Cellular Automata/Glossary


 * lattice
 * cellular automaton
 * neighborhood
 * A neighborhood of a cell $$c$$ is the set formed by all cells in the lattice that will drive the change of the state of $$c$$ when the transition rule $$f$$ acts upon them. See definition and examples.


 * preimage
 * preimage matrix
 * boundary
 * cyclic boundary


 * configuration
 * A configuration of a Cellular Automaton $$A$$ is a collection $$c_t^A$$ of all status of its components cells $$c$$ at instant $$t\in$$$$\mathbb{N}$$. It can be understood as a snapshot of the automaton at a point of its history in a way that at any instant $$t>0$$ we have $$c_t^A=\delta(c_{t-1}^A)$$


 * sequence
 * pattern


 * evolution


 * Quiescent state
 * A cell is in a quiescent state $$a$$, if all cells in its neighborhood are the same quiescent state.
 * $$ f(aaa \dots a) = a $$


 * Nilpotent rule (of order n)
 * Any configuration evolves in at most $$n$$ steps into a configuration with all cells in any quiescent state $$a$$.
 * $$\forall C^t \; \Delta t \geq n \; : \; C^{t+\Delta t} = \dots aaa \dots $$


 * Idempotent configuration (of order n)
 * A configuration that in at most $$n$$ steps evolves into a steady configuration (C^{t+1}=C^t).
 * $$\Delta t \geq n \; : \; C^{t+\Delta t} = C^{t+\Delta t+1} $$


 * Idempotent rule
 * A rule for which all configurations are idempotent.
 * $$\forall C^t \; \Delta t \geq n \; : \; C^{t+\Delta t} = C^{t+\Delta t+1} $$


 * Superluminal configuration
 * A configuration for which the phase speed is greater than the speed of light. The phase speed is the shift of the configuration per time.


 * Glider


 * Eather pattern
 * A background for gliders, somethimes the most common background.