Example 2: n=2 bit AND, NAND, OR and NOR

• transformation matrices depend upon number of input bits
• there are 2^12<<406>>2=16 possible functions.
• Each function node has two $16\times 16\times 16$ transition matrices.

  functions are still symmetric $\Rightarrow$ only consider one of each pair

• average transition matrix is irreducible, stochastic, with non-zero diagonal elements but not symmetric.

  each function is NOT equally likely

  $\Rightarrow$ limiting distribution independent of the inputs not uniform.

• several non-zero eigenvalues, so while convergence is rapid it is not instantaneous