
close all;
k = 2;
figure; hold on;

Z  = -1+2*rand(2,1000);
nz = repmat(sqrt(Z(1,:).^2 + Z(2,:).^2),2,1);
Z  = Z ./nz;
Z(2,:) = abs(Z(2,:));
z  = Z(1,:) + Z(2,:)*i;



for l = 1:20;

r = rand(1)

if r < .3;
M = [1 2; 0 1];
disp('translate')
elseif r < .6
M = [sqrt(k) 0 ; 0 1/sqrt(k)];
elseif r < 1
M = [0 i; i 0];
end


for j = 1:1000;
	Tz(j) = MobiusOnPoint(M,z(j));
end


	plot(real(z),imag(z),'r.')
	pause(.01)
	plot(real(Tz),imag(Tz),'.')

	z = Tz;
end
