A. Kalay et al., NEURONAL GROWTH VIA HYBRID SYSTEM OF SELF-GROWING AND DIFFUSION-BASEDGRAMMAR RULES .1., Bulletin of mathematical biology, 57(2), 1995, pp. 205-227
The formation of neuronal networks requires axonal growth towards targ
et neurons. A simple set of grammar rules is introduced to describe ax
onal growth towards target cells situated both at short and long dista
nces from the growing neuron. Growth for short distances is described
by growth following the highest gradient of a chemical compound (which
is spread by diffusion from the targets). This approach fails to desc
ribe long-distance growth, which is addressed by adopting a graph gram
mar theory for growing toes. With these rules a flexible tool to draw
network of neurons by computer can be developed.