function logistic(A,B)
%logistic.m plots images of the longterm behaviar of iterates generated by
%
%     g(x)=a*x*(1-x)
%
%It turns out that as a is varied on 0<=A<a<B<=4, the long term behavior of
%this iteration forms an interesting and beautiful pattern.  Enjoy!

rp=4000;    %resolution of points between 0 and 1
ra=4000;    %resolution of values of a
a=linspace(A,B,ra);  %have a go from A to B, where 0<=A<B<=4
map=zeros(100,ra);
for m=1:ra  %cycle through values of a
    x=0.1;
    for k=1:1000    %flush out transients
        x=a(m)*x*(1-x);
    end
    for k=1:100
        x=a(m)*x*(1-x);
        map(k,m)=x;
    end
end
a=ones(100,1)*a;
fig=figure; 
set(fig,'color',[1 1 1])
L=line(a(:),map(:));
set(L,'markersize',1,...
      'marker','.',...
      'linestyle','none')