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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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