Cellular Automata/Sandbox

some definitions

Quiescent state

A cell is in a qiescent state a, if all cells in its neighborhood are the same quescent 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 beckground for gliders, somethimes the most common bacground.