  The actin cortex is a thin layer of actin filaments and myosin motors beneath
the outer membrane of animal cells. It determines the cells' mechanical
properties and forms important morphological structures. Physical descriptions
of the cortex as a contractile active gel suggest that these structures can
result from dynamic instabilities. However, in these analyses the cortex is
described as a two-dimensional layer. Here, we show that the dynamics of the
cortex is qualitatively different when gel fluxes in the direction
perpendicular to the membrane are taken into account. In particular, an
isotropic cortex is then stable for arbitrarily large active stresses. If
lateral contractility exceeds vertical contractility, the system can either
from protrusions with an apparently chaotic dynamics or a periodic static
pattern of protrusions.
