[R] dynamics of functions

[Hotz, T.]

Dear Tobias,

> I would like to study the dynamics of
> functions using R (instead of mathematica e.g.),
> i.e. the behavior of points under iteration
> of a function.
> So I tried (in vain) writing a function
> myfunction <- function(f,n,x){...}
> in order to compute f^{n}(x), f^{n}(x) being
> the function f composed with itself n-1 times.
> n is a natural number, and the argument x is
> the abscissa of the point I would like to
> `follow'.
 
What about the following function?

iterate<-function(f,n,x){
  if(n==0) return(x)
  y<-x
  for(i in 1:n)y<-f(y)
  y
}
iterate(sqrt,3,256)

Hope that helps.

Best wishes

Thomas


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Thomas Hotz
Research Associate in Medical Statistics
University of Leicester
United Kingdom

Department of Epidemiology and Public Health
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Leicester
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Tel +44 116 252-5410
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Division of Medicine for the Elderly
Department of Medicine
The Glenfield Hospital
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LE3 9QP
Tel +44 116 256-3643
Fax +44 116 232-2976