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This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power-law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review.

This essay is designed to organize a range of experimental findings and theoretical insights of the past 25 years into a coherent view of the brain's style of function. The view that emerges places the brain firmly into the conceptual framework of Nonlinear Dynamics, operating at the brink of criticality which is achieved and maintained by self-organization. Application of the twin concepts of scaling and universality of the theory of non-equilibrium phase transitions will then be introduced as an approach to elucidating the nature of underlying neural processes, notably with reference to the role of reentrant activity in neural circuits of cerebral cortex and subcortical structures.

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