# 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 beckground for gliders, somethimes the most common bacground.