  A new type of deformation for microscopic laser disks, the
\textit{equiangular spiral deformation} is proposed. First a short review of
the geometry of light paths in equiangular spirals in the language of real
two-dimensional geometric calculus is given. Second, the constituting equations
for \textit{closed paths} inside equiangular spirals are derived. Third, their
numerical solution is performed and found to yield two generic types of closed
light paths. \textit{Degenerate} closed paths that exist over large intervals
of the deformation parameter, and \textit{nondegenerate} closed paths which
only exist over relatively small deformation parameter intervals spanning less
than 1% of the nondegenerate intervals. Fourth, amongst the nondegenerate paths
a \textit{stable asymmetric bow-tie} shaped light trajectory was found.
