The intuitive notion that a healthy organism is characterised by regular, homeostatic function has been challenged by observations that a loss of complexity is, in fact, indicative of ill-health. Monofractals succinctly describe complex processes and are controlled by a single time-invariant scaling exponent, H, simply related to the fractal dimension. Previous analyses of resting fMRI time-series demonstrated that ageing and scopolamine administration were both associated with increases in H and that faster response in a prior encoding task was also associated with increased H. We revisit this experiment with a novel, multifractal approach in which fractal dynamics are assumed to be non-stationary and defined by a spectrum of local singularity exponents. Parameterisation of this spectrum was capable of refracting the effects of age, scopolamine and task performance as well as a refining a description of the associated signal changes. Using the same imaging data, we also explored turbulence as a possible mechanism underlying multifractal dynamics. Evidence is provided that Carstaing's model of turbulent information flow from high to low scales has only limited validity, and that scale invariance of energy dissipation is better explained by critical-phase phenomena, supporting the proposition that the brain maintains a state of self-organised criticality.