  A difference analogue of the logistic equation, which preserves
integrability, is derived from Hirota's bilinear difference equation. The
integrability of the map is shown to result from the large symmetry associated
with the B\"acklund transformation of the KP hierarchy. We introduce a scheme
which interpolates between this map and the standard logistic map and enables
us to study integrable and nonintegrable systems on an equal basis. In
particular we study the behavior of Julia set at the point where the
nonintegrable map passes to the integrable map.
