Neurophysiology
What are the physical structures of the brain that are necessary prerequisites to understanding consciousness? Obviously it isn't necessary to have a full knowledge of the most complex organ ever evolved in order to make effective life choices. But it is useful to understand the major structural components of the brain and how they operate in order to create a robust operator's manual for brain-owners.
The fractal metaphor extends to the brain, in that the neurons form the base unit, neural network clusters that encode our instincts, training, and memories, which are then grouped into functional structures like the cerebellum, temporal lobe, and cerebral cortex, that all work together holistically to form our consciousness and subjective experience. Each larger grouping of neurons repeats the fractal pattern on a new level of scale, with the reinforcement mechanism of neurons forming the generating equation.
As mentioned, the fractal is simply a useful metaphor for understanding how billions of individual neurons can self-organize into the incredible complexity of the human brain. This is not meant to imply that the brain itself has fractal dimension in some way. There is much evidence of fractal patterns of organization in neural networks, which is part of why the metaphor is apt. But the fractal is an apt metaphor for any self-organizing complex system, which the brain absolutely is.
See Neurophysiology on Wikipedia, brains, and neural networks for more hardware related information.