Cellular Automata/Sandbox

Some Definitions

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 $a$.

$\mathrm{\forall }{C}^t\mathrm{\Delta }t\ge n:C^{t+\mathrm{\Delta }t}=\dots aaa\dots$

Idempotent configuration (of order n)

A configuration that in at most $n$ steps evolves into a steady configuration (C^{t+1}=C^t).

$\mathrm{\Delta }t\ge n:C^{t+\mathrm{\Delta }t}=C^{t+\mathrm{\Delta }t+1}$

Idempotent rule

A rule for which all configurations are idempotent.

$\mathrm{\forall }{C}^t\mathrm{\Delta }t\ge n:C^{t+\mathrm{\Delta }t}=C^{t+\mathrm{\Delta }t+1}$

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.