Logistic map and randomness

Networking/Security Forums -> Cryptographic Theory and Cryptanalysis - Internal and Transmission Security

Author: mazing82 PostPosted: Thu Jan 24, 2008 5:07 pm    Post subject: Logistic map and randomness
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I've read that the logistic map can be used to generate random numbers for K=4 (chaos regime)

x_n+1 = K*x_n*(1-x_n)

The logistic map for K=4 is isomorphic to the tent map. However, orbits in the tent map are non-periodic only for irrational initial values (x_0). For rational x_0, the tent map generates always periodic orbits.

http://mathworld.wolfram.com/LogisticMapR=4.html

My question is, is this the case also for the logistic map with K=4?. In that case, all orbits would be periodic, because computers can only handle rational numbers, and therefore x_0 must be a rational number.

Author: GingerdaveLocation: Leeds PostPosted: Thu Jan 24, 2008 5:44 pm    Post subject:
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is it wrong that I understand the individual words, put not the post as a whole? Embarassed

Author: mazing82 PostPosted: Thu Jan 24, 2008 5:53 pm    Post subject:
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Gingerdave wrote:
is it wrong that I understand the individual words, put not the post as a whole? Embarassed


Probably not Very Happy. I'm not a native English speaker, so probably I didn't explain myself clearly.

In a few words:

x_n+1 = 4 * x_n * (1-x_n) is the logistic map in the chaotic regime (K=4)

let's suppose x_0 is a rational number (the initial value of x).

Is the orbit of x_0 periodic or non-periodic? (i.e. does it repeat itself or not?)

Author: AdamVLocation: Leeds, UK PostPosted: Thu Jan 24, 2008 7:14 pm    Post subject:
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I suspect the problem is more that Dave is not a native crypto-speaker rather than issues with the English language. Me neither, unfortunately.

As they say - you know when the crypto-mafia are out to get you - they make you an offer you can't understand.

Author: Pillow Whisperer PostPosted: Mon Feb 18, 2008 12:03 pm    Post subject: hey
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well since computers are finite state machines then yes it'll have to repeat therefore periodic. furthermore since this 'random' number generator generates its value from a constant and with a formula its pseudo random, therefore by definition again its periodic it might be a long period but it is periodic. if you plug in the same seed you'll get the same output stream.

Author: mazing82 PostPosted: Fri Nov 21, 2008 2:03 pm    Post subject: Re: hey
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Pillow Whisperer wrote:
well since computers are finite state machines then yes it'll have to repeat therefore periodic. furthermore since this 'random' number generator generates its value from a constant and with a formula its pseudo random, therefore by definition again its periodic it might be a long period but it is periodic. if you plug in the same seed you'll get the same output stream.


Indeed, it's pseudo-random, but that does not mean it is periodic. For instance, the sequence 0.1, 0.01, 0.001, ... it's definitely not random, but it's not periodic either.



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