```sir=[0 3 1 0 3 0 2 1 3 2 1 0 2 1 3 1 0 2 1 0 2 3 2 3 0 2 1 0 3 0 2 1 3 1 0 2 1 0 2 1 0 2 3 1 0 3 0 2 1 0 2 1 0 2 1 0 3 0 2 1 0 2 1 0 2 1 0 3 2 3 1 0 2 1 0 3 1 0 2 3 1 3 2 1 0 2 3 0 2 1 0 2 1 0 2 1 0 2 3 3 0]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%  A one state model
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i=0:3
histo(i+1)=sum(sir==i);
end
histo
pist=histo/sum(histo);
h1(1)=-sum(pist.*log2(pist));

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%  A two state model
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
warning off
A=[0 0 1 0
3 0 3 0 ];
hh2=[];Aaa=[];
for machines=0:(2^8-1)
aa= bitget(machines,8:-1:1);
A = [aa(1:4); aa(5:8)];
s_crt=0;
for i=1:length(sir)
symbol=sir(i);
state(i)=s_crt;
%s_next=mod1(s_crt,symbol,A);
s_next=A(s_crt+1,symbol+1);
s_crt=s_next;
end
for i=0:1
for j=0:3
counti(i+1,j+1)=sum((state==i).*(sir==j));
end
end
for i=0:1
for j=0:3
counti(i+1,j+1)=sum((state==i).*(sir==j));
end
histo=counti(i+1,:);
ivalid=find(histo>0);
pist=histo/sum(histo);
h2(i+1)=-sum(pist(ivalid).*log2(pist(ivalid)));
end
pstate=sum(counti')/sum(sum(counti));
hh2=[hh2 sum(pstate.*h2)];
hh3(machines+1)=sum(pstate.*h2);
Aaa=[Aaa;A];
end

[val ind]=sort(hh3);
for i=1:length(ind)
machines=ind(i)-1;
aa= bitget(machines,8:-1:1);
A = [aa(1:4); aa(5:8)];
s_crt=0;
for i=1:length(sir)
symbol=sir(i);
state(i)=s_crt;
%s_next=mod1(s_crt,symbol,A);
s_next=A(s_crt+1,symbol+1);
s_crt=s_next;

if(s_next==3)
error3
end
end
for i=0:1
for j=0:3
counti(i+1,j+1)=sum((state==i).*(sir==j));
end
end
for i=0:1
for j=0:3
counti(i+1,j+1)=sum((state==i).*(sir==j));
end
histo=counti(i+1,:);
ivalid=find(histo>0);
pist=histo/sum(histo);
h2(i+1)=-sum(pist(ivalid).*log2(pist(ivalid)));
end
pstate=sum(counti')/sum(sum(counti));
hh2=[hh2 sum(pstate.*h2)];
clf
%hh=plot(0,5,'o','MarkerSize',20)
xx=1:500;
circ=[];elip=[];
circ(1,:)= 5*cos(2*pi*xx/500);
circ(2,:)= 5*sin(2*pi*xx/500);
elip(1,:)= 8*cos(2*pi*xx/520-pi/2+pi/15);
elip(2,:)= 20*sin(2*pi*xx/520-pi/2+pi/15);
elip=[elip(1,:) elip(1,1)+3*(0:0.1:1) elip(1,1)+1*(0:0.1:1)
elip(2,:) elip(2,1)+1*(0:0.1:1) elip(2,1)+3*(0:0.1:1)];

plot(0,-30,'.k',100,70,'k.')
