# Cellular Automata/Sandbox

## Some Definitions

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 background for gliders, sometimes the most common background.