%eye of Sauron script

%so it turns out that the 1D FT of a ring looks remarkebly like the Eye of
%Sauron

%make a ring
rWidth = 512;
ring = zeros(rWidth);
for i=1:rWidth
    x = i - rWidth/2;
    for j=1:rWidth
        y = j - rWidth/2;
        
        if(x*x + y*y < rWidth*rWidth/4)
           ring(j,i) = ring(j,i) + 1; 
        end
        if(x*x + y*y < 0.6*rWidth*rWidth/4)
           ring(j,i) = ring(j,i) - 1; 
        end
    end
end

%take the FT along the rows
for j=1:rWidth
   FTring(j,:) = abs(fftshift(fft(ring(j,:)))); 
end

ring(1,1) = 1.5;%so the ring will be colored gold
figure;imagesc(ring,[0 1.5]);colormap('hot');axis off;axis equal;
figure;imagesc(FTring,[0 30]);colormap('hot');axis off;axis equal;