% LOGMAPIT Iterations of the logistic map.

clear

r=4;
x=.2;
y=.2;
Nk=100;

X=[]; X=[X x];
Y=[]; Y=[Y y];
for k=1:Nk-1
   x=logistic(x,r); X=[X;x];
   y=logistic(y,r,'expanded'); Y=[Y;y];
end
h=plot(0:Nk-1,X,'r',0:Nk-1,Y,'g');
xlabel('$k$','Interpreter','LaTeX')
ylabel('$x_k$','Interpreter','LaTeX')
legend({'$x''=rx(1-x)$';'$x''=rx-rxx$'},'Interpreter','LaTeX')

K=(0:Nk-1)';
fid=fopen('data.txt','w');
fprintf(fid,'  k      r*x_k*(1-x_k)   r*x_k-r*x_k*x_k\n');
fprintf(fid,'%3i %16.8f  %16.8f\n',[K X Y]');
fclose(fid);

data=[K X Y];
save data dat