Gray-Scott reaction-diffusion rule. More...

#include <tpl_ca_continuous_rules.H>

Collaboration diagram for Aleph::CA::Gray_Scott_Rule< Real, Kernel >:

Public Types
using	state_type = Reaction_Diffusion_Cell< Real >
	Cell state consumed and produced by the rule.

using	kernel_type = Kernel
	Laplacian kernel type.

Public Member Functions
	Gray_Scott_Rule (Real feed, Real kill, Real du, Real dv, Real dt=Real{1}, Kernel laplacian=laplacian_5p_kernel< Real >())
	Build a Gray-Scott rule.

Real	feed () const noexcept

Real	kill () const noexcept

Real	Du () const noexcept

Real	Dv () const noexcept

Real	dt () const noexcept

const Kernel &	laplacian () const noexcept

state_type	operator() (const state_type &current, Neighbor_View< state_type > neighbours) const
	Compute the next Gray-Scott state.

Private Member Functions
Real	laplace_u (Neighbor_View< state_type > neighbours, const state_type &current) const

Real	laplace_v (Neighbor_View< state_type > neighbours, const state_type &current) const

Private Attributes
Real	feed_

Real	kill_

Real	du_

Real	dv_

Real	dt_

Kernel	lap_

Detailed Description

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>
class Aleph::CA::Gray_Scott_Rule< Real, Kernel >

Gray-Scott reaction-diffusion rule.

Explicit Euler update:

du/dt = Du * Lap(u) - u*v*v + F*(1 - u)

dv/dt = Dv * Lap(v) + u*v*v - (F + K)*v

Aleph::CA::Gray_Scott_Rule::Dv

Real Dv() const noexcept

Definition tpl_ca_continuous_rules.H:399

Aleph::CA::Gray_Scott_Rule::dt

Real dt() const noexcept

Definition tpl_ca_continuous_rules.H:405

Aleph::CA::Gray_Scott_Rule::Du

Real Du() const noexcept

Definition tpl_ca_continuous_rules.H:393

Aleph::blossom_maximum_cardinality_matching

size_t blossom_maximum_cardinality_matching(const GT &g, DynDlist< typename GT::Arc * > &matching, SA sa=SA())

Alias of compute_maximum_cardinality_general_matching().

Definition Blossom.H:466

The default 5-point Laplacian expects a Moore<2, 1> neighbourhood; diagonal neighbour weights are zero. Concentrations are contracted to [0, 1] for documented stable parameters. The constructor enforces 0 < dt <= 1.0, which covers the standard Gray-Scott presets with dx = 1 used by CA examples.

Template Parameters

Real	floating-point field type.
Kernel	Laplacian kernel type.

Definition at line 317 of file tpl_ca_continuous_rules.H.

Member Typedef Documentation

◆ kernel_type

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>

using Aleph::CA::Gray_Scott_Rule< Real, Kernel >::kernel_type = Kernel

Laplacian kernel type.

Definition at line 323 of file tpl_ca_continuous_rules.H.

◆ state_type

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>

using Aleph::CA::Gray_Scott_Rule< Real, Kernel >::state_type = Reaction_Diffusion_Cell<Real>

Cell state consumed and produced by the rule.

Definition at line 321 of file tpl_ca_continuous_rules.H.

Constructor & Destructor Documentation

◆ Gray_Scott_Rule()

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>

Aleph::CA::Gray_Scott_Rule< Real, Kernel >::Gray_Scott_Rule	(	Real	feed,
		Real	kill,
		Real	du,
		Real	dv,
		Real	dt = `Real{1}`,
		Kernel	laplacian = `laplacian_5p_kernel<Real>()`
	)

inline

Build a Gray-Scott rule.

Parameters

[in]	feed	feed rate `F`, usually in `[0, 0.1]`.
[in]	kill	kill rate `K`, usually in `[0, 0.1]`.
[in]	du	diffusion coefficient for `u`.
[in]	dv	diffusion coefficient for `v`.
[in]	dt	explicit Euler time step; stable contract: `0 < dt <= 1.0`.
[in]	laplacian	convolution kernel; defaults to 5-point Laplacian.

Exceptions

std::domain_error if any parameter is outside its documented range.

Definition at line 363 of file tpl_ca_continuous_rules.H.

Member Function Documentation

◆ dt()

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>

Real Aleph::CA::Gray_Scott_Rule< Real, Kernel >::dt ( ) const

inlinenoexcept

Returns: explicit Euler time step.

Definition at line 405 of file tpl_ca_continuous_rules.H.

