Rules
As with any cellular automaton, the cyclic cellular automaton consists of a regular grid of cells in one or more dimensions. The cells can take on any of states, ranging from to . The first generation starts out with random states in each of the cells. In each subsequent generation, if a cell has a neighboring cell whose value is the successor of the cell's value, the cell is "consumed" and takes on the succeeding value. (Note that 0 is the successor of ; see also modular arithmetic.) More general forms of this type of rule also include a threshold parameter, and only allow a cell to be consumed when the number of neighbors with the successor value exceeds this threshold.
Read more about this topic: Cyclic Cellular Automaton
Famous quotes containing the word rules:
“Trust men, and they will be true to you; treat them greatly, and they will show themselves great, though they make an exception in your favor to all their rules of trade.”
—Ralph Waldo Emerson (1803–1882)
“Fergus rules the brazen cars,
And rules the shadows of the wood,
And the white breast of the dim sea
And all dishevelled wandering stars.”
—William Butler Yeats (1865–1939)
“There are ... two minimum conditions necessary and sufficient for the existence of a legal system. On the one hand those rules of behavior which are valid according to the system’s ultimate criteria of validity must be generally obeyed, and on the other hand, its rules of recognition specifying the criteria of legal validity and its rules of change and adjudication must be effectively accepted as common public standards of official behavior by its officials.”
—H.L.A. (Herbert Lionel Adolphus)