Re: [Rd] When 1+2 != 3 (PR#9895)

From: Ted Harding <Ted.Harding_at_manchester.ac.uk>
Date: Mon, 03 Sep 2007 21:02:31 +0100 (BST)


On 03-Sep-07 19:25:58, Gabor Grothendieck wrote:
> Not sure if this counts but using the Ryacas package

Gabor, I'm afraid it doesn't count! (Though I didn't exclude it explicitly). I'm not interested in the behaviour of the sequence with denominator = 7 particularly. The system is in fact an example of simulating chaotic systems on a computer.

For instance, one of the classic illustrations is

  next x = 2*x*(1-x)

for any real x. The question is, how does a finite-length binary representation behave?

Petr Savicky [privately] sent me a similar example: Starting with r/K:

nextr <- function(r){ifelse(r<=K/2, 2*r, 2*(K-r))}

  "For K = 7 and r = 3, this yields r = 3, 6, 2, 4, 6, ...    Dividing this by K=7, one gets the correct period with    approximately correct numbers."

Best wishes,
Ted.



E-Mail: (Ted Harding) <Ted.Harding_at_manchester.ac.uk> Fax-to-email: +44 (0)870 094 0861
Date: 03-Sep-07                                       Time: 21:02:27
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