# Cellular Automata/Glossary

lattice
cellular automaton
neighborhood
A neighborhood of a cell ${\displaystyle c}$ is the set formed by all cells in the lattice that will drive the change of the state of ${\displaystyle c}$ when the transition rule ${\displaystyle f}$ acts upon them. See definition and examples.
preimage
preimage matrix
boundary
cyclic boundary
configuration
A configuration of a Cellular Automaton ${\displaystyle A}$ is a collection ${\displaystyle c_{t}^{A}}$ of all status of its components cells ${\displaystyle c}$ at instant ${\displaystyle t\in }$${\displaystyle \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 ${\displaystyle t>0}$ we have ${\displaystyle c_{t}^{A}=\delta (c_{t-1}^{A})}$
sequence
pattern
evolution

Quiescent state
A cell is in a quiescent state ${\displaystyle a}$, if all cells in its neighborhood are the same quiescent state.
${\displaystyle f(aaa\dots a)=a}$
Nilpotent rule (of order n)
Any configuration evolves in at most ${\displaystyle n}$ steps into a configuration with all cells in any quiescent state ${\displaystyle a}$.
${\displaystyle \forall C^{t}\;\Delta t\geq n\;:\;C^{t+\Delta t}=\dots aaa\dots }$
Idempotent configuration (of order n)
A configuration that in at most ${\displaystyle n}$ steps evolves into a steady configuration (C^{t+1}=C^t).
${\displaystyle \Delta t\geq n\;:\;C^{t+\Delta t}=C^{t+\Delta t+1}}$
Idempotent rule
A rule for which all configurations are idempotent.
${\displaystyle \forall C^{t}\;\Delta t\geq n\;:\;C^{t+\Delta t}=C^{t+\Delta t+1}}$
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.