Classes
struct	Avalanche
	Avalanche measurements for one BTW grain drop. More...

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

struct	Gray_Scott_Preset
	One named Gray-Scott parameter preset. More...

struct	Linear_Fit
	Least-squares result for a log-log histogram. More...

struct	Native_Png
	Decoded subset of the dependency-free native PNG format. More...

Typedefs
using	Gray_Scott_Cell = Reaction_Diffusion_Cell< double >

using	Gray_Scott_Lattice = Lattice< Dense_Cell_Storage< Gray_Scott_Cell, 2 >, NeumannBoundary >

Functions
Linear_Fit	fit_log_log_histogram (const std::vector< std::size_t > &samples, const std::size_t min_value, const std::size_t max_value, const std::size_t bins, const double sample_weight_power=0.0)
	Fit a power-law exponent from logarithmically binned samples.

void	write_histogram_csv (const std::filesystem::path &path, const std::vector< std::size_t > &samples)
	Write an exact discrete histogram as CSV.

template<typename Lattice >
double	morans_i_binary (const Lattice &frame, const typename Lattice::state_type empty_state, const typename Lattice::state_type type_a, const typename Lattice::state_type type_b)
	Compute Moran's I for two occupied Schelling cell types.

Gray_Scott_Lattice	make_gray_scott_seed (const ca_size_t side, const std::uint64_t master_seed)
	Build the deterministic finite-amplitude Gray-Scott perturbation.

Gray_Scott_Lattice	run_gray_scott (const Gray_Scott_Preset &preset, const ca_size_t side, const std::size_t steps, const std::uint64_t master_seed)
	Run one Gray-Scott preset from the shared deterministic seed.

RGB8	gray_scott_rgb (const Gray_Scott_Cell &cell)
	Convert one Gray-Scott state to an RGB colour.

void	write_gray_scott_png (const std::filesystem::path &path, const Gray_Scott_Lattice &frame)
	Write a Gray-Scott frame as a native Aleph RGB PNG.

Native_Png	decode_native_png (std::istream &in)
	Decode a PNG emitted by `Aleph::CA::write_png`.

Native_Png	read_native_png (const std::filesystem::path &path)
	Read and decode a native Aleph PNG.

double	mean_channel_difference (const Native_Png &lhs, const Native_Png &rhs)
	Compute normalized mean absolute per-channel PNG difference.

template<typename F >
void	for_each_gosper_gun_cell (F &&visitor, const std::int64_t offset_x=0, const std::int64_t offset_y=0)
	Visit every live coordinate in the canonical Gosper gun.

Variables
constexpr std::array< Gray_Scott_Preset, 3 >	gray_scott_presets
	Canonical visual presets used by the weekly Gray-Scott reproduction.

constexpr std::array< std::array< std::int64_t, 2 >, 36 >	gosper_gun_cells
	Canonical 36-cell Gosper glider gun.

Typedef Documentation

◆ Gray_Scott_Cell

using Aleph::CA::Reproductions::Gray_Scott_Cell = typedef Reaction_Diffusion_Cell<double>

Definition at line 432 of file ca_reproduction_support.H.

◆ Gray_Scott_Lattice

using Aleph::CA::Reproductions::Gray_Scott_Lattice = typedef Lattice<Dense_Cell_Storage<Gray_Scott_Cell, 2>, NeumannBoundary>

Definition at line 433 of file ca_reproduction_support.H.

Function Documentation

◆ decode_native_png()

Native_Png Aleph::CA::Reproductions::decode_native_png ( std::istream & in )

inline

Decode a PNG emitted by Aleph::CA::write_png.

Only the dependency-free writer's filter-0, stored-deflate output is accepted. This keeps golden comparisons strict and avoids a PNG dependency.

Parameters

in	binary PNG stream.

Returns: decoded dimensions and scanline bytes.

Exceptions

std::runtime_error if the stream is malformed or unsupported.

Definition at line 528 of file ca_reproduction_support.H.

References ah_runtime_error_if, and Aleph::blossom_maximum_cardinality_matching().

Referenced by read_native_png(), and TEST().

◆ fit_log_log_histogram()

Linear_Fit Aleph::CA::Reproductions::fit_log_log_histogram	(	const std::vector< std::size_t > &	samples,
		const std::size_t	min_value,
		const std::size_t	max_value,
		const std::size_t	bins,
		const double	sample_weight_power = `0.0`
	)

inline

Fit a power-law exponent from logarithmically binned samples.

Each populated bin contributes its geometric midpoint and probability density (count / width) to an ordinary least-squares fit in log space. The omitted global normalization does not affect the slope.

Parameters

samples	positive integral event sizes.
min_value	smallest sample included in the fit.
max_value	largest sample included in the fit.
bins	number of logarithmic bins.
sample_weight_power	weight each sample `s` by `s^-sample_weight_power`. The default `0.0` fits directly observed event probabilities.

Returns: fitted slope, intercept, R-squared and populated-bin count.

Exceptions

std::domain_error	if the fit range is invalid or fewer than two logarithmic bins are requested.
std::runtime_error	if fewer than two populated bins remain.

Complexity: O(samples.size() + bins).

Definition at line 107 of file ca_reproduction_support.H.

References ah_domain_error_if, ah_runtime_error_if, Aleph::and, Aleph::blossom_maximum_cardinality_matching(), Aleph::CA::density(), Aleph::CA::Reproductions::Linear_Fit::intercept, Aleph::max_value(), Aleph::min_value(), offset, Aleph::CA::Reproductions::Linear_Fit::points, Aleph::CA::Reproductions::Linear_Fit::r_squared, Aleph::CA::Reproductions::Linear_Fit::slope, and y.

Referenced by main(), main(), and TEST().

◆ for_each_gosper_gun_cell()

template<typename F >

void Aleph::CA::Reproductions::for_each_gosper_gun_cell	(	F &&	visitor,
		const std::int64_t	offset_x = `0`,
		const std::int64_t	offset_y = `0`
	)

Visit every live coordinate in the canonical Gosper gun.

Template Parameters

F	callable accepting `(x, y)`.

Parameters

visitor	coordinate callback.
offset_x	horizontal offset.
offset_y	vertical offset.

Definition at line 666 of file ca_reproduction_support.H.

References Aleph::blossom_maximum_cardinality_matching(), cell(), and gosper_gun_cells.

Referenced by main(), and TEST().

◆ gray_scott_rgb()

RGB8 