The Image of the Dragon
MATLAB, 237 bytes

function A=r(A);n=size(A,1);p=@(a,v)permute(a,[v,3]);k=n/8;v=1:2;while k&gt;=1;b=mod(0:n-1,4*k)&lt;2*k;x=find(b);y=find(~b);c=[k+1:n,1:k;n-k+1:n,1:n-k];A=p(A,v);c=c(3-v,:);A(x,:,:)=A(x,c(1,:),:);A(y,:,:)=A(y,c(2,:),:);A=p(A,v);k=k/2;v=3-v;end


Took a little bit of guess work as I did not understand the procedure from the specs, but with the help of the image it worked.