function chaos(N)

% The input variable represents the number of iterations
% made by the chaos game.

% Close all open figure windows. Delete this line if you
% don't want to do this.
close all;

% Create a new figure window, axes, and scale the axes.
fig1=figure;
ax1=axes;
axis([0,1,0,1])

% Place a message on the screen for the user.
txt1=text(.1,.5,'Select three points vertices with the mouse.');

% This command allows user to select vertices with the mouse.
[x,y]=ginput(3);
A=[x(1);y(1)];
B=[x(2);y(2)];
C=[x(3);y(3)];

% Delete the text message.
delete(txt1)

% Plot and label vertices selected by user.
text(A(1),A(2),'A')
text(B(1),B(2),'B')
text(C(1),C(2),'C')

% Place a text message on the screen for the user.
txt2=text(.1,.5,'Select initial point.');

% This command allows user to select initial point with the mouse.
x=ginput(1);
x=x(:);   % Makes x a column vector

% Delete the text message
delete(txt2);

% Main algorithm begins. The idea is this: Roll a 3-sided
% die with the letters A, B, and C on the faces. If A comes
% up, plot the midpoint of the segment joining the current
% point with the point A. Similar comments apply if B or C 
% are rolled.

% Reserve space for the N points (2 by 1 column vectors) 
% produced by the following iteration.
X=zeros(2,N);

% Main loop begins
for i=1:N

% The function rand produces a random number between 0 and 1.
	r=rand;  % Roll the die
	if r<1/3
		x=mid(x,A);  % A was rolled. Find midpoint of current point and A.
		X(:,i)=x;  % store the result for later plotting
	elseif r<2/3
		x=mid(x,B); % B was rolled. Find midpoint of current point and B.
		X(:,i)=x;  % store the result for later plotting
	else
		x=mid(x,C);  % C was rolled. Find midpoint of current point and C.
		X(:,i)=x;  % store the result for later plotting
	end  % end if
end  % end for loop

line(X(1,:),X(2,:),...
	'linestyle','none',...
   'marker','.',...
   'markersize',1);

function u = mid(x,vert)
% Find the midpoint of the segment joining current point and vert.
u=0.5*(x+vert);