Link to TFA
And I come to the stark realisation that I probably should have used the coraleCDN. Oh well, near the end of the month so more bandwidth soon 
so lets see.
If he uses 3 shapes, and 5 colours, that’s 13 possibilities per “dot”. For example, Circle, Square, Triangle, Red, Blue, Green, Black, White. All he has to do, s find another 3 permutations, and he has 16 options per pixel. For those of you out there that didn’t notice, white can’t have a shape, as the paper is white.
If the data to be stored were to be translated into hexidecimal, you can store 1 hexidecimal digit per “dot”.
1 Hex digit is equivalent to a nibble, so for every 2 dots you have encoded one byte.
256 gigabytes is 274877906944 bytes. Now, most printers can easily do 1200 dpi. This is linear DPI though, so they can actually do 1440000 dots per square inch. Now, if we assume that we would need at least 9 dots to do all three shapes:
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As shown above, that reduces the shape density to 360000 shapes per square inch, or 180000 bits per square inch.
A4 paper which is almost foolscap has an area of 96.6763 square inches, so we can store, using my methods, 17401734 bytes, so 16 megabytes, much higher than people here so far have been claiming, and using very, very conservative colour choices and resolutions.
While this is an order of magnitude away from the stated values, this could easily be much higher.
I have assumed a very low resolution (laser printers can easily get up to 2000 DPI these days), no compression, and a very restricted subset of values. I should think it would be easily possible to use 8 bit colour, with no risk of data loss.
Add to this 8 to 14 conversion, or parity values, to ensure data integrity, and I think that what this guy is claiming is within the realms of possibility.
FYI, using 8 bit colour which yields 256 possibilities
3×256-3 = 765
765 is almost 3 bytes per dot
using 2000 DPI,
2000×2000 is 4000000 divided by 9 is 444444 shapes per square inch.
444444×3 makes 1333332 bytes per square inch.
so, 128901604 bytes per sheet of A4
which is 128 megabytes per sheet of A4.
So as you can see, it’s not a case of “is it possible to fit that much data”, it’s just a case of howdetailed it has to be; add another shape, and the desity per dot goes up massively,
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maybe?
Is it possible to fit 256 gigs of data on a sheet of A4 with ink?: Yes.
Is it possible to retrieve it?: Possibly, depends how small you go.
If you want precendent, think how small the pits are on a Blu Ray disk are; if we can retrieve a single bit from something that small, can we can surely retrieve something a bit bigger and a bit more detailed.
My maths isn’t to strong, so if I’ve made a mistake, feel free to correct me.
