Local approximation of the Schelling segregation model. More...

#include <tpl_ca_stochastic_rules.H>

Public Types
using	engine_type = Engine

Public Member Functions
	Schelling_Rule (const double threshold, const double p_move=1.0, const double p_fill=1.0, const std::uint64_t master_seed=0)
	Build a Schelling rule.

double	threshold () const noexcept

double	p_move () const noexcept

double	p_fill () const noexcept

std::uint64_t	master_seed () const noexcept

void	set_master_seed (std::uint64_t s) noexcept

template<typename State , std::size_t Rank>
State	operator() (const State &current, Neighbor_View< State > neighbours, const Cell_Context< Rank > &ctx) const
	Compute the next Schelling state for cell `current`.

Private Attributes
double	threshold_

double	p_move_

double	p_fill_

std::uint64_t	master_seed_

Detailed Description

template<typename Engine = std::mt19937_64>
class Aleph::CA::Schelling_Rule< Engine >

Local approximation of the Schelling segregation model.

The classical Schelling model is non-local: unhappy agents move to a vacant cell anywhere on the lattice. The CA-friendly local approximation implemented here updates each cell synchronously:

For an occupied cell, count same-type and other-type occupied neighbours. The cell is unhappy when the fraction same / (same + other) is strictly below threshold. An unhappy cell vacates with probability p_move (becomes EMPTY); otherwise it stays put.
For an empty cell, look at its occupied neighbours: if one type strictly dominates, the cell is filled with that type with probability p_fill. With equal counts (or no occupied neighbours), the cell stays EMPTY.

This is not the canonical Schelling dynamics — it is the standard local CA approximation used in pedagogical settings (Vinkovic & Kirman, 2006, similar). It preserves the qualitative segregation behaviour while remaining fully synchronous and local.

Template Parameters

Engine RNG engine; defaults to std::mt19937_64.

Definition at line 603 of file tpl_ca_stochastic_rules.H.

Member Typedef Documentation

◆ engine_type

template<typename Engine = std::mt19937_64>

using Aleph::CA::Schelling_Rule< Engine >::engine_type = Engine

Definition at line 611 of file tpl_ca_stochastic_rules.H.

Constructor & Destructor Documentation

◆ Schelling_Rule()

template<typename Engine = std::mt19937_64>

Aleph::CA::Schelling_Rule< Engine >::Schelling_Rule	(	const double	threshold,
		const double	p_move = `1.0`,
		const double	p_fill = `1.0`,
		const std::uint64_t	master_seed = `0`
	)

inline

Build a Schelling rule.

Parameters

[in]	threshold	minimum same-type fraction below which an agent becomes unhappy. Must be in `[0, 1]`.
[in]	p_move	probability that an unhappy agent vacates the cell (default `1.0`). Must be in `[0, 1]`.
[in]	p_fill	probability that an empty cell with a strict majority of one neighbour type is filled (default `1.0`). Must be in `[0, 1]`.
[in]	master_seed	master seed forwarded to `cell_seed()`.

Exceptions

std::domain_error if any probability is outside [0, 1].

Definition at line 625 of file tpl_ca_stochastic_rules.H.

References ah_domain_error_if, Aleph::blossom_maximum_cardinality_matching(), Aleph::CA::Schelling_Rule< Engine >::p_fill(), Aleph::CA::Schelling_Rule< Engine >::p_move(), and Aleph::CA::Schelling_Rule< Engine >::threshold().

Member Function Documentation

◆ master_seed()

template<typename Engine = std::mt19937_64>

std::uint64_t Aleph::CA::Schelling_Rule< Engine >::master_seed ( ) const

inlinenoexcept

Definition at line 654 of file tpl_ca_stochastic_rules.H.

References Aleph::CA::Schelling_Rule< Engine >::master_seed_.

◆ operator()()

template<typename Engine = std::mt19937_64>

template<typename State , std::size_t Rank>

State Aleph::CA::Schelling_Rule< Engine >::operator()	(	const State &	current,
		Neighbor_View< State >	neighbours,
		const Cell_Context< Rank > &	ctx
	)		const