1. Emergence: Complex systems exhibit properties that arise from interactions among components, which cannot be deduced simply by examining individual parts.

2. Nonlinearity: Small changes can have disproportionate effects due to feedback loops and intricate interdependencies.

3. Self-Organization: Systems often develop order spontaneously through internal dynamics without centralized control.

4. Adaptation and Co-evolution: Components and systems adjust in response to environmental changes, highlighting a process of mutual influence and evolution.

5. Interdisciplinary Perspective: Complexity theory transcends traditional disciplinary boundaries, encouraging holistic and integrative approaches to understanding systems.

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.