From Ted.Harding at manchester.ac.uk  Mon Sep  3 22:02:31 2007
From: Ted.Harding at manchester.ac.uk ( (Ted Harding))
Date: Mon, 03 Sep 2007 21:02:31 +0100 (BST)
Subject: [Rd] When 1+2 != 3 (PR#9895)
In-Reply-To: <971536df0709031225g54c6cfj2df54f3400720f61@mail.gmail.com>
Message-ID: <XFMail.070903210231.Ted.Harding@manchester.ac.uk>

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.

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Date: 03-Sep-07                                       Time: 21:02:27
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[Rd] When 1+2 != 3 (PR#9895)
 (Ted Harding