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256GB Geometrically Encoded Paper Storage Device
jrieth50 noted that a method of using geometric shapes combined with color to store up to 256GB of data on a sheet of paper or plastic. The article says "Files such as text, images, sounds and video clips are encoded in 'rainbow format' as colored circles, triangles, squares and so on, and printed as dense graphics on paper at a density of 2.7GB per square inch. The paper can then be read through a specially developed scanner and the contents decoded into their original digital format and viewed or played."
according to this Indian blogger.
http://itsoup.blogspot.com/2006/11/scam-of-indian- student-developing.htmle nt_developing_technology_to_store_450_GB_on_paper
http://www.digg.com/tech_news/Scam_of_Indian_stud
I expect to see a story like this on Digg, but I thought Slashdot was better than this.
It's a scam.
I dunno who it is
but it prolly is fhqwhgads.
Here's an upper bound as a check on your numbers (not restricting ourselves to a small dictionary of shapes). I'll give away the punchline: My numbers agree with yours, but 256 GB is not possible using printers and paper.
Assumptions: I use your printer linear resolution of 1200 dpi, and assume that adjacent pixels can be resolved at this resolution. I also assume that 256 different colors can be distinguished, as you do, and that the paper we are using has an area of 96.6763 inches^2, also as you do.
Calculation: With a linear resolution of 1200 dpi, one can fit 1440000 dots per square inch (Check!), and so 139213872 dots on a sheet of A4. With 256 colors we can store a number as large as (number_of_colors)^(number_of_dots). So:
256^139213872 = 2^N (where N is the equivalent number of bits)
(2^8)^(139213872) = 2^N (recognizing that 256 = 2^8)
2^(8*139213872) = 2^N
N = 8*139213872 (bits)
(and if we just divide by 8 again to get bytes...) => 139213872 bytes = 139 MB
Discussion: This theoretical upper bound is three orders of magnitude smaller than what is being claimed by the article: It is not possible to store 256 GB on a sheet of A4. My result does however agree with your result in that the inequality (my_result)>(your_result) holds, as it should. Ad it's really not too shabby: Accounting for 8-to-14 conversion for some error correction, we can store slightly under 80 MB in this way.
Different assumptions: If I instead use your 2000 dpi laser printer figure, then I can fit 4000000 dots per square inch, and so 386705200 dots on a sheet of A4 and so almost 386 MB. (Including error correction, one might store 220 MB.) Pretty impressive!
The Absurd: Right now, many modern semiconductor fabs have working 90 nm photolithographic processes. That means that the smallest feature size is 3.54330709×10^(-6) in, and the linear resolution is about 282222 dpi. If all we print is the first metal layer, then a dot can either be "with metal" or "without metal" -- that is, one bit. And on a silicon wafer with an area the same as that of a sheet of A4 paper, we can then fit 7700207603555 dots, or 962 GB. Hard drives are about halfway there!