  There are circular planar null geodesics at $r=3M$ around a Schwarzschild
black hole of mass $M$. These geodesics form a photon sphere. Null geodesics of
the Schwarzschild space-time which do not form the photon sphere are either
escape to null infinity or get captured by the black hole. Thus, from the
dynamical point of view, the photon sphere represents a smooth basin boundary
that separates the basins of escape and capture of the dynamical system
governing the null geodesics. Here we consider a Schwarzschild black hole
distorted by an external, static, and axisymmetric quadrupolar gravitational
field. We study null geodesics around such a black hole and show that the
photon sphere transforms into a fractal basin boundary that indicates chaotic
behavior of the null geodesics. We calculate the box-counting fractal dimension
of the basin boundary and the related uncertainty exponent, which depend on the
value of the quadrupole moment.
