Heat dissipation is a critical issue for various engineering applications such as electronic devices, turbine blades and batteries. Existing heat sink structures contained inherent shortages in geometric flexibility which prevented further development of heat dissipation technologies. This study proposed a self-organized design method for heat sinks inspired by Turing Patterns (TP) in nature morphogenesis. The biomimetic structures were parametrically controlled with the aid of reaction-diffusion equations in terms of feature size, feature density, structural morphology and structural orientation. The metallic selective laser melting (SLM) technology was adopted to fabricate the three-dimensional (3-D) heat sinks. Experimental and numerical evaluations were conducted to compare TP structures with traditional pin-fin (PF) arrays baselines. Results showed substantial advantages of the TP structures in regulating flow field and enhancing height-wise fluid mixing. The thermal performance factor (TPF) of TP structures is approximately 45 % higher than traditional PF structures with similar feature sizes. The globally averaged magnitude of height-wise velocities of TP structure is around 2.4 times larger than that of PF structures due to the existence of the threshold-like and bridge-like structures. With the aid of three-dimensional structures, full utilization of the coolant was achieved to further increase the heat transfer intensity, while a high synergic level was formed within the flow field and temperature field to reduce the pressure drop. The design method proposed in this study demonstrated strong capability in tuning three-dimensional flow field and is expected to provide new insights to the heat transfer area that faces nonuniform thermal conditions and inhomogeneous flow conditions.