%Animation showing A_4->A_3->A_2, etc.
%
%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);
d1=ones(size(b1));
y1=b1.^2+c;
plot(x,x,'k',b1,-2*d1,'b',b1,2*d1,'b',2*d1,b1,'b',-2*d1,b1,'b',b1,y1,'r');

x1=b1.^2+c;
idx1=find(abs(x1)>2);

b2=b1;
b2(idx1)=[];
x1=b2.^2+c;
x1=x1.^2+c;
idx1=find(abs(x1)>2);

b3=b2;
b3(idx1)=[];
x1=b3.^2+c;
x1=x1.^2+c;
x1=x1.^2+c;
idx1=find(abs(x1)>2);

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);
b5=b4(idx1);

%
% Animation starts here
%

xx=b5;
t=linspace(0,1,50);
yy=xx.^2+c;
for j=1:length(t)
    temp=(1-t(j))*xx+t(j)*yy;
    plot(xx,temp,'r*',x,x,'k',b1,-2*d1,'b',b1,2*d1,'b',2*d1,b1,'b',-2*d1,b1,'b',b1,y1,'r');
    M(j)=getframe;
end
pause
jj=j;
t=linspace(0,1,50);
for j=1:length(t)
    temp=(1-t(j))*xx+t(j)*yy;
    plot(temp,yy,'r*',x,x,'k',b1,-2*d1,'b',b1,2*d1,'b',2*d1,b1,'b',-2*d1,b1,'b',b1,y1,'r');
    M(jj+j)=getframe;
end
jj=j+jj;
pause
xx=yy;
t=linspace(0,1,50);
yy=xx.^2+c;
for j=1:length(t)
    temp=(1-t(j))*xx+t(j)*yy;
    plot(xx,temp,'r*',x,x,'k',b1,-2*d1,'b',b1,2*d1,'b',2*d1,b1,'b',-2*d1,b1,'b',b1,y1,'r');
    M(jj+j)=getframe;
end

jj=j+jj;
pause

t=linspace(0,1,50);
for j=1:length(t)
    temp=(1-t(j))*xx+t(j)*yy;
    plot(temp,yy,'r*',x,x,'k',b1,-2*d1,'b',b1,2*d1,'b',2*d1,b1,'b',-2*d1,b1,'b',b1,y1,'r');
    M(jj+j)=getframe;
end
jj=jj+j;
pause
xx=yy;
t=linspace(0,1,50);
yy=xx.^2+c;
for j=1:length(t)
    temp=(1-t(j))*xx+t(j)*yy;
    plot(xx,temp,'r*',x,x,'k',b1,-2*d1,'b',b1,2*d1,'b',2*d1,b1,'b',-2*d1,b1,'b',b1,y1,'r');
    M(jj+j)=getframe;
end
jj=j+jj;
pause

t=linspace(0,1,50);
for j=1:length(t)
    temp=(1-t(j))*xx+t(j)*yy;
    plot(temp,yy,'r*',x,x,'k',b1,-2*d1,'b',b1,2*d1,'b',2*d1,b1,'b',-2*d1,b1,'b',b1,y1,'r');
    M(jj+j)=getframe;
end
jj=jj+j;
pause
xx=yy;
t=linspace(0,1,50);
yy=xx.^2+c;
for j=1:length(t)
    temp=(1-t(j))*xx+t(j)*yy;
    plot(xx,temp,'r*',x,x,'k',b1,-2*d1,'b',b1,2*d1,'b',2*d1,b1,'b',-2*d1,b1,'b',b1,y1,'r');
    M(jj+j)=getframe;
end
jj=jj+j;
pause

t=linspace(0,1,50);
for j=1:length(t)
    temp=(1-t(j))*xx+t(j)*yy;
    plot(temp,yy,'r*',x,x,'k',b1,-2*d1,'b',b1,2*d1,'b',2*d1,b1,'b',-2*d1,b1,'b',b1,y1,'r');
    M(jj+j)=getframe;
end