Angular distribution and correlation measurements are an essential tool in nuclear structure experiments, especially when spectroscopic information on a specific nucleus is unknown. In most cases, the experimental determination of the spins and parities of the studied nuclear states, as well as the possible mixing between two electric/magnetic multipoles of a transition are determined using angular correlation measurements. In this work, the full effect of directional $\gamma $ correlations is simulated, by using the formal theory of angular correlations. The statistical tensor formalism is employed, enabling to perform a full simulation of the angular correlation effects in a cascade of an arbitrary number of $\gamma $ transitions. The present approach was coupled with the Monte Carlo code FIFRELIN, which can simulate the de-excitation of fission fragments or of excited nuclei after neutron capture. It provides a complete description of the spatial distributions of all the $\gamma $ rays in the cascade, that can be used for simulation purposes in various applications both in nuclear and particle physics. The potential for a novel approach in data analysis of angular correlation measurements is discussed thoroughly.