  A model of a galactic disk is presented which extends the homogeneous one
zone models by incorporating propagation of material and energy in the disk.
For reasonable values of the parameters the homogeneous steady state is
unstable to the development of inhomogeneities, leading to the development of
spatial and temporal structure. At the linearized level a prediction for the
length and time scales of the patterns is found. These instabilities arise for
the same reason that pattern formation is seen in non-equilibrium chemical and
biological systems, which is that the positive and negative feedback effects
which govern the rates of the critical processes act over different distance
scales, as in Turing's reaction-diffusion models. This shows that patterns
would form in the disk even in the absence of gravitational effects, density
waves, rotation, shear and external perturbations. These nonlinear effects may
thus explain the spiral structure seen in the star forming regions of isolated
flocculent galaxies.
