Biofilms are dense clusters of bacteria joined together by strands of Extracellular Polymeric Substance (EPS) which strengthens the community against environmental hazards such as antibiotics, pesticides and water flow. Biofilms can be both detrimental, such as in healthcare, food production and infrastructure management, and beneficial, such as in wastewater treatment. Understanding biofilm formation and survival can lead to new insights into how to destroy detrimental biofilms and strengthen beneficial biofilms. Biofilm research has recently became interested in the role that surface topology and material play on early biofilm attachment and growth. However, experimental research in this field requires nano- to micro-scale control of the surface. Computational modelling then provides a powerful tool that experimental research can utilise to investigate biofilm adhesion and formation on more controlled surfaces. Agent-Based Modelling (ABM) is modelling the behaviours of individual, autonomous agents to create complex systems. This type of modelling is adept for microbial systems as bacteria cells are autonomous beings that influence and react to their immediate surroundings. This work showcases a three-dimensional ABM of planktonic bacteria attaching to complex surfaces and growing into a mature biofilm. This model is implemented as part of the BioDynaMo collaboration. This work includes an investigation into how the surface topology and material affect the bacteria physiology during attachment, mechanical interactions between bacteria and the morphology of the matured biofilm. This model can be used to gain insight into how surface structure can be manipulated to destroy or strengthen biofilms, as well as provide a foundation for future ABMs of biofilms to incorporate complex surfaces into their models.