%Script file to show A_1, A_2, A_3 (Intervals that leave I=[-2,2])
% after 1 iteration, 2 iterations, 3 iterations.  In these pictures, we
% will set c=-3
c=-2.3;
x=linspace(-3,3,500);
b1=linspace(-2,2,500);
b2=ones(size(b1));
y1=b1.^2+c;
plot(x,x,'k',b1,-2*b2,'b',b1,2*b2,'b',2*b2,b1,'b',-2*b2,b1,'b',b1,y1,'r');

x1=b1.^2+c;
idx1=find(abs(x1)>2);
hold on
plot(b1(idx1),b1(idx1),'g*');
hold off

pause
b2=b1;
b2(idx1)=[];
x1=b2.^2+c;
x1=x1.^2+c;
idx1=find(abs(x1)>2);
hold on
plot(b2(idx1),b2(idx1),'m*');
hold off

pause
b3=b2;
b3(idx1)=[];
x1=b3.^2+c;
x1=x1.^2+c;
x1=x1.^2+c;
idx1=find(abs(x1)>2);
hold on
plot(b3(idx1),b3(idx1),'b*');
hold off

pause
b4=b3;
b4(idx1)=[];
x1=b4.^2+c;
x1=x1.^2+c;
x1=x1.^2+c;
x1=x1.^2+c;
idx1=find(abs(x1)>2);
hold on
plot(b4(idx1),b4(idx1),'r.');
hold off