Understanding network development in the brain is of tremendous fundamental importance, but it is immensely challenging because of the complexity of both its architecture and function. The mechanisms of axonal navigation to target regions and the specific interactions with guidance factors such as membrane-bound proteins, chemical gradients, mechanical guidance cues, etc., are largely unknown. A current limitation for the study of neural network formation is the ability to control precisely the connectivity of small groups of neurons. A first step in designing such networks is to understand the "rules" central nervous system (CNS) neurons use to form functional connections with one another. Here we begin to delineate novel rules for growth and connectivity of small numbers of neurons patterned on Au substrates in simplified geometries. These studies yield new insights into the mechanisms determining the organizational features present in intact systems. We use a previously reported atomic force microscopy (AFM) nanolithography method to control precisely the location and growth of neurons on these surfaces. By examining a series of systems with different geometrical parameters, we quantitatively and systematically analyze how neuronal growth depends on these parameters.