So:

• The order of operations can be variable dependent on the number

• The notation method effects pattern

• The pattern can change if primes are always used

• Etc.

How many ways can we change the rules? How many rules are there?

It is amazing just how much variation in pattern can be achieved just by changing and/or adding/subtracting rules.

There is the general rule of rules:

The fewer the rules, the less variable the pattern, and the inverse, the more rules the more variable the pattern.

• Sorry for the late edit, but, I would also add that the fewer the rules the less adaptable as well...