Self-organization can be leveraged in software design by creating systems that operate without heavy centralized control. This can be achieved by employing modular, decentralized components that interact locally, adapting dynamically to runtime conditions. For instance, distributed computing frameworks and microservices architectures enable parts of a system to self-manage tasks like load balancing and fault tolerance. Additionally, incorporating mechanisms such as peer-to-peer communication and automatic recovery protocols allows the system to evolve and refine its performance over time, mirroring the adaptive, emergent properties found in natural complex systems.