  This paper is devoted to the formulation of a complexity factor for dynamical
anisotropic sphere in the framework of $f(G,T)$ gravity, where $G$ is the
Gauss-Bonnet invariant and $T$ is the trace of energy-momentum tensor.
Inhomogeneous energy density, anisotropic pressure, heat dissipation and
modified terms create complexity within the self-gravitating system. We
evaluate the structure scalars by orthogonal splitting of the Riemann tensor to
evaluate a complexity factor which incorporates all the fundamental properties
of the system. Moreover, we examine the dynamics of the sphere by assuming
homologous mode as the simplest pattern of evolution. We also discuss
dissipative as well as non-dissipative scenarios corresponding to homologous
and complexity free conditions. Finally, we establish a criterion under which
the complexity free condition remains stable throughout the process of
evolution. We conclude that the presence of dark source terms of $f(G,T)$
gravity increase the system's complexity.
