The Collatz sequence starts with a positive integer
is even, then divide it by 2. If
is odd, then multiply it by 3 and add 1. The sequence is the result of iterating this process.
We can modify this sequence by deleting all the
numbers in the sequence by noticing that if
is odd, then
is even and the next number in the modified sequence should be
Liesbeth De Mol described a set of rules for a tag system that computes this slightly modified view of the Collatz sequence. An
-tag system is a machine that starts with a finite string of symbols, removes the first
of them, and then appends some other string to the end, according to the value of the first symbol of the string at each click of the clock.
At each time step, the machine here removes two symbols from the beginning and then, depending on the first symbol, appends a string according to the rules:
The colors pink, red, and yellow stand for
of the sequence (including the initial condition) is encoded as a string of
" symbols (or pink cells).