"active" or "inactive" (output of 1 or 0), with 1 implying that the neuron is part of the solution. Each neuron also has a state function (described below) which is initialized to 0. When the network is allowed to run, each neuron can change its state and output based on the states and outputs of its neighbors (those exactly one knight's move away) according to the following transition rules: where represents discrete intervals of time, is the state of the neuron connecting square to square , is the output of the neuron from to , and is the set of neighbors of the neuron. Although divergent cases are possible, the network should eventually converge, which occurs when no neuron changes its state from time to . When the network converges, either the network encodes a knight's tour or a series of two or more independent circuits within the same board. See also Abu Bakr bin Yahya al-Suli Eight queens puzzle George Koltanowski Longest uncrossed knight's path Self-avoiding walk Notes External links H. C. von Warnsdorf 1823 in Google Books Introduction to Knight's tours by George Jelliss Knight's tours complete notes by George Jelliss Chess problems Graph algorithms Hamiltonian paths and cycles Mathematical chess problems Mathematical problems