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# Menger Sponge Barcode

Three-dimensional barcode equivalent
 (+5) [vote for, against]

You will note that this is under "Storage". There is a reason for this.

A QR code is of course a 2-D array of white and black squares which enables more data to be stored in the same space than a stripy barcode. This could be further increased.

At first I considered a cube with a QR code on each face. This would, however, only multiply storage capacity by six. Then of course, being me, I considered the dodecahedron and once again rejected it because that would at best only multiply it by twelve. Also, all polyhedral solutions to barcode format storage would need each face of the solid to be scanned.

Enter the Menger Sponge Barcode. Each exposed surface of the cube is covered in green and magenta squares. White light is used to scan the internal and external surfaces, increasing the storage capacity of the cube by several orders of magnitude. Simply place the sponge in a receptacle of white light and photocells and wait for it to scan. Use magenta and green in order to reduce problems with shadows. The maximum storage capacity of the cube seems to be approximately half a terabit. At such a large degree of capacity, it effectively becomes a storage device rather than simply a record of a small quantity of data. Having said that, I recognise that that's an ideal sponge and that the practical capacity is far lower. It would also be very vulnerable to dust and dirt.

I would also like to make it writable.

 — nineteenthly, Dec 09 2017

[zen_tom, Dec 15 2017]

[+]
 — 8th of 7, Dec 09 2017

 Hang on a mo.

I don't understand this. Do you only read the surfaces that are visible from the outside? If so, then why the Menger sponge?
 — MaxwellBuchanan, Dec 09 2017

To soak up the gravy ?
 — 8th of 7, Dec 09 2017

Just design this Menger Sponge bit box jnside out so when place in the receptacle the white light source is at a central point inside the storage medium. The light can then touch and reflect all the information.
 — wjt, Dec 09 2017

[MB], the idea is that you can fit more in, but not necessarily read the whole surface. However, you can, as has been suggested, penetrate it with multiple sensors, in which case it blends into an actual storage device relying on light rather than electrical charge or magnetism.
 — nineteenthly, Dec 10 2017

Yes, but how do you "penetrate it with multiple sensors"? If one of the internal facelets is obscured behind another, how do you read it? Are you using a semitransparent material, and scanning it with a confocal system to peer inside it?
 — MaxwellBuchanan, Dec 10 2017

Yes, that was one thought. I had a couple of ideas about that. One is that it's just about the cubic faces with dents in them, so it's not literally a Menger sponge but appears to be one from the outside. Every depression on the outward-facing surfaces of the cube would be readable, which already gets you quite far as for a level 3 "sponge" without lateral or back-facing depressions there would still be more than two thousand visible faces, thereby multiplying possible storage by several times that much if each surface of that area can be used like a QR code. However, you can go further than that, which is where it becomes more of a component. My idea there is to have tubes inserted into the cube with LEDs, photocells and wires.
 — nineteenthly, Dec 10 2017

// cubic faces with dents in them// And do you view this orthogonally to the main face (so that only the bottoms of the dents are visible)? If so, why the dents? Or do you view from an angle so that the walls of the dents are visible?
 — MaxwellBuchanan, Dec 10 2017

 Sorry, I should've mentioned how.

Either there are arrays of wide angle lenses or the cube is moved about to change the viewing angle and bring the perpendicular sides into sight. The change in colour would enable the information to be distinguished if it was one bit per surface.
 — nineteenthly, Dec 10 2017

How dense can it get before you start creating interference patterns?
 — RayfordSteele, Dec 11 2017

Interesting thought, to which I would respond, I wonder how much information you could extract from those and whether you could use them as a method of storage in themselves. And possibly naively, my next thought is, is this holographic storage if it does use interference patterns?
 — nineteenthly, Dec 13 2017

 // is this holographic storage if it does use interference patterns? //

What ??????
 — 8th of 7, Dec 13 2017

 He said " is this holographic storage if it does use interference patterns?".

Do try to keep up.
 — MaxwellBuchanan, Dec 13 2017

Suppose, for the sake of argument, that the colour of a surface can be seen as a collection of wavelengths reflected by that surface. Suppose that these collections can be discontinuous. Suppose that your incident ray of light is white, you reflect it off several surfaces in succession, and the ultimately reflected ray (back to your sensor) is the result of successive subtractions of wavelengths. If you could colour your surfaces cleverly enough to allow the individual original colours to be inferred from that finally reflected ray, would that allow you to get around the problem of hidden faces?
 — pertinax, Dec 13 2017

 [pertinax] do you mean that each reflection would subtract a particular wavelength (or wavelengths) from the ray of white light?

