function out=ccat(z,cc)
%
% CCAT(z,cc). z is a complex number. cc is a (1,3)-color vecor.
% SELFDEMONSTRATING when called w/o parameters.
%
% Visualizing multiplication by a complex number by its
% effects on a cat's face. 
%
% Author:  Matthias  Kawski. http://math.asu.edu/~kawski
%          All rights reserved.
% Date:    September 2002.
% Updates: None yet.

% Define the vertices for the face.
%
clf
axis equal
format short
topx=[1 .98 .8  .83 .8  .77  .5 .25 0 -.25 -.5 -.8 -.8 -.98 -1];
topy=[0 .15 .7 1.15 1.03 1.15 .85 .95 1  .95 .85 1.2  .7  .15  0];
botx=-cos(pi*[1:10]/10);
boty=-sin(pi*[1:10]/10);
wiskx=[.2 1.3 .2 1.4 .2 1.4 .2 1.3 .2 .17 .13 .08 .03 0];
wisky=[ 0  .3  0  .1  0 -.1  0 -.3  0  .1 -.1 .1  -.1 0]-.2;
xeye=[0  .2  .3 .4 .43 .45 .43 .4 .37 .35 .37 .4  .5 .6 .5  .4 .3  .2  0];
yeye=[.5 .5 .43 .4 .42 .5  .58 .6 .58 .5  .42 .4  .43 .5 .57 .6 .57 .5 .5]-.2;
x=[topx,botx,wiskx,xeye,-xeye,fliplr(-wiskx)]';
y=[topy,boty,wisky,yeye, yeye,fliplr(wisky)]';
%
% Draw the original face.
%
pts = x + i*y;
%
fill(x,y,[0,.3,1])
plot(x,y,'m-')
%
%
% Apply the linear transformation. 
% If none is given, a random COMPLEX INTEGER is generated
%
if nargin < 1
   z = floor(5*rand(1,1)-2) + i * floor(5*rand(1,1)-2);
   end
newpts = z * pts;
%
% Overlay the transformed image.
%
xnew = real( newpts )
ynew = imag( newpts )
axis(5*[-1,1,-1,1])
hold on
if nargin < 2
   cc=rand(1,3)
   end
fill( xnew, ynew, cc)
%
% Replot the original face as it may have been covered up.
%
plot(x,y,'m-')
axis('equal')