s=2, k=2 Turing machines

As illustrated on page 761, even extremely simple Turing machines can have behavior that depends in a somewhat complicated way on initial conditions. Thus, for example, with the rule

{{1, 0}  {1, 1, -1}, {1, 1}  {2, 1, 1}, {2, 0}  {1, 0, -1}, {2, 1}  {1,0,1}}

the head moves to the right whenever the initial condition consists of odd-length blocks of 1's separated by single 0's; otherwise it stays in a fixed region.