http://scienceblogs.com/cognitivedaily/2007/03/modeling_a_real_brain.php - Modeling a real brain
A rat's brain has millions of neurons, each with up to 10,000 connections to other neurons. This "simple" animal's neural network is mind-bogglingly complex. Yet a Swiss laboratory has achieved remarkable success duplicating a vast region of a rat's brain using a supercomputer. They still have a ways to go, however. The computer currently has 10,000 microprocessors, each representing a single neuron in the rat's brain. To duplicate the entire brain they'll need a computer 2,000 times bigger.
It's not quite a positronic brain, but still cool.