%Example script file to construct the Serpinski Gasket.

x=rand(2,1);
A=[0.5,0;0,0.5];
b1=[0;0];
b2=[0;0.5];
b3=[0.5;0];

numits=50000;
y=zeros(2,numits);

%We'll be throwing away the first few points...
for i=1:100
   k=ceil(3*rand);
   if k==1
      z=A*x+b1;
   elseif k==2
      z=A*x+b2;
   else
      z=A*x+b3;
   end
x=z;   
end

%Keep these for plotting
for i=1:numits
   k=ceil(3*rand);
   if k==1
      y(:,i)=A*x+b1;
   elseif k==2
      y(:,i)=A*x+b2;
   else
      y(:,i)=A*x+b3;
   end
x=y(:,i);   
end

%Now use the command:
%plot(y(1,:),y(2,:),'k.','Markersize',3);

%The Markersize command reduces the size of each
%point.  If you leave it off, the dots are kind of big.