Aleph::CA::Reproductions::BTW_Sandpile Class Reference

Deterministic open-boundary Bak-Tang-Wiesenfeld sandpile. More...

#include <ca_reproduction_support.H>

Collaboration diagram for Aleph::CA::Reproductions::BTW_Sandpile:

Public Types
using	Grid = Lattice< Dense_Cell_Storage< int, 2 >, OpenBoundary >
using	update_scheme = Sequential_Update< RowMajor >

Public Member Functions
	BTW_Sandpile (const ca_size_t side, const std::uint64_t seed=0)
	Construct an empty square sandpile.
Avalanche	drop_random ()
	Drop one grain at a uniformly selected cell and stabilise.
Avalanche	drop_at (const ca_size_t row, const ca_size_t column)
	Drop one grain at (row, column) and stabilise.
const Grid &	frame () const noexcept
	Return the current stable grid.
bool	stable () const
	Test whether every cell is below the toppling threshold.

Private Member Functions
void	add_if_inside (const ca_index_t row, const ca_index_t column)
	Add one grain when (row, column) lies inside the open grid.

Private Attributes
Grid	grid_
std::mt19937_64	rng_

Detailed Description

Deterministic open-boundary Bak-Tang-Wiesenfeld sandpile.

The implementation performs in-place row-major toppling sweeps. It names Sequential_Update<RowMajor> as its update scheme because direct BTW toppling writes both the selected cell and its neighbours; a pull-only local rule cannot preserve grains while expressing that operation.

Definition at line 312 of file ca_reproduction_support.H.

Member Typedef Documentation

Grid

using Aleph::CA::Reproductions::BTW_Sandpile::Grid = Lattice<Dense_Cell_Storage<int, 2>, OpenBoundary>

Definition at line 315 of file ca_reproduction_support.H.

update_scheme

using Aleph::CA::Reproductions::BTW_Sandpile::update_scheme = Sequential_Update<RowMajor>

Definition at line 316 of file ca_reproduction_support.H.

Constructor & Destructor Documentation

BTW_Sandpile()

Aleph::CA::Reproductions::BTW_Sandpile::BTW_Sandpile ( const ca_size_t  side, const std::uint64_t  seed = 0  )

inlineexplicit

Construct an empty square sandpile.

Parameters

side	grid side length.
seed	seed used for uniformly distributed grain drops.

Exceptions

std::domain_error

if side == 0.

Definition at line 323 of file ca_reproduction_support.H.

References Aleph::blossom_maximum_cardinality_matching().

Member Function Documentation

add_if_inside()

void Aleph::CA::Reproductions::BTW_Sandpile::add_if_inside ( const ca_index_t  row, const ca_index_t  column  )

inlineprivate

Add one grain when (row, column) lies inside the open grid.

Parameters

row	candidate row.
column	candidate column.

Definition at line 406 of file ca_reproduction_support.H.

References Aleph::CA::Lattice< Storage, Boundary >::at(), Aleph::blossom_maximum_cardinality_matching(), grid_, row, Aleph::CA::Lattice< Storage, Boundary >::set(), and Aleph::CA::Lattice< Storage, Boundary >::size().

Referenced by drop_at().

drop_at()

Avalanche Aleph::CA::Reproductions::BTW_Sandpile::drop_at ( const ca_size_t  row, const ca_size_t  column  )

inline

Drop one grain at (row, column) and stabilise.

Parameters

row	zero-based row.
column	zero-based column.

Returns

avalanche size and duration.

Exceptions

std::domain_error

if the coordinate is out of range.

Definition at line 344 of file ca_reproduction_support.H.

References add_if_inside(), ah_domain_error_if, Aleph::CA::Lattice< Storage, Boundary >::at(), Aleph::blossom_maximum_cardinality_matching(), Aleph::CA::Reproductions::Avalanche::duration, grid_, r, row, Aleph::CA::Lattice< Storage, Boundary >::set(), Aleph::CA::Reproductions::Avalanche::size, and Aleph::CA::Lattice< Storage, Boundary >::size().

Referenced by drop_random().

drop_random()

Avalanche Aleph::CA::Reproductions::BTW_Sandpile::drop_random ( )

inline

Drop one grain at a uniformly selected cell and stabilise.

Returns

avalanche size and duration.

Definition at line 332 of file ca_reproduction_support.H.

References drop_at(), grid_, rng_, and Aleph::CA::Lattice< Storage, Boundary >::size().

frame()

const Grid & Aleph::CA::Reproductions::BTW_Sandpile::frame ( ) const

inlinenoexcept

Return the current stable grid.

Returns

const lattice reference.

Definition at line 381 of file ca_reproduction_support.H.

References grid_.

stable()

bool Aleph::CA::Reproductions::BTW_Sandpile::stable ( ) const

inline

Test whether every cell is below the toppling threshold.

Returns

true when the frame is stable.

Definition at line 389 of file ca_reproduction_support.H.

References Aleph::CA::Lattice< Storage, Boundary >::at(), grid_, r, and Aleph::CA::Lattice< Storage, Boundary >::size().

Member Data Documentation

grid_

Grid Aleph::CA::Reproductions::BTW_Sandpile::grid_

private

Definition at line 399 of file ca_reproduction_support.H.

Referenced by add_if_inside(), drop_at(), drop_random(), frame(), and stable().

rng_

std::mt19937_64 Aleph::CA::Reproductions::BTW_Sandpile::rng_

private

Definition at line 400 of file ca_reproduction_support.H.

Referenced by drop_random().

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The documentation for this class was generated from the following file:

• reproductions/ca_reproduction_support.H