Solar active regions are the source of many energetic and geo-effective events such as solar flares and coronal mass ejections (CMEs). Understanding how these complex source regions evolve and produce these events is of fundamental importance, not only to solar physics, but also to the demands of space weather forecasting. As we are becoming more aware of the local inhomogeneity in the magnetic field configuration of active region, I propose to investigate the physical properties of complexity using new multifractal and multiscale algorithms. These will ultimately provide precise and accurate estimates of the fractality, turbulence energy spectrum, neutral line and flux emergence components of active regions. The correlation of these parameters with solar activity will provide a flare-prediction tool based on a causal understanding of the Sun. This represents a non-phenomenological approach to describing and understanding active region evolution and the conditions that result in energy release. I will further develop these tools in a general sense to study any self-organised, turbulent system. This work is vital to the European community as evidenced by the recent ESA Space Weather Working Team and the Pathfinder Initiative to study complex systems. I also envisage career training in developing my supervisory, grant-writing, interdisciplinary, and conference-organising skills, allowing me to extend and diversify my knowledge to a level of professional maturity whereby I can successfully continue research in a tenure track academic post at a European research institute.