Before people get too carried away by the pictures, according to my reading of the article, the wires in these pictures are not actual wires (axons, whatever). They are streamlines of local directions of statistical orientations of fibres. This figure from the paper includes in part D optical microscopy of tissue for comparison. The orangey thing bottom right is the autocorrelation map of the microscopy image. I couldn't say whether the autocorrelation is strong enough to rule out this actual network looking locally like the image linked in the OP of "tangled up neuronal cells".
http://www.nih.gov/news/health/mar2012/nimh-29.htm has images of human and monkey brain scans which reveal an amazingly grid-like pattern of neuronal connections. What are the implications? Could brain scanning, emulation etc be simpler than would appear from images of tangled up neuronal cells (eg here: http://www.willamette.edu/~gorr/classes/cs449/brain.html)?
(My mother is a retired neuroscientist... I'd ask her for comment, but she is on holidays.)