  The proper functioning of the nervous system depends critically on the
intricate network of synaptic connections that are generated during the system
development. During the network formation, the growth cones migrate through the
embryonic environment to their targets using chemical communication. A major
obstacle in the elucidation of fundamental principles underlying this
self-wiring is the complexity of the system being analyzed. Hence much effort
is devoted to in-vitro experiments of simpler 2D model systems. In these
experiments neurons are placed on Poly-L-Lysine (PLL) surfaces so it is easier
to monitor their self-wiring. We developed a model to reproduce the salient
features of the 2D systems, inspired by the study of bacterial colony's growth
and the aggregation of amoebae. We represent the neurons (each composed of
cell's soma, neurites and growth cones) by active elements that capture the
generic features of the real neurons. The model also incorporates stationary
units representing the cells' soma and communicating walkers representing the
growth cones. The stationary units send neurites one at a time, and respond to
chemical signaling. The walkers migrate in response to chemotaxis substances
emitted by the soma and communicate with each other and with the soma by means
of chemotactic ``feedback''. The interplay between the chemo-repulsive and
chemo-attractive responses is determined by the dynamics of the walker's
internal energy which is controlled by the soma. These features enable the
neurons to perform the complex task of self-wiring.
