Despite the increasing interest in mycelium-based materials, understanding of fungal growth mechanics remains limited, especially regarding the physical forces such as turgor pressure and cell wall elasticity that drive hyphal expansion and network formation. Existing models often neglect these crucial aspects, hindering predictions of structural development in engineered mycelial systems. This research introduces a novel twodimensional, lattice-free computational model to simulate fungal mycelium growth, addressing limitations of lattice-based frameworks by allowing unrestricted hyphal expansion. The model integrates fundamental growth behaviors, including hyphal tip extension, apical and lateral branching, and positive and passive anastomosis. A probability-based function for tip placement, a corrected gamma cumulative distribution for tip extension rates, and a Gaussian inverse cumulative distribution for branching angles were employed. Simulations validated the model\\\'s ability to replicate diverse mycelial structures under varying growth strategies. Results showed that the model could generate intricate network topologies, reflecting the stochastic yet structured nature of fungal growth. Apical branching facilitated directional exploration, while lateral branching enhanced local network densification. Additionally, the model differentiated passive and positive anastomosis, effectively representing hyphal fusion and improved connectivity. It also demonstrated adaptive responses, such as navigating around obstacles. This approach advances fungal growth modeling with applications in material science, structural biomimetics, and engineered mycelium systems.

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