Coral reefs, vital ecosystems supporting diverse marine life, are primarily shaped by the clonal expansion of coral colonies. Although the principles of coral clonal growth, involving polyp division for spatial extension, are well-understood, numerical modelling efforts are notably scarce in the literature. In this article, we present a parsimonious numerical model based on the cloning of polyps, using five key parameters to simulate a range of coral shapes. The model is agent-based, where each polyp represents an individual. The colony’s surface expansion is dictated by the growth mode parameter (s), guiding the preferred growth direction. Varying s facilitates the emulation of diverse coral shapes, including massive, branching, cauliflower, columnar and tabular colonies. Additionally, we introduce a novel approach for self-regulatory branching, inspired by the intricate mesh-like canal system and internode regularity observed in Acropora species. Through a comprehensive sensitivity analysis, we demonstrate the robustness of our model, paving the way for future applications that incorporate environmental factors, such as light and water flow. Coral colonies are known for their high plasticity, and understanding how individual polyps interact with each other and their surroundings to create the reef structure has been a longstanding question in the field. This model offers a powerful framework for studying these interactions, enabling a future implementation of environmental factors and the possibility of identifying the key mechanisms influencing coral colonies’ morphogenesis.