Hodgepodge machine
The hodgepodge machine, a model of a chemical reaction whose waves form spirals.
- Name:
hodgepodge - Field:
chemistry/kinetics - Formalism: lattice dynamics
- References: Gerhardt and Schuster 1989; Charbonneau 2017
Factory
@register_model(
field='chemistry/kinetics',
tags=('lattice', 'excitable media', 'spirals'),
references=('Gerhardt and Schuster 1989', 'Charbonneau 2017'),
defaults={'until': 200, 'dt': 1},
)
def hodgepodge(
shape: Sequence[int] = (100, 100),
*,
n: float = 100.0,
k1: float = 2.0,
k2: float = 3.0,
g: float = 34.0,
random_state: int | np.random.Generator | None = 0,
) -> System:
"""Return the hodgepodge machine, a model of a chemical reaction whose waves form spirals.
Args:
shape:
The number of rows and columns.
n:
The level of illness.
k1:
The weight of infected neighbours for healthy cells.
k2:
The weight of ill neighbours for healthy cells.
g:
The speed of the infection.
random_state:
The seed or generator of the initial levels.
Returns:
system:
The model, with the levels `cells.level`.
Examples:
>>> from skcomplex.models.chemistry.kinetics import hodgepodge
>>> hodgepodge((10, 10)).elements[0].values['g']
34.0
"""
levels = np.random.default_rng(random_state).integers(0, int(n) + 1, size=tuple(shape)).astype(float)
space = LatticeSpace(tuple(shape))
return System(
elements=[
LatticeElement(
'cells',
element=HodgepodgeCellElement,
space=space,
values={'level': levels, 'n': n, 'k1': k1, 'k2': k2, 'g': g},
),
],
interactions=[
LocalRuleInteraction(
'infection',
target='cells',
state='level',
rule=_infect,
neighborhood=MooreNeighborhood(center=True),
),
],
)
Components
class HodgepodgeCellElement(Element):
"""Cell of the hodgepodge machine of Gerhardt and Schuster, healthy at 0, infected below `n`, and ill at `n`.
Healthy cells catch the infection from their infected and ill neighbours, infected cells worsen by the mean of their
neighbourhood plus `g`, and ill cells heal, by the local rule of `hodgepodge`.
Args:
label:
The label of the cell or the lattice group.
visual:
How the element is drawn, or `None` for `default_visual_`.
level:
The initial level of infection from 0 to `n`.
n:
The level of illness.
k1:
The weight of infected neighbours for healthy cells.
k2:
The weight of ill neighbours for healthy cells.
g:
The speed of the infection.
Examples:
>>> from skcomplex.models.chemistry.kinetics import HodgepodgeCellElement
>>> HodgepodgeCellElement('cell').n
100.0
"""
def __init__(
self,
label: str,
visual: VisualSpec | None = None,
*,
level: Annotated[float, StateSpec(domain=NN)] = 0,
n: Annotated[float, ParameterSpec(domain=RealSet.open(0, oo))] = 100.0,
k1: Annotated[float, ParameterSpec(domain=RealSet.open(0, oo))] = 2.0,
k2: Annotated[float, ParameterSpec(domain=RealSet.open(0, oo))] = 3.0,
g: Annotated[float, ParameterSpec(domain=RealSet.closed_open(0, oo))] = 34.0,
) -> None:
super().__init__(label, visual=visual)
self.level = level
self.n = n
self.k1 = k1
self.k2 = k2
self.g = g
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,
),
]