  In this article, we have studied a cylindrically symmetric self-gravitating
dynamical object via complexity factor which is obtained through orthogonal
splitting of Reimann tensor in $f(R,T)$ theory of gravity. Our study is based
on the definition of complexity for dynamical sources, proposed by Herrera
\cite{12b}. We actually want to analyze the behavior of complexity factor for
cylindrically symmetric dynamical source in modified theory. For this, we
define the scalar functions through orthogonal splitting of Reimann tensor in
$f(R,T)$ gravity and work out structure scalars for cylindrical geometry. We
evaluated the complexity of the structure and also analyzed the complexity of
the evolutionary patterns of the system under consideration. In order to
present simplest mode of evolution, we explored homologous condition and
homogeneous expansion condition in $f(R,T)$ gravity and discussed dynamics and
kinematics in the background of a generic viable non-minimally coupled
$f(R,T)=\alpha_1 R^m T^n +\alpha_2 T(1+\alpha_3 T^p R^q)$ model. In order to
make a comprehensive analysis, we considered three different cases
(representing both minimal and non-minimal coupling) of the model under
consideration and found that complexity of a system is increased in the
presence of higher order curvature terms, even in the simplest modes of
evolution. However, higher order trace terms affects the complexity of the
system but they are not crucial for simplest modes of evolution in the case of
minimal coupling. The stability of vanishing of complexity factor has also been
discussed.

General Relativity and Quantum Cosmology