%Script file to run Experiment 3.6, The Computer May Lie.
%  We'll take 10 different initial seeds for each of
%  three functions:  F(x)=x^2-2, G(x)=x^2+c for c<-2
%  (Here, we'll take c=-3)
%  and the doubling function D(x)  (double1).

xF=4*rand(1,10)-2;  %10 random numbers between -2 and 2
xG=rand(1,10);
xD=rand(1,10);

%Initialize the orbits:
yF(1,:)=xF;
yG(1,:)=xG;
yD(1,:)=xD;

%Get the next 100 points on the orbit:
for i=2:100
   yF(i,:)=xF.^2-2;
   xF=yF(i,:);
   yG(i,:)=xG.^2-3;
   xG=yG(i,:);
   yD(i,:)=double1(xD);
   xD=yD(i,:);
end

%Another check:  Try a rational orbit.  1/9 is on a 6-cycle
%for double1
x0=1/9;
for i=1:100
   y(i)=double1(x0);
   x0=y(i);
end
format long
y'