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.