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 $$a$$.
 * $$\forall C^t \; \Delta t \geq n \; : \; C^{t+\Delta t} = \dots aaa \dots $$


 * 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 background for gliders, sometimes the most common background.