Pattern Formation in Networks Inspired by Biological Development

We present a system for pattern formation in networks that is inspired by biological development. The system hierarchically forms a specific pattern in a rough-to-detail manner as seen in biological development. We apply the system to generating gray-scaled images. In this application, a network topology is first generated from a given original image in which pixels correspond to network nodes and the nodes are linked to one another in a certain way, and then the system is run in the generated network. The pattern formed by the system within the network is a distribution of brightness of pixels which are equal to nodes. The system is shown to create a variety of images which are influenced by the structure in the original image in a rough-to-detail manner. This feature would be useful for designing patterns under some structural constraints.