This GitHub repository serves as the culmination of my final project for the Simulation Methods subject in my master's program. It focuses on investigating the Degenerate Optical Parametric Oscillator (DOPO) and studying pattern formation in its output beams around the threshold. Quantum fluctuations are taken into account by a noise term in the equations. The project tackles a system of two coupled partial stochastic nonlinear differential equations in complex variables, addressing it through the centered-space Heun method. The repository includes code and resources essential for reproducing our study's findings, enabling exploration of pattern evolution with changes in system size.