Many of the great challenges of our age are ultimately challenges of complexity. Anthropogenic climate change threatens to destabilise the ecological connections that span the biosphere as well as the delicate geopolitical functioning of our globalised civilisation. It seems a push towards developing an understanding of the seemingly unpredictable behaviour of such highly connected complex systems could hardly come at a more critical time. It is the spontaneous emergence of macroscopic phenomena from these complex systems that forms the core of this thesis. Complexity generally results from the multiplicity of system components and is ubiquitous in natural systems. Developing an understanding of how macroscopic structures emerge from microscopic dynamics is central to furthering our understanding of complex systems. However, there exists a gulf between our capacity to formulate complex models and our ability to predict their behaviour. Additionally, large and complicated models require vast computational resources and will remain out of reach for many years, even when considering Moore's law, the observation that the increase of computing power is approximately exponential with time. This thesis contributes to building the bridge between model formulation and prediction with multiple directions of attack. We begin by analysing Watson and Lovelock's (1983) Daisyworld model by making explicit the relationship between the various model time scales, laying the foundation for our own conceptual ecosystem model with an arbitrarily diverse biota and a multidimensional environment. We make the important step of providing a framework to translate the model formulation and determine the collective behaviour of the biota. Cellular automata and networks are methods for modelling discrete complex systems and are widely considered a staple of the complex systems simulator's toolbox. We go on to develop the analytical tools available to these models with a real space renormalisation of two dimensional non-equilibrium cellular automata along with demonstrating the utility of a master equation approach by analysing the properties of a new algorithm for growing complex networks. Lastly we investigate the utility of thermodynamic principles in predicting self-organisation in dissipative systems.