One problem is that you wouldn't know the order in which the colours had been subtracted (ie, if you fed in R+G+B and you only got R out, you wouldn't know whether the first surface absorbed G and the second surface B, or vice versa). That would suggest that your two surfaces (G-absorbing and B-absorbing) could be replaced by a single [G+B-absorbing] surface.
 — MaxwellBuchanan, Dec 13 2017

 Of course, and the solution involves a large number of subtly different colours and a convention about where in the sponge they're used. Chirality would certainly be involved, and widdershins, and suchlike.

You see, if your left-hand shade of green is different from your right-hand shade of green, and the ray is known to have started from the right and then bounced around to the left, then your sensor would receive a different shade of red depending on whether the blue bounce happened before or after.
 — pertinax, Dec 13 2017

 // your sensor would receive a different shade of red depending on whether the blue bounce happened before or after.//

Hang on. No it wouldn't.
 — MaxwellBuchanan, Dec 13 2017

The diminishing distance between the filters may help, as you would get with the increasing in Menger order, if the light was at the centre. Of course the distance numbers would have to be unique and have no other factors which sort of distorts the Menger aesthetic.
 — wjt, Dec 14 2017

 //No it wouldn't.//

 Mai si, Maisie, also doch und chigaimasu.

 Look, I've made it all quite clear on this whiteboard in my head. Imagine, for simplicity, an ordered array of two information- bearing cells, which we shall call Right Cell and Left Cell. Each cell may be in one of two states, named after the colours green and blue, according to which wavelengths they absorb (NB, "absorb", not "reflect"). However, in Left Cell, the "green" state absorbs wavelengths around 555nm, whereas, in Right Cell, the "green" state absorbs wavelengths around 545nm.

 If the light picked up by our sensor is mostly red, then we'll know it's hit one "blue" state and one "green" state. I think we're all agreed on that. But we *also* know ...

 No! Bad dog! Put that down... No, it's OK, I have another one.

 ... we also know *which* cell was in the "green" state. Assuming that our original incident ray included both 555nm light and 545nm light, if our reflected reddish colour includes a small greenish residue around 555nm but none around 545nm, then we'll know it was Right Cell that was in the "green" state.

Now it is just possible that David Hume's "missing shade of blue" problem also applies to green at this scale, and that I have ignominiously fallen over a quantum effect. Otherwise, I shall feel entitled to declare victory and hop around the room on one leg, whistling "La Vida Loca".
 — pertinax, Dec 14 2017

 Our porpoises may be crossed.

 I'm saying that if light reflects off two or more surfaces, and each surface absorbs/reflects different parts of the spectrum, then the light coming out the other end will be the same regardless of the order in which it hits the surfaces.

So, if you take white (RGB) light and bounce it off a blue-absorbing surface and then a red-absorbing surface, you'll get green light out. And you'll get the same if it bounces off the blue-absorber first and the red-absorber second.
 — MaxwellBuchanan, Dec 14 2017

 The green light would indicate that there are both red and blue surfaces in the box, even if unseen. The light would be more intense on the surface it reflects off first than the second surface but I don't know if anything can be done with this. However, one would still be able to distinguish between a completely blue box and a completely red one, so maybe there needs to be a way of storing the data without the order being important when this happens. There are still three states: red, blue and green. Smaller boxes with different colours would make smaller differences to the colour of the light, though not ones which would allow the exact positions of the coloured walls in the smaller boxes. Even so, more information is still available than on a flat surface.

 Something else has occurred to me, possibly not in a good way.

I've looked at the interference issue again and I _still_ think it has similarities to holography. That is, the light reflected from surfaces of the same colour interfere with each other. My understanding of maths is rather limited, but I know there's something out there called discrete cosine transformation used to compress bitmap images into JPEGs. It seems to me that there must be a way to compress data lossily by doing something like printing 8x8 JPEG-like squares in combinations of two colours on the viewable surfaces, which could even be lossless in the sense that sufficiently large features on even a really crappy JPEG would still be discernible. Hence the capacity of this thing could be larger than I think, and if it's something like photorealistic images, videos or audio, even lossy data.
 — nineteenthly, Dec 14 2017

 //light reflected from surfaces of the same colour interfere with each other//

 Yes, sort of, as long as the surface is smooth and sufficiently reflective, and so long as it is illuminated with coherent (laser) light.