hold on
hhp=plot(circ(1,:), 5+circ(2,:),'-b','LineWidth',3);
if(sum(A(1,:)==0)>0)
plot(elip(1,:), 30+elip(2,:))
end

plot(60+circ(1,:), 5+circ(2,:),'-b','LineWidth',3)
if(sum(A(2,:)==1)>0)
plot(60+elip(1,:), 30+elip(2,:),'-b')
end
if(sum(A(1,:)==1)>0)
plot( [60-9 9],[8 8],'b-',[60-9-3 60-9],[8+1.5 8],'b-',[60-9-3 60-9],[8-1.5 8],'b-')
end
if(sum(A(2,:)==0)>0)
plot( [60-9 9],[2 2],'b-',[9+3 9],[2+1.5 2],'b-',[9+3 9],[2-1.5 2],'b-')
end
for i=1:4
if( A(1,i)==0 )
hhpp=text(11,46-(i-1)*4,[6*16+i   '   n_' 6*16+i '=' num2str(counti(1,i))],'FontSize',14);
end
end

for i=1:4
if(A(1,i)==1)
text(21,25-(i-1)*4,[6*16+i   '   n_' 6*16+i '=' num2str(counti(1,i))],'FontSize',14)
end
end
for i=1:4
if(A(2,i)==0)
text(21,-5-(i-1)*4,[6*16+i   '   n_' 6*16+i '=' num2str(counti(2,i))],'FontSize',14)
end
end
for i=1:4
if(A(2,i)==1)
text(72,46-(i-1)*4,[6*16+i   '   n_' 6*16+i '=' num2str(counti(2,i))],'FontSize',14)
end
end
text(60,-20,['Entropy = ' num2str(sum(pstate.*h2))],'FontSize',14)
A
% pause
axis off
end
```
```sir =

Columns 1 through 13

0     3     1     0     3     0     2     1     3     2     1     0     2

Columns 14 through 26

1     3     1     0     2     1     0     2     3     2     3     0     2

Columns 27 through 39

1     0     3     0     2     1     3     1     0     2     1     0     2

Columns 40 through 52

1     0     2     3     1     0     3     0     2     1     0     2     1

Columns 53 through 65

0     2     1     0     3     0     2     1     0     2     1     0     2

Columns 66 through 78

1     0     3     2     3     1     0     2     1     0     3     1     0

Columns 79 through 91

2     3     1     3     2     1     0     2     3     0     2     1     0

Columns 92 through 101

2     1     0     2     1     0     2     3     3     0

histo =

30    26    26    19

A =

1     0     0     0
0     0     0     0

A =

1     0     0     0
0     1     0     0

A =

1     0     0     0
1     0     0     0

A =

1     0     0     0
1     1     0     0

A =

0     0     1     1
0     1     1     1

A =

0     1     1     1
0     1     1     1

A =

1     0     1     1
0     1     1     1

A =

1     1     1     1
0     1     1     1

A =

1     0     1     1
0     0     1     0

A =

1     0     1     1
1     0     1     0

A =

1     0     0     1
1     0     1     1

A =

1     0     1     1
1     0     1     1

A =

1     1     0     1
1     0     1     1

A =

1     1     1     1
1     0     1     1

A =

1     0     1     0
0     0     0     0

A =

1     0     1     0
1     0     0     0

A =

1     0     1     0
0     0     1     0

A =

1     0     1     0
1     0     1     0

A =

1     0     1     1
1     0     0     0

A =

1     0     0     1
1     0     0     0

A =

0     1     0     0
0     0     0     0

A =

0     1     0     0
0     0     1     0

A =

0     1     0     0
0     1     0     0

A =

0     1     0     0
0     1     1     0

A =

1     1     0     1
0     1     0     0

A =

1     0     0     1
1     0     1     0

A =

0     0     1     0
0     0     0     0

A =

0     0     1     0
0     0     1     0

A =

0     0     1     0
1     0     0     0

A =

0     0     1     0
1     0     1     0

A =

0     1     1     1
0     1     0     0

A =

0     1     0     1
0     1     0     0

A =

1     0     0     0
0     0     1     0

A =

1     0     0     0
1     0     1     0

A =

0     0     1     1
0     0     1     1

A =

0     1     1     1
0     0     1     1

A =

0     1     1     1
0     1     0     1

A =

0     1     1     1
0     1     1     0

A =

1     1     1     1
0     1     0     1

A =

1     1     0     0
1     0     0     0

A =

1     1     0     0
1     1     0     0

A =

0     0     1     0
0     0     0     1

A =

0     1     0     1
0     1     0     1

A =

0     1     0     1
0     1     1     0

A =

0     1     0     1
1     1     0     1

A =

0     1     1     1
1     1     0     1

A =

1     1     0     1
0     1     0     1

A =

1     0     0     1
0     0     1     0

A =

1     1     0     1
1     1     0     1

A =

1     1     1     1
1     1     0     1

A =

1     0     1     0
1     1     0     0

A =

0     0     1     0
0     0     1     1

A =

1     1     1     0
1     1     0     1

A =

1     0     0     1
1     0     0     1

A =

1     0     1     1
1     0     0     1

A =

1     1     0     1
0     1     1     0

A =

1     0     0     0
1     0     0     1

A =

0     1     0     1
0     1     1     1

A =

1     1     0     0
1     1     0     1

