# Neighbor-Dependent Network Systems

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The initial state of a network system consists of a network with two connections per node, an "above" connection (shown with a directed arc above the connected nodes) and a "below" connection (shown with an arc below the connected nodes in the opposite direction). Network systems then evolve based on rules that specify how the "above" and "below" connections should be rerouted. [*NKS*, p. 199]

Contributed by: Abigail Nussey (August 2010)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Each node is denoted by a pair , where is the node reached by traveling the "above" connection and is the node reached by traveling the "below" connection. So, for instance, a cyclic network of five nodes can be denoted by the array .

The rules describe how each "above" and "below" connection should be rerouted on the next step. 1 denotes an "above" connection and 2 denotes a "below" connection.

For more information on the implementation of these systems, please see S. Wolfram, *A New Kind of Science*, Champaign, IL: Wolfram Media, Inc., 2002 p. 935.

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