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mazing82 Just Arrived
Joined: 24 Jan 2008 Posts: 0
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Posted: 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.
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Gingerdave Just Arrived
Joined: 14 Aug 2006 Posts: 0 Location: Leeds
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Posted: 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?
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mazing82 Just Arrived
Joined: 24 Jan 2008 Posts: 0
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Posted: 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? |
Probably not . 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?)
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AdamV SF Mod
Joined: 06 Oct 2004 Posts: 24 Location: Leeds, UK
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Posted: 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.
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Pillow Whisperer Just Arrived
Joined: 18 Feb 2008 Posts: 0
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Posted: 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.
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mazing82 Just Arrived
Joined: 24 Jan 2008 Posts: 0
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Posted: 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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