A =

1     1     0     1
0     1     1     1

A =

0     0     1     1
0     1     0     1

A =

1     0     0     1
0     0     0     0

A =

0     1     1     0
0     1     0     0

A =

0     1     1     0
0     1     1     0

A =

0     1     1     0
1     1     0     1

A =

0     1     1     0
0     1     1     1

A =

1     0     1     1
0     0     0     0

A =

0     1     0     0
1     1     0     1

A =

1     0     1     1
0     0     1     1

A =

1     1     1     1
0     0     1     1

A =

0     0     1     1
1     0     1     1

A =

0     1     1     1
1     0     1     1

A =

0     0     1     0
1     0     0     1

A =

1     0     0     0
1     1     0     1

A =

0     1     1     0
0     0     0     1

A =

0     0     1     0
1     0     1     1

A =

0     0     1     1
0     0     1     0

A =

0     1     1     0
0     0     1     1

A =

0     1     1     1
0     0     1     0

A =

0     0     1     0
0     1     1     1

A =

0     1     1     1
0     0     0     0

A =

1     0     1     0
0     1     0     0

A =

1     1     1     0
1     0     0     1

A =

1     0     1     0
1     0     1     1

A =

0     1     0     0
1     0     0     0

A =

0     1     0     0
1     1     0     0

A =

0     0     1     1
0     0     0     1

A =

1     1     1     1
0     1     1     0

A =

1     1     0     0
1     0     0     1

A =

1     1     1     1
1     0     0     0

A =

1     1     0     1
1     0     0     0

A =

1     0     1     1
1     1     0     0

A =

1     1     0     0
0     0     0     0

A =

1     1     0     0
0     1     0     0

A =

1     1     0     1
1     1     0     0

A =

1     0     0     1
1     1     0     0

A =

1     1     1     0
1     1     0     0

A =

1     1     1     1
0     1     0     0

A =

1     1     1     1
1     0     1     0

A =

1     0     1     0
1     0     0     1

A =

1     0     0     1
1     1     0     1

A =

1     0     1     1
1     1     0     1

A =

0     1     1     0
0     0     0     0

A =

0     1     1     0
0     0     1     0

A =

0     1     1     1
0     0     0     1

A =

0     0     1     0
0     1     0     0

A =

0     0     1     0
0     1     1     0

A =

0     0     1     1
0     1     0     0

A =

0     0     1     1
0     1     1     0

A =

0     1     0     0
0     1     0     1

A =

1     1     0     1
1     0     0     1

A =

1     1     1     1
1     0     0     1

A =

1     1     1     0
1     0     0     0

A =

0     0     1     1
0     0     0     0

A =

0     1     1     0
0     1     0     1

A =

1     0     1     1
0     1     0     1

A =

1     0     0     0
1     0     1     1

A =

1     1     1     1
1     1     0     0

A =

0     1     0     1
0     0     0     0

A =

1     1     1     0
1     0     1     1

A =

0     0     1     1
1     0     1     0

A =

1     1     0     1
1     0     1     0

A =

0     1     0     0
0     1     1     1

A =

0     1     1     1
1     0     1     0

A =

1     1     1     0
0     1     1     1

A =

1     0     1     0
1     1     0     1

A =

1     0     1     0
0     0     1     1

A =

0     0     1     0
0     1     0     1

A =

0     1     0     0
0     0     0     1

A =

0     1     0     0
1     0     0     1

A =

1     0     0     0
0     0     0     1

A =

0     1     0     1
1     0     0     0

A =

1     1     1     0
1     0     1     0

A =

0     1     0     1
0     0     1     0

A =

1     1     0     1
0     0     0     0

A =

1     0     0     0
0     1     0     1

A =

1     0     1     0
0     1     1     1

A =

0     1     0     1
1     1     0     0

A =

0     1     0     1
0     0     0     1

A =

1     1     1     0
0     0     1     1

A =

1     0     0     1
0     0     1     1

A =

1     1     0     0
0     1     0     1

A =

0     1     1     0
1     0     1     0

A =

1     1     0     0
1     0     1     1

A =

0     1     1     0
1     0     1     1

A =

0     1     0     1
1     0     0     1

A =

1     1     1     1
0     0     1     0

A =

0     1     0     0
0     0     1     1

A =

1     1     1     0
0     0     1     0

A =

1     0     1     1
0     1     0     0

A =

1     1     0     0
1     0     1     0

A =

1     1     0     0
0     1     1     0

A =

1     0     0     1
0     0     0     1

A =

1     0     0     0
0     0     1     1

A =

1     1     0     0
0     0     0     1

A =

0     1     0     1
0     0     1     1

A =

1     1     1     0
0     1     1     0

A =

1     1     0     1
