The generation of robust spatial patterns in biological systems remains a significant yet largely unresolved question. Beyond fundamental science, answering this question would lead to ground-breaking advances in the generation of synthetic tissues, organoids, and new biomaterials. Among various hypotheses, Alan Turing proposed a model to explain pattern formation based on reaction-diffusion networks. These networks are formed of components which travel throughout space and react with each other, leading to spatial periodic patterns. However, this model is far from biological complexity and requires fine-tuning of the parameters to produce such patterns. Furthermore, natural relevant phenomena such as non-linearities, large network sizes, growth and different boundary conditions are often not addressed in Turing models. In this mathematical study, our primary objective is to investigate the characteristics of Turing patterns when these realistic phenomena are introduced. We also aim to enhance the Turing robustness of an engineered reaction-diffusion circuit to guide experimental design. Our final aim is to replicate and scrutinise experimental results where patterning occurs in bacterial tissues with synthetic reaction-diffusion gene circuits. Using high-throughput analytical and numerical methods, we examine how predictions from linear stability analysis are affected by multi-stability, absorbing boundary conditions, and growth. Subsequently, by modelling the synthetic reaction-diffusion circuit, we identify strategies to increase Turing robustness. This enhanced robustness is then experimentally tested to observe periodic patterns. Furthermore, we model these experiments by integrating a colony growth model with a PDE solver for non-linear reaction-diffusion models. To align our mathematical model more closely with experimental data, we employ machine learning techniques for parameter estimation. Our model successfully replicates experimental results, shedding light on the path forward to engineer robust patterns for downstream biotechnology applications.