Other conserved quantities

The conserved quantities discussed so far can all be thought of as taking values assigned to blocks of different kinds in a given state and then just adding them up as ordinary numbers. But one can also imagine using other operations to combine such values. Addition modulo n can be handled by inserting Modulusn in NullSpace in the previous note. And doing this shows for example that rule 150 conserves the total number of black cells modulo 2. But in general not many additional conserved quantities are found in this way. One can also consider combining values of blocks by the multiplication operation in a group—and seeing whether the conjugacy class of the result is conserved.