Final Activity Report Summary - THE COMPLEX SUN (Flares, Fractals and Forecasts: A study of turbulence and complexity in the solar atmosphere) Our life on Earth is entirely governed by the Sun, a main-sequence star which is midway through its own stellar life and whose variability profoundly affects the viability of our existence. Compared to other stars, the inherent stability of solar radiation is remarkable, controlling climate and sustaining the entire biosphere. This stability in a parent star is indeed a key component in searching for other life traces in the universe. However, our dependence on this stability poses us at the risk of any small changes. In our daily life, powerful solar storms, know as solar flares, impact Earth, disrupt telecommunications and navigation, threaten astronauts, damage satellites and disable electric power grids. As we continuously become more dependent on technology and as our presence extends beyond the confines of Earth to the Moon, Mars and beyond, it is essential to become more aware of this solar-terrestrial connection. The main objective of this proposal was to provide a new method for forecasting solar storms. The work carried out in this project led to many significant advances in our understanding of the Sun and our ability to predict solar storms. The project was based on the simple premise that solar flares are caused by sudden changes in the magnetic structure in active regions of the Sun. Active regions are areas in the Sun atmosphere with a strong magnetic field component. As the structure evolves it becomes more and more complex, storing up more and more energy, in a manner akin to winding up an elastic band. At some point in this evolution the energy must be released, resulting in an explosion known as a solar flare. In an ideal world we could view this magnetic structure directly; however this is not possible with current technology. We had instead to study the base of the structure and infer the complexity. This was like trying to forecast thunderstorms on earth by taking a picture of the clouds from a satellite and had previously been a very subjective subject, with teams of space weather forecasters looking at data and providing their personal opinion on what size of explosions and how many explosions could occur from certain areas on the Sun. The main result of this proposal was the automatic and objective provision of solar flare forecasts, creating a paradigm shift in this vital area of research. The method used to achieve this was found in the strange world of fractals and turbulence. Fractals, as well as their multi-fractal cousins are found throughout nature, describing a plethora of phenomena from snails to leaves, earthquakes and financial markets. They form a natural way of mathematically describing how complex something appears. Turbulence is a natural bedfellow to fractals and mathematically describes the flow and mixing of a fluid, from cups of tea to ocean currents. By combining these techniques and applying them to the Sun magnetic structure this project delivered a method of objectively describing the complex nature of the Sun. As expected, the more complex regions produced bigger flares.