References Aleph::CA::Gray_Scott_Rule< Real, Kernel >::dt_.

◆ Du()

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>

Real Aleph::CA::Gray_Scott_Rule< Real, Kernel >::Du ( ) const

inlinenoexcept

Returns: u diffusion coefficient.

Definition at line 393 of file tpl_ca_continuous_rules.H.

References Aleph::CA::Gray_Scott_Rule< Real, Kernel >::du_.

◆ Dv()

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>

Real Aleph::CA::Gray_Scott_Rule< Real, Kernel >::Dv ( ) const

inlinenoexcept

Returns: v diffusion coefficient.

Definition at line 399 of file tpl_ca_continuous_rules.H.

References Aleph::CA::Gray_Scott_Rule< Real, Kernel >::dv_.

◆ feed()

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>

Real Aleph::CA::Gray_Scott_Rule< Real, Kernel >::feed ( ) const

inlinenoexcept

Returns: feed rate F.

Definition at line 381 of file tpl_ca_continuous_rules.H.

References Aleph::CA::Gray_Scott_Rule< Real, Kernel >::feed_.

◆ kill()

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>

Real Aleph::CA::Gray_Scott_Rule< Real, Kernel >::kill ( ) const

inlinenoexcept

Returns: kill rate K.

Definition at line 387 of file tpl_ca_continuous_rules.H.

References Aleph::CA::Gray_Scott_Rule< Real, Kernel >::kill_.

◆ laplace_u()

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>

Real Aleph::CA::Gray_Scott_Rule< Real, Kernel >::laplace_u	(	Neighbor_View< state_type >	neighbours,
		const state_type &	current
	)		const

inlineprivate

Definition at line 333 of file tpl_ca_continuous_rules.H.

References Aleph::blossom_maximum_cardinality_matching(), k, Aleph::CA::Gray_Scott_Rule< Real, Kernel >::lap_, and Aleph::CA::Reaction_Diffusion_Cell< Real >::u.

Referenced by Aleph::CA::Gray_Scott_Rule< Real, Kernel >::operator()().

◆ laplace_v()

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>

Real Aleph::CA::Gray_Scott_Rule< Real, Kernel >::laplace_v	(	Neighbor_View< state_type >	neighbours,
		const state_type &	current
	)		const

inlineprivate

Definition at line 341 of file tpl_ca_continuous_rules.H.

References Aleph::blossom_maximum_cardinality_matching(), k, Aleph::CA::Gray_Scott_Rule< Real, Kernel >::lap_, and Aleph::CA::Reaction_Diffusion_Cell< Real >::v.

Referenced by Aleph::CA::Gray_Scott_Rule< Real, Kernel >::operator()().

◆ laplacian()

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>

const Kernel & Aleph::CA::Gray_Scott_Rule< Real, Kernel >::laplacian ( ) const

inlinenoexcept

Returns: Laplacian kernel.

Definition at line 411 of file tpl_ca_continuous_rules.H.

References Aleph::CA::Gray_Scott_Rule< Real, Kernel >::lap_.

◆ operator()()

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>

state_type Aleph::CA::Gray_Scott_Rule< Real, Kernel >::operator()	(	const state_type &	current,
		Neighbor_View< state_type >	neighbours
	)		const

inline

Compute the next Gray-Scott state.

Parameters

[in]	current	current `(u, v)` concentration.
[in]	neighbours	neighbour cells in `Moore<2, Kernel::radius_v>` order.

Returns: next concentration pair.

Exceptions

std::length_error	if neighbour count does not match the kernel.
std::runtime_error	if the update leaves the stable `[0, 1]` concentration interval beyond roundoff tolerance.

Definition at line 426 of file tpl_ca_continuous_rules.H.

References ah_length_error_if, Aleph::blossom_maximum_cardinality_matching(), Aleph::CA::ca_continuous_detail::clamp_unit_after_check(), Aleph::CA::Gray_Scott_Rule< Real, Kernel >::dt_, Aleph::CA::Gray_Scott_Rule< Real, Kernel >::du_, Aleph::CA::Gray_Scott_Rule< Real, Kernel >::dv_, Aleph::CA::Gray_Scott_Rule< Real, Kernel >::feed_, Aleph::CA::Gray_Scott_Rule< Real, Kernel >::kill_, Aleph::CA::Gray_Scott_Rule< Real, Kernel >::laplace_u(), Aleph::CA::Gray_Scott_Rule< Real, Kernel >::laplace_v(), Aleph::CA::Reaction_Diffusion_Cell< Real >::u, and Aleph::CA::Reaction_Diffusion_Cell< Real >::v.