTOH, I've heard others say that by volume, the smaller cups are a better deal. Has anyone filled the two cup sizes with water and compared their actual volume, and then divided by the cost? I can easily do that tonight, but it seems such an easy test that someone's surely done it.
-The inclusion of about 30 1x2 trans clear bricks (which were mixed in the bin with the 1x1 trans clear round plates on the PaB wall) could throw this experiment off, but it wouldn't be by much.
-It seems obvious that for larger, odd shaped pieces, the effect of efficient packing would be maximized. For instance, I didn't get any, but some odd bracket piece was on the wall (this or something similar
). I am certain there would be a huge difference between the number of those you could randomly throw in a cup vs efficiently packing them.
-I've always held that I would rather just pay an extra eight dollars than go to all this trouble in the store. I stack at home while doing something mindless like watching TV, but I wouldn't stand there in the store for a half hour stacking bricks. Of course, the bigger volume of ABS you get, the more $ you would save this way, but then of course you would also spend that much longer in the store. Does anyone know if there comes a point that the store employees ask you to move along? Or do they just understand that there are going to be some obsessive AFOLs who will do this? Most store employees I've spoken with are very well acquainted with the AFOL community, if not actually involved themselves.
-Just thinking in two dimensions, squares can tesselate - that is, they can stack together to fill up an area without having any gaps. Circles cannot - there are always gaps. So perhaps there would be a significant difference between stacking 1x1 plates and 1x1 round plates.
-OTOH, these are ultimately going in a cylindrical cup at the LEGO store. So that might give the advantage back to the round elements vs the square elements.
Okay, I got even geekier in a response to a comment on Flickr. I'll repost this here:
BTW, I should note that in real life I'm a chemist, and there are many areas in chemistry where how things pack together closely is very important, like when you look at the structure of crystals, or how molecules in a liquid are in contact but shift past each other. I'm sure there are similar discussions in mathematics, engineering, etc. And this can have very practical effects. For instance, if you produced a product that could be packed together in different ways, but one way took up much less space, that would have serious consequences for shipping costs, warehouse space requirements, shelf space requirements at stores, etc, that all impact on profits. A 20% difference in space requirements would make a serious impact on the company bottom line.
If I think about this much more I might totally geek out and come up with a scholarly paper based on this (if someone hasn't already done that). How cool would that be to come up with a paper based on the Pick-a-Brick wall and publish it in some scientific journal like Acta Crystallographica (an actual journal on crystal structure science).