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PI compression

Started by Nice Coder May 6, 2004 at 4:32 AM 9 replies 1.2k views

Original Post

101

May 6, 2004 at 4:32 AM

(second post... still getting used to this...) I have build my own little PI compression scheme.... search for PI compressor in www.planetsourcecode.com for the source. (i''ll lget a link in soon, do you use the A tags?) go to http://www.google.com/url?sa=U&start=20&q=http://3.141592653589793238462643383279502884197169399375105820974944592.jp/&e=7629 to get PI. Is this anything new/revolutionary? Basically the algarithm works like this: You get the series of numbers "141" you scan PI until you find them, (86 decimals in), You also add how long the string is, in this case the reference is 86:3 Do decode, look at the 86th digit of PI, and grab the next 3 numbers... and you get your number back again. What do you think? (please leave comments)

haro

May 6, 2004 at 4:41 AM

Any examples of success with it or proof of reliability? I'm just not convinced in the statistical chances of the compression actually compressing anything.

[edited by - haro on May 6, 2004 5:47:45 AM]

ToohrVyk

238

ToohrVyk

May 6, 2004 at 4:45 AM

- Do you have any examples of compressed data being shorter than uncompressed data?
- How do you compute/store Pi? How does it affect the time complexity of the compression algorithm?
- Does the algorithm terminate? (Does it always find an occurence of a given number in the base 10 decimals of Pi? This has only been proven to be true in base 2.)
- Isn''t there another chaotic number (ie for which the algorithm terminates) but where the range of decimals (as far as our problem is concerned) is smaller?

Victor Nicollet, INT13 game programmer

Sneftel

296

Sneftel

May 6, 2004 at 4:51 AM

Statistically, the average length of the offset into pi will be the same as the length of the string. So no, this isn''t actually useful. Still kinda neat, tho.

"Sneftel is correct, if rather vulgar." --Flarelocke

Nice Coder

Author

101

Nice Coder

May 6, 2004 at 4:53 AM

I built my compressor for fun.... (so i''ve tried it for a few values).

I''m not sure about the references being larger then the numbers... i wrote this in about 10 min, so i haven''t had time to do the proper checks.

3:4

Is 1022, but is compressed to 3:4.

I was just wondering if anybody has done anything like this before?

Polymorphic OOP

May 6, 2004 at 5:27 AM

Yes, this is nothing new, and it is also nothing magical. In general, it''s no where near as efficient as other compression schemes. Usually when the concept is presented, people talk about it as using transcendental numbers (not necessarily pi) to be able to compress potentially random values. Again, that is a pipe dream as in both theory and in practice, the size needed to represent the offset into the number is on average no gain. In fact, it''s very likely that it will take even more memory to store the "compressed" data. If anything, the concept works better as a way of crudely encrypting data than compressing it.

flangazor

106

flangazor

May 6, 2004 at 5:33 AM

Nice Coder

Author

101

Nice Coder

May 6, 2004 at 5:42 AM

Yet another project for the dustbin next to the drawing board (i only spent about 10-20 minutes coding , so its not much of a loss)... maybe a PI RNG would be more appropriate?

Ind += seed
RND = GENPI[ind]

Is this idea any better?

[edited by - Nice coder on May 6, 2004 6:44:59 AM]

ToohrVyk

238

ToohrVyk

May 6, 2004 at 6:00 AM

flangazor : your argument is true, in that it''s not enough to say "Pi is irrational" to prove that any sequence can be found in the digits of Pi.

However, there are strong conjectures based on other properties of Pi than its irrationalness (namely its ties to chaos theory), that say not only any sequence can be found in the digits of Pi, but all sequences are found with equal probability.

Besides, normality has been experimentally verified up to the 206millionth digit of pi, so I still believe that, while it''s not proven that ANY sequence can be found in Pi''s digits, it has been proven unquestionably (they just looked after them all) that short enough sequences can be found at least once.

Victor Nicollet, INT13 game programmer

flangazor

106

flangazor

May 6, 2004 at 6:26 AM

Then add my argument to Polymorphic OOP''s argument and I think that you will see that Pi compression is a fun concept for mathematicians to joke about. Not a lot more.

SiCrane

Mod

473

SiCrane

May 6, 2004 at 11:29 AM

In this thread someone raises the possibility of compressing screen shots with it. I give a somewhat overly verbose explanation of why its computationally impractical to do so.

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