At the end of the day, the amount of information you can store depends only on the surface area available, and on the spatial, spectral and intensity resolution of your camera. The only advantage of using a Menger sponge is that you can look at it from an angle to see parts of the surface inside. But, ultimately, you will absolutely be no better off than if you just used a regular cube, with a hole in one face, so that you could view all of its square surfaces apart from the inside of the one with the hole in it.
 — MaxwellBuchanan, Dec 14 2017

Coffee you can stand a spoon up in.
 — nineteenthly, Dec 14 2017

 //regardless of the order in which it hits the surfaces//

 Conceded, in the sense that transposing the light source and the sensor would yield the same result.

However, this reversal would be a bit like switching betwee "big- endian" and "little-endian" representations of conventional memory words. The important thing is that you can still infer an *ordered* array of bit-values (because of the small differences in wavelength), not just an opaque sum of those bit values. So long as that's the case, we've still got a way (in theory) to read the hidden surfaces.
 — pertinax, Dec 14 2017

Far be it from me to disagree, but I think you're wrong.
 — MaxwellBuchanan, Dec 14 2017

 A priori I'm quite sure I'm wrong, but I have yet to be convinced that I'm wrong *about this*.

 In the worked example I gave, is it that 1. You don't believe the coloured cells can be engineered to absorb very slightly different wavelengths of green or 2. You don't believe the sensor could distinguish between the resulting very-similar-but-not-identical impure reds or 3. You think there's something wrong with the inference I'm drawing from that small difference picked up by the sensor ?

These are all possible points of failure, but I'm curious as to which you had in mind.
 — pertinax, Dec 14 2017

My point is, isn't there going to be problems reflecting/absorbing the light on the way into the sponge to absorb and reflect on the way out especially since a specific sequence is wanted. Or maybe the double path is an advantage by giving a boost in reading effect.
 — wjt, Dec 15 2017

 Well, since I'm probably relying on nanomaterial magic to produce arbitrarily small differences in hue and cry, I may as well return to nanomaterial magic to produce surfaces arbitrarily reflective of any wavelengths I don't want absorbed.

I shall wave [2 fries]' carpentry pencil and declaim "arbitrispeculum spectridiffracto!"
 — pertinax, Dec 15 2017

 There's a very definite example of a strong sequential effect, demonstrated by aligning polarising filters oriented at 45 degree increments (link to follow) - slightly different case I know to absorbtive/reflective sequencing, but interesting if only analogously.

If the problem is squeezing more information into a 2- dimensional projection (which is what you have when a camera, or an eye 'looks' at something else), then fractality is definitely the way to go - it might however be better to keep the fractal dimension in the same plane as the final projection - i.e. rather than having the QR code extended into a third dimension and fractally encode stuff there, how about injecting the fractallness into the edges of the QR code, making them Koch-snowflake like instead? That way, if you read the QR code from a distance, you'd get a low-resolution response, while at closer distances/higher resolutions, you'd get increasingly more detail as you got to register more snowflakeian projections.
 — zen_tom, Dec 15 2017

 //I'm curious as to which you had in mind.//

 We may be at cross purposes here. I believe all of 1-3, no problem with any of them.

 I *thought* you were saying that the spectrum of light reaching the sensor would be different, depending on the *order* in which it bounced off different coloured surfaces (ie, the path "surface 1, surface 2, sensor" would give a different result from "surface 2, surface 1, sensor"). I am sure that's wrong (ie, either order gives the same result; so the order is indistinguishable).

But if you're just saying that you can work out which surfaces the light bounced off (without regard to order) on its path to the sensor, then I have no problem with that.
 — MaxwellBuchanan, Dec 15 2017

In that case, I shall stop hopping and subside. My knees aren't really up to it anyway, and it worries the dog.
 — pertinax, Dec 15 2017

 Now I see to, base2, blue there or not there order 1 surface , green there or not there order two surface and then another colour there or not there for the next order surface. Not any of the order surfaces carrying green or blue or nothing (base 3).

The position definition welded to the colour. Less storage of infomation but clearer.
 — wjt, Dec 15 2017

 Zigackly!

 So, we access the hidden surfaces by a series of increasingly fiddly zigzag reflections. Because we're in a recursive structure (a menger sponge), there's probably a neatly recursive algorithm for calculating the initial orientation for the light source.

The next stage will be full-blown pool trick-shots. To get there, we'll need a way to lash neutrinos to a photon and make it spin.
 — pertinax, Dec 15 2017

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