I liked the explanation on the linked "Rewrite systems" page of the connection to "Fractran", an esoteric language devised by John Conway. A program in this language consists of simply an ordered list of fractional numbers that "act on" a single positive integer "accumulator" in the following way: if dividing the accumulator by the current fraction's denominator would leave an integer result, do so and then multiply by the numerator, otherwise do nothing. Either way, move to the next fraction, or back to the top if you are at the end. That page shows programs for performing simple arithmetic, FizzBuzz, etc.

Interpreting all numbers involved as multisets of their prime factors leads to the representation in TFA.

For anyone using ISO paper the above zine will not work since it's done for US letter paper.