Cellular Automata/Glossary

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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.