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If we use strict math terms, f[g(x)] is a composite function.
[2-11 Definition in Tom Apostol, Mathematical Analysis, Addison-
Wesley. I did not use it to avoid confusion with the AFL composites
and the AddToComposite() function]
The function g is applied on x and then the function f is applied on g
(x).
If f=g then f[g(x)] becomes f[f(x)].
Example:
If f(x)=sinx and g(x)=cosx, then we speak for
f[g(x)]=sin(cosx)
and
f[f(x)]=sin(sinx)
A power form is used in printed formulas. Since it is not easy to use
exponents here, I decided to use f2(x) for f(f(x)) and f5(x) for
f(f(f(f(f(x))))).
According to the http://www.hypertextbook.com/chaos/11.shtml we may
speak for iterated mapping, the symbol fn(x) will represent the "nth
iterate" of x and, finally, the series
x, f(x), f2(x), f3(x),...,fn(x),...
will form the "orbit" of the function f. The initial value x is
called the "seed" of the orbit.
I hope it is more clear now.
I also hope the math educated will excuse the naive style of my title.
Dimitris
--- In amibroker@xxxxxxxxxxxxxxx, "dingo" <dingo@xxxx> wrote:
> no - recursive is when you call the function f1 from within the
function f1.
> all of these calls to f1 were from outside the function - in f10.
>
> d
>
>
> _____
>
> From: mmqp [mailto:mmqp@x...]
> Sent: Tuesday, October 05, 2004 12:14 PM
> To: amibroker@xxxxxxxxxxxxxxx
> Subject: [amibroker] Re: The function of a function of a function
>
>
>
> Is this equivalent to recursive function call?
>
> --- In amibroker@xxxxxxxxxxxxxxx, "DIMITRIS TSOKAKIS"
> <TSOKAKIS@xxxx> wrote:
> >
> > The function f1 returns the sin of x.
> > The function f10 returns the sin of the sin of the sin...10
> times...
> > of x.
> > The f10(f10(f10(x))) applies the sin transformation 1000 times
> over
> > the result of sin(x).
> > The respective AFL would be
> >
> > //The function of a function
> > function f1(x)
> > {
> > return sin(x);
> > }
> > function f10(x)
> > {
> > return f1(f1(f1(f1(f1(f1(f1(f1(f1(f1(x))))))))));
> > }
> > x=2*3.14*10*Cum(1);
> > Plot(f1(x),"f1",colorBlack,1);
> > Plot(f10(x),"f10",colorWhite,1);
> > Plot(f10(f10(f10(x))),"f1000",colorRed,1);
> >
> > Dimitris
>
>
>
>
>
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