  The Dirichlet-to-Neumann maps connect boundary values of harmonic functions.
It is an amazing fact that the square of the non-local Dirichlet-to-Neumann map
for the uniform conductivity 1 on the unit disc equals minus the local(!)
Laplace operator on the boundary circle. To establish a new connection between
discrete and continuous Dirichlet-to-Neumann maps and for the approximations I
construct a finite and an infinite graphs which Dirichlet-to-Neumann map have
the same property: \Lambda^2(1) = - d^2/d \theta^2. The construction gives a
new continued fraction identity. It is interesting to consider the geometric
and probabilistic (trajectories of the random walk) consequences of this
localizing identity unifying discrete and continuous equations for potentials.