0     0     0     1

A =

0     0     1     1
1     0     0     0

A =

1     0     0     1
0     1     0     0

A =

1     0     1     1
0     0     0     1

A =

1     0     1     0
0     0     0     1

A =

1     1     1     0
0     1     0     0

A =

1     1     0     1
0     0     1     0

A =

1     1     1     0
0     1     0     1

A =

1     1     0     0
0     1     1     1

A =

0     1     1     0
1     0     0     1

A =

1     0     1     0
0     1     0     1

A =

0     1     1     1
1     1     0     0

A =

0     0     1     1
1     0     0     1

A =

0     1     1     0
1     1     0     0

A =

1     0     1     1
0     1     1     0

A =

0     0     0     1
1     0     1     1

A =

1     0     0     0
1     1     1     0

A =

1     0     1     0
1     1     1     0

A =

1     0     1     1
1     1     1     0

A =

1     1     0     0
0     0     1     1

A =

0     0     0     1
1     0     1     0

A =

0     1     0     1
1     0     1     1

A =

0     0     0     1
0     1     1     1

A =

0     0     0     1
0     1     0     1

A =

0     0     0     1
0     1     0     0

A =

0     1     0     0
1     1     1     0

A =

0     0     0     1
1     0     0     0

A =

1     0     1     0
0     1     1     0

A =

0     0     0     1
1     0     0     1

A =

0     1     1     1
1     0     0     0

A =

0     1     0     0
1     0     1     0

A =

0     0     0     1
1     1     0     1

A =

1     0     0     1
0     1     0     1

A =

1     0     0     1
1     1     1     0

A =

0     0     1     0
1     1     1     0

A =

0     1     1     0
1     0     0     0

A =

0     1     1     1
1     0     0     1

A =

0     1     0     1
1     1     1     0

A =

0     1     0     1
1     0     1     0

A =

1     1     1     0
1     1     1     0

A =

0     0     0     1
0     1     1     0

A =

0     1     1     1
1     1     1     0

A =

0     1     1     0
1     1     1     0

A =

0     0     1     1
1     1     1     0

A =

0     0     0     1
0     0     0     1

A =

1     1     1     1
1     1     1     0

A =

1     0     0     0
0     1     1     0

A =

0     0     1     1
1     1     0     1

A =

0     0     0     1
0     0     0     0

A =

1     0     0     1
0     1     1     1

A =

1     1     1     0
0     0     0     0

A =

0     0     1     0
1     1     0     0

A =

1     1     0     0
1     1     1     0

A =

0     0     0     1
0     0     1     1

A =

0     1     0     0
1     0     1     1

A =

1     1     1     1
0     0     0     1

A =

0     0     0     1
1     1     1     1

A =

0     0     1     1
1     1     1     1

A =

0     1     0     1
1     1     1     1

A =

0     1     1     1
1     1     1     1

A =

0     0     0     1
1     1     0     0

A =

0     0     0     1
0     0     1     0

A =

1     0     0     0
1     1     1     1

A =

1     0     0     1
1     1     1     1

A =

1     0     1     0
1     1     1     1

A =

1     0     1     1
1     1     1     1

A =

1     1     0     0
1     1     1     1

A =

1     1     0     1
1     1     1     1

A =

1     1     1     0
1     1     1     1

A =

1     1     1     1
1     1     1     1

A =

1     1     0     1
1     1     1     0

A =

0     1     0     0
1     1     1     1

A =

0     1     1     0
1     1     1     1

A =

1     1     0     1
0     0     1     1

A =

0     0     1     0
1     1     1     1

A =

1     1     0     0
0     0     1     0

A =

1     1     1     0
0     0     0     1

A =

1     1     1     1
0     0     0     0

A =

1     0     0     1
0     1     1     0

A =

0     0     1     0
1     1     0     1

A =

1     0     0     0
0     1     1     1

A =

0     0     0     1
1     1     1     0

A =

0     0     1     1
1     1     0     0

A =

0     0     0     0
0     0     0     0

A =

0     0     0     0
0     0     0     1

A =

0     0     0     0
0     0     1     0

A =

0     0     0     0
0     0     1     1

A =

0     0     0     0
0     1     0     0

A =

0     0     0     0
0     1     0     1

A =

0     0     0     0
0     1     1     0

A =

0     0     0     0
0     1     1     1

A =

0     0     0     0
1     0     0     0

A =

0     0     0     0
1     0     0     1

A =

0     0     0     0
1     0     1     0

A =

0     0     0     0
1     0     1     1

A =

0     0     0     0
1     1     0     0

A =

0     0     0     0
1     1     0     1

A =

0     0     0     0
1     1     1     0

A =

0     0     0     0
1     1     1     1

```