Abstract
The principles of complexity science can be applied to systems with natural hazards, and also human social and economic systems. Disruptive, extreme events result from emergent properties of complex, nonequilibrium systems that consist of interdependent components whose interactions result in a competition between organized, interaction-dominated behavior and irregular or stochastic, fluctuation-dominated behavior. The use of fractal analysis allows insights into the development of such extreme events, and provides input and constraints for models. The main goal of this paper is to share and expand the scope of some of the fractal methods commonly used in complex systems studies. A proper appreciation of the strengths and limitations of fractal methods can improve the assessment and analysis of risks associated with systems that exhibit extreme events.