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Dimitris,
it seems to me that in the
http://www.hypertextbook.com/chaos/43.shtml
where it starts to consider two points in a space X0 & X0+Dx0, I
guess that X0 would be the Close value.
Maybe I'm wrong (cause I really don't understand all of this
stuff)....
In any case I wait until you will be ready with it.
Thanks,
Hans
--- In amibroker@xxxxxxxxxxxxxxx, "DIMITRIS TSOKAKIS" <TSOKAKIS@xxxx>
wrote:
>
> Hans,
>
> I wrote to Petr Dostal to explain his calculations in
> http://www.iqnet.cz/dostal/CHA1.htm
> I have not received any reply yet.
> I know how to calculate the Lyapunov exponent for a function but I
do
> not see how to introduce Close values in this procedure.
> Dimitris
> --- In amibroker@xxxxxxxxxxxxxxx, "Hans" <hansib@xxxx> wrote:
> >
> > Dear Dimitris,
> > sorry to reply after a long time.
> >
> > It is surely intresting to proceed furter. If you remember I'm
> > intrested on determine Lyapunov Exponent, that is one of the last
> > chapters in chaos hypertextbook.
> >
> > Thanks a lot.
> >
> > Hans
> >
> > --- In amibroker@xxxxxxxxxxxxxxx, "DIMITRIS TSOKAKIS"
> <TSOKAKIS@xxxx>
> > wrote:
> > >
> > > Hans,
> > > Chapters
> > > http://www.hypertextbook.com/chaos/11.shtml
> > > and
> > > http://www.hypertextbook.com/chaos/12.shtml
> > > are already complete in details.
> > > Would it be interesting to post the AFL translation for this
> part ?
> > > [The AFL part is quite interesting...]
> > > Dimitris
> > > --- In amibroker@xxxxxxxxxxxxxxx, "Hans" <hansib@xxxx> wrote:
> > > >
> > > > Dimitris,
> > > > happy to see that you proceed with "Hypertext book,
chaos" ...
> > this
> > > > is a great work..
> > > >
> > > > Thanks,
> > > > Hans
> > > >
> > > > --- In amibroker@xxxxxxxxxxxxxxx, "DIMITRIS TSOKAKIS"
> > > <TSOKAKIS@xxxx>
> > > > wrote:
> > > > >
> > > > > AFL structure helps to reproduce the tables of
> > > > > http://www.hypertextbook.com/chaos/11.shtml
> > > > > The initial function is applied 1, 5, 10, 50, 100, 500 and
> 1000
> > > > times
> > > > > [!!]
> > > > > In an Indicator builder window paste the
> > > > >
> > > > > Title="The orbits of 9 seeds of the f(x)=x^2+1/4";
> > > > > function f1(x)
> > > > > {return x^2+1/4;}
> > > > > function f5(x)
> > > > > {return f1(f1(f1(f1(f1(x)))));}
> > > > > function f10(x)
> > > > > {return f5(f5(x));}
> > > > > function f50(x)
> > > > > {return f10(f10(f10(f10(f10(x)))));}
> > > > > function f100(x)
> > > > > {return f50(f50(x));}
> > > > > function f500(x)
> > > > > {return f100(f100(f100(f100(f100(x)))));}
> > > > > function f1000(x)
> > > > > {return f500(f500(x));}
> > > > > for(i=-1;i<=1;i=i+0.25)
> > > > > {
> > > > > Title=Title+"\ni="+
> > > > > WriteIf(i>=0," ","")+WriteVal(i,1.2)+
> > > > > WriteIf(f1(i)>0," "," ")+WriteVal(f1(i),1.3)+
> > > > > WriteIf(f5(i)>0," "," ")+WriteVal(f5(i),1.3)+
> > > > > WriteIf(f10(i)>0," "," ")+WriteVal(f10(i),1.3)+
> > > > > WriteIf(f50(i)>0," "," ")+WriteVal(f50(i),1.3)+
> > > > > WriteIf(f100(i)>0," "," ")+WriteVal(f100(i),1.3)+
> > > > > WriteIf(f500(i)>0," "," ")+WriteVal(f500(i),1.3)+
> > > > > WriteIf(f1000(i)>0," "," ")+WriteVal(f1000(i),1.3);
> > > > > }
> > > > >
> > > > > and, with a few changes, in a new IB window, paste the
> > > > >
> > > > > Title="The orbits of 15 seeds of the f(x)=x^2-3/4";
> > > > > function f1(x)
> > > > > {return x^2-3/4;}
> > > > > function f5(x)
> > > > > {return f1(f1(f1(f1(f1(x)))));}
> > > > > function f10(x)
> > > > > {return f5(f5(x));}
> > > > > function f50(x)
> > > > > {return f10(f10(f10(f10(f10(x)))));}
> > > > > function f100(x)
> > > > > {return f50(f50(x));}
> > > > > function f500(x)
> > > > > {return f100(f100(f100(f100(f100(x)))));}
> > > > > function f1000(x)
> > > > > {return f500(f500(x));}
> > > > > for(i=-1.75;i<2;i=i+0.25)
> > > > > {
> > > > > Title=Title+"\ni="+
> > > > > WriteIf(i>=0," ","")+WriteVal(i,1.2)+
> > > > > WriteIf(f1(i)>0," "," ")+WriteVal(f1(i),1.3)+
> > > > > WriteIf(f5(i)>0," "," ")+WriteVal(f5(i),1.3)+
> > > > > WriteIf(f10(i)>0," "," ")+WriteVal(f10(i),1.3)+
> > > > > WriteIf(f50(i)>0," "," ")+WriteVal(f50(i),1.3)+
> > > > > WriteIf(f100(i)>0," "," ")+WriteVal(f100(i),1.3)+
> > > > > WriteIf(f500(i)>0," "," ")+WriteVal(f500(i),1.3)+
> > > > > WriteIf(f1000(i)>0," "," ")+WriteVal(f1000(i),1.3);
> > > > > }
> > > > >
> > > > > Glenn Elert, the author of this interesting book,
> > writes :"...if
> > > > you
> > > > > wait long enough..."
> > > > > The AFL time is ~2sec and it is not bad at all !!
> > > > >
> > > > > Dimitris
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