  We demonstrate that the single-channel transmission in the resonance
tunneling regime exhibits self-similarity as a function of the nanowire length
and the energy of incident electrons. The self-similarity is used to design the
nonlinear transformation of the nanowire length and energy which, on the basis
of known values of transmission for a certain region on the energy-length
plane, yields transmissions for other regions on this plane. Test calculations
with a one-dimensional tight-binding model illustrate the described
transformations. Density function theory based transport calculations of Na
atomic wires confirm the existence of the self-similarity in the transmission.
