  We show that the pattern of tunnelling rates can display a vivid and regular
pattern when the classical dynamics is of mixed chaotic/regular type. We
consider the situation in which the dominant tunnelling route connects to a
stable periodic orbit and this orbit is surrounded by a regular island which
supports a number of quantum states. We derive an explicit semiclassical
expression for the positions and tunnelling rates of these states by use of a
complexified trace formula.
