  In this paper we construct a large class of non-trivial (non-radial)
self-similar solutions of the generalized surface quasi-geostrophic equation
(gSQG). To the best of our knowledge, this is the first rigorous construction
of any self-similar solution for these equations. The solutions are of spiral
type, locally integrable, and may have mixed sign. Moreover, they bear some
resemblance with the finite time singularity scenario numerically proposed by
Scott and Dritschel [R. K. Scott, D. G. Dritschel., Journal of Fluid Mechanics,
863:R2, 2019] in the SQG patch setting.
