  In this letter, we demonstrate the cyclically symmetric Thomas oscillators as
swarmalators and describe their possible collective dynamics. We achieve this
by sewing Kuromoto-type phase dynamics to particle dynamics represented by the
Thomas model. More precisely, this is equivalent to a non-linear particle
aggregation model with cyclic symmetry of coordinates and position-dependent
phase dynamics. The non-linear equations describe spatiotemporal patterns of
crystalline order and chaotic randomness at two extreme values of the system
parameter. This pattern is the outcome of non-linear self-organization, which
leads to a new class of turbulent flow - active turbulence. We claim that this
model can capture the dynamics of many naturally occurring microorganisms and
micro-swimmers. The model described in this letter can be a prototypical model
for understanding active systems and may shed light on the possibility of
making novel materials(active matter) with exciting biomedical and industrial
applications. The key to this is the understanding and control over the complex
dynamics of active systems, an out-of-equilibrium system, which is potentially
helpful in making functional materials, nano and micromachines.
