This Demonstration shows that it is possible to emulate a register machine using an arithmetic system. From A New Kind of Science
, page 673: "The arithmetic system takes the value
that it obtains at each step, computes
, and then depending on the result applies to
one of the arithmetic operations specified by the rule [as shown in the rule icon]. The rule is set up so that if the value of
is written in the form
then the values of
on successive steps correspond respectively to the position of the register machine in its program, and to the values of the two registers."