  In this paper, a complexity factor is devised for a non-static cylindrical
system in the framework of massive Brans-Dicke theory. The definition of
complexity is developed by taking into account the essential physical
characteristics (such as anisotropy, inhomogeneity, etc.) of the system. In
order to determine the complexity factor of the self-gravitating object, we
acquire structure scalars from the orthogonal splitting of the Riemann tensor.
Moreover, we discuss two patterns of evolution and choose the homologous mode
as the simplest pattern under the influence of massive scalar field. We derive
solutions in the absence as well as presence of heat dissipation for a specific
form of the scalar field. The factors that induce complexity in an initially
complexity-free system are also examined. It is concluded that the massive
scalar field as well as heat dissipation contribute to the complexity of the
celestial system. Thus, a dynamical cylinder is more complex as compared to its
static counterpart.
