Cellular Nonlinear Networks: State of the Art and Applications - Systematic Design for Emergence in Cellular Nonlinear Networks - page 11

% 1 function implementing the cell. It also contains the gene
function y=gca_u_cell(u1,u2,u3,u4,u5,u6,u7,u8,u9)
Z=[0.9, 0.3, 0.3, 2, 0.3, .6, 0.5]; B=0.5*[1.1 1 1 1 0 1 1 1 1];
sigm=B(1)*u1+B(2)*u2+B(3)*u3+B(4)*u4+B(5)*u5+B(6)*u6+B(7)*u7+B(8)*u8+B(9)*u9;
w=Z(1)+Z(2)*u5+Z(3)*sigm-abs(Z(4)+Z(5)*u5+Z(6)*sigm)+Z(7)*abs(sigm);
y=w;

% 2 main program running the GCA for a given number of steps
function y=gca_u( steps )
% e.g. steps=100 (runs the GCA for 100 iterations)
x0=-ones(199,199);
x0(100,100)=1;
[m n]=size(x0);
i=1:m; j=1:n;
left_j=[n,1:n-1];
right_j=[2:n,1];
up_i=[m,1:m-1];
low_i=[2:m,1]; y=x0;
for s=1:steps
u9=y(up_i,left_j); u8=y(up_i,j); u7=y(up_i,right_j);
u6=y(i,left_j); u5=y; u4=y(i,right_j);
u3=y(low_i,left_j); u2=y(low_i,j); u1=y(low_i,right_j);
y=gca_u_cell(u1,u2,u3,u4,u5,u6,u7,u8,u9);
end
set(1, 'Position' ,[291 180 505 540]);
image(20*y+32);
axis image;
colormap gray

any part of a real image. The extreme case is when one of the resulting images has
to be compressed. Then since it is the result of running the above programs (acting
as decompressing engines) an extremely high compression rate is achieved. As-
suming that each of the 17 parameters as well as the pixels from the image are rep-

resented with 8 bits, for a 200 × 200 pixels image a compression rate of
×

200 200

can be obtained. This is a rate far beyond any of the actual com-

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17

pression scheme. A challenging task remains to find families of cellular systems

capable to approximate quite well larger blocks from real natural images. The
larger the blocks the higher the compression rate, which in the limits can reach
values as high as thousands or tens of thousands. The advantage of a very simple
decompression scheme (the above programs) shall be exploited in making

compressed documents such as journals, books or compact encyclopedias.