Cellular Automata/Glossary

lattice

cellular automaton

neighborhood

A neighborhood of a cell $c$ is the set formed by all cells in the lattice that will drive the change of the state of $c$ when the transition rule $f$ acts upon them. See definition and examples.

preimage

preimage matrix

boundary

cyclic boundary

configuration

A configuration of a Cellular Automaton $A$ is a collection $c_t^A$ of all status of its components cells $c$ at instant $t\in$$\mathbb{N}$. It can be understood as a snapshot of the automaton at a point of its history in a way that at any instant $t>0$ we have $c_t^A=\delta(c_{t-1}^A)$

sequence

pattern

evolution

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 beckground for gliders, somethimes the most common bacground.