Noisy automata
An elementary cellular automaton whose outputs are flipped at random with a small probability.
- Name:
noisy_automata - Field:
computer_science/automata - Formalism: lattice dynamics
- References: Lindgren 2024
Factory
@register_model(
field='computer_science/automata',
tags=('lattice', 'elementary', 'noise', 'stochastic'),
references=('Lindgren 2024',),
defaults={'until': 100, 'dt': 1},
)
def noisy_automata(
rule: int = 18,
*,
noise: float = 0.01,
size: int = 101,
density: float = 0.5,
random_state: int | np.random.Generator | None = 0,
) -> System:
"""Return an elementary cellular automaton whose outputs are flipped at random with a small probability.
Args:
rule:
The Wolfram number from 0 to 255.
noise:
The probability that a cell's output is flipped in a step.
size:
The number of cells of the ring.
density:
The probability that a cell starts alive.
random_state:
The seed or generator of the random initial cells.
Returns:
system:
The model, with the cells `cells.alive`.
Examples:
>>> from skcomplex.models.computer_science.automata import noisy_automata
>>> noisy_automata(184, size=11).elements[0].check().prepare().size_
11
"""
values = _random_cells((size,), density, random_state)
space = LatticeSpace(size)
return System(
elements=[
LatticeElement(
'cells',
element=NoisyElementaryCellElement,
space=space,
values={'alive': values, 'noise': noise},
),
],
interactions=[
LocalRuleInteraction(
'rule',
target='cells',
state='alive',
rule=_noisy_rule(rule),
neighborhood=BoxNeighborhood(),
stochastic=True,
),
],
)
Components
class NoisyElementaryCellElement(BinaryCellElement):
"""Binary cell that holds the probability that the output of its local rule is flipped.
Args:
label:
The label of the cell or the lattice group.
visual:
How the element is drawn, or `None` for `default_visual_`.
alive:
The initial value, 0 or 1.
noise:
The probability that the output of the rule is flipped.
Examples:
>>> from skcomplex.models.computer_science.automata import NoisyElementaryCellElement
>>> NoisyElementaryCellElement('cell', noise=0.1).noise
0.1
"""
def __init__(
self,
label: str,
visual: VisualSpec | None = None,
*,
alive: float = 0,
noise: Annotated[float, ParameterSpec(domain=RealSet.closed_open(0, oo))] = 0.01,
) -> None:
super().__init__(label, visual=visual, alive=alive)
self.noise = noise
class LocalRuleInteraction(Interaction):
"""Local rule of a cellular automaton, which sets the next value of every cell from its ordered neighbourhood.
The rule is a table of the next value of every configuration of the neighbourhood, `TableSpec`, a rule of the sum
of the neighbourhood, `TotalisticSpec`, a rule of the cell and the sum of its neighbours, `OuterTotalisticSpec`, an
object whose `table()` returns a `TableSpec`, or a function. A function receives one array per neighbour of every
read state, in neighbourhood order, with one value per cell, the uniform array `random` when the rule is stochastic,
and the parameters of the bound group it names, and returns the next values of the states, one array per state.
Args:
label:
The label of the interaction, unique among the parts of its system.
target:
The path of the group on the cells of a lattice, the nodes of a network, or a Cayley graph.
state:
The name of the state the rule sets, or a tuple of the names of the states it sets together.
rule:
The table, the totalistic rule, or the function.
neighborhood:
The ordered neighbourhood of every cell, such as `VonNeumannNeighborhood(center=True)`.
reads:
The names of the states whose neighbourhoods a function reads, or `None` for the states it sets.
schedule:
`'synchronous'`, `'random-sequential'`, `'random-site'`, `'checkerboard'`, or `'colored'`.
stochastic:
Whether a function receives the uniform random array `random`.
Raises:
ValidationError:
The state or the read states are not names, or the neighbourhood is not a neighbourhood.
Examples:
>>> from skcomplex.core.interactions import LocalRuleInteraction
>>> from skcomplex.core.spaces import VonNeumannNeighborhood
>>> from skcomplex.specs import TotalisticSpec
>>> parity = TotalisticSpec({1: 1, 3: 1})
>>> around = VonNeumannNeighborhood(n_dim=1, center=True)
>>> rule = LocalRuleInteraction('parity', target='cells', state='cell', rule=parity, neighborhood=around)
>>> rule.check().schedule
'synchronous'
"""
def __init__(
self,
label: str,
*,
target: Annotated[str, RoleSpec()],
state: str | tuple[str, ...],
rule: object,
neighborhood: BaseNeighborhood,
reads: Sequence[str] | None = None,
schedule: str = 'synchronous',
stochastic: bool = False,
) -> None:
super().__init__(label)
self.target = target
self.state = state
self.rule = rule
self.neighborhood = neighborhood
self.reads = reads
self.schedule = schedule
self.stochastic = stochastic
def _get_names(self) -> tuple[str, ...]:
"""Return the names of the states the rule sets."""
return (self.state,) if isinstance(self.state, str) else tuple(self.state)
def _check(self) -> None:
"""Raise an error for states that are not names, or a neighbourhood that is not one.
Raises:
ValidationError:
The state or the read states are not names, or the neighbourhood is not a neighbourhood.
"""
super()._check()
names = [*self._get_names(), *(self.reads or ())]
if not names or not all(isinstance(name, str) and name.isidentifier() for name in names):
error_msg = f'The local rule {self.label!r} sets {self.state!r} and reads {self.reads!r}. Give state names.'
raise ValidationError(error_msg)
if not isinstance(self.neighborhood, BaseNeighborhood):
error_msg = f'The neighbourhood of the local rule {self.label!r} is {self.neighborhood!r}. Give one.'
raise ValidationError(error_msg)
def _get_laws(self, namespace: SimpleNamespace) -> list[BaseLaw]:
"""Return the local rule law of the states of the target.
Args:
namespace:
The namespace of the symbols the laws can use, with `namespace.target`.
Returns:
laws:
The local rule law.
"""
targets = tuple(getattr(self._get_member(namespace, 'target'), name) for name in self._get_names())
reads = (
None
if self.reads is None
else tuple(getattr(self._get_member(namespace, 'target'), name) for name in self.reads)
)
return [
LocalRuleLaw(
targets[0] if isinstance(self.state, str) else targets,
self.neighborhood,
self.rule,
reads=reads,
schedule=self.schedule,
stochastic=self.stochastic,
label=self.label,
),
]