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.

• Ant Colonies: Individual ants follow simple rules, yet collectively they create complex, adaptive colony behaviors without centralized oversight.

• Bird Flocking: The coordinated movement of birds emerges from local interactions among individuals, creating dynamic, cohesive patterns.

• Ecosystems: Various species interact through food webs and symbiosis, resulting in ecosystem-level processes such as nutrient cycling and energy flow.

• The Human Brain: Neurons interact to give rise to consciousness and complex cognitive functions that are not evident from single neuronal behavior.

• Weather Systems: Local atmospheric interactions lead to the formation of organized patterns like hurricanes and jet streams, illustrating emergent dynamics.