The brain is a vastly complex dynamical system. Cognitive functions such as memory, learning, volition and consciousness seem to emerge as high level properties from the activity of billions of neurons sparsely connected into complex networks. What is it about networks that allows such emergence to happen? I will argue that the basic level of emergence is a network's ability to categorise its space of possible patterns of distributed activation. Categorisation occurs far from equilibrium as well as at attractors, giving a role to chaotic dynamics. A network self-organises its state-space into a basin of attraction field, a space-time abstraction representing the network's latent distributed memory. When networks link up with other networks, the system is able to use memory in individual fields to provide the components for the emergence of higher level cognitive states. This paper examines the idea of basins of attraction in the context of a simple yet powerful neural model - random Boolean networks.
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