Random Boolean Network

A Boolean network consists of a set of Boolean variables whose 
state is determined by other variables in the network. 
In a random boolean network the connections are wired 
randomly and the output of nodes are determined by randomly 
generated logic functions.

'''Random Boolean Networks''' are therefore networks of boolean nodes that can 
be in one of two possible states, 0 or 1, and whose evolution 
from one time point to another is governed by simple boolean 
transition rules. The nodes change their states according to 
this boolean transition rules that depend on their current states 
and those of their neighbors. 
RBNs are closely related to [[Cellular Automata]] (CA) and are
used to study [[Complex System|complex systems]]. Both are usually
based on local boolean transition functions.
In RBNs we have nodes instead of Cells in CA, and connections 
to remote neighbors instead of a local neighborhood grid as in CA.
RBNs and NK Networks have been proposed as a biological
model by Stuart Kauffman, see his book "The Origins of Order".

== NK Network ==

An NK-Boolean network is defined as a network of N nodes with connectivity K, 
where K refers to the maximum number of nodes that regulate some othernode, 
i.e. each of the N nodes has K inputs and one output.
It can be considered as a network of N light bulbs. At every timestep,
each bulb changes the state: the light bulbs can only be on or off, and each 
of the bulbs influences K other bulbs in the network.

* [http://www-users.cs.york.ac.uk/susan/cyc/n/nk.htm Applet for NK networks]

== Links ==

Tutorials

* [http://www.itee.uq.edu.au/~kaiw/RBN/ RBN Tutorial] from Kai Willadsen 

* [http://homepages.vub.ac.be/~cgershen/rbn/tut/index.html RBN Tutorial] from Carlos Gershenson

arXiv papers

* [http://www.arxiv.org/abs/nlin.AO/0408006 Introduction to Random Boolean Networks] from Carlos Gershenson

* [http://arxiv.org/abs/nlin/0204062 Boolean Dynamics with Random Couplings] from Leo Kadanoff et al.

Wikipedia Pages

* Wikipedia page for [http://en.wikipedia.org/wiki/Boolean_network Boolean Network]


== Examples ==

The Finite State Machine (FSM) for the whole boolean network reveals 
the attractor structures and the basins of attraction. The
attractor - if one exists - is a fixed point or a discrete 
limit cycle. The limit cycle is of course shorter than the
total number of states, which is 2^N for N nodes (2^3=8 for 
3 nodes).

[[Image:RBNExample1.png|left|RBN Examples]]

[[Image:RBNExample2.png|left|RBN Examples]]