Rule manipulation

HCELL uses overloaded operator $\star$ to indicate superposition of two rules. Consider, for example, elementary rule 18 and the identity rule 204. Their superposition is clearly rule 18, and HCELL allows you to find this easily:

CArule1d rule1(1,18);
CArule1d rule2(1,204);
CArule1d rule3;
rule3=rule1*rule2;
cout << Distance(rule1, rule3);

Another useful operator is $+$, which is used to compute a sum two rules. When $f$ and $g$ have the same radius, the ruletable of $f+g$ is a bitwise mod 2 sum of ruletables of $f$ and $g$. The following program, when executed, will print 72, which is the rule number of the sum of rules 18 and 90.

CArule1d f(1,18);
CArule1d g(1,90);
CArule1d h;
h=f+g;
cout << h.GetNumber()<<endl;

Arrays of rules can be constructed using the default constructor. The following program will create an array A containing all elementary rules, and then test which of these rules commute with rule 43.

CArule1d r(1,43);
CArule1d *A;
A=new CArule1d[256];
int i;
for(i=0; i<256; i++)
 {CArule1d s(1,i);  A[i]=s;}
 
for(i=0; i<256; i++) 
 if (Distance(A[i]*r,r*A[i])==0) 
  cout << "Rule "<<i<< " commutes with rule 43"<<endl;