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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E-Mail: (Ted Harding) <[EMAIL PROTECTED]>
Fax-to-email: +44 (0)870 094 0861
Date: 03-Sep-07 Time: 21:02:27
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