  We put forward a powerful technique that allows generating
quasi-non-diffracting light beams with a variety of complex transverse shapes
and topologies. We show that, e.g., spiraling patterns, patterns featuring
curved or bent bright stripes, or patterns featuring arbitrary combinations of
harmonic, Bessel, Mathieu and parabolic beams occupying different domains in
the transverse plane can be produced. The quasi-non-diffracting patterns open
up a wealth of opportunities for the manipulation of matter and optical waves,
colloidal and living particles, with applications in biophysics, and quantum,
nonlinear and atom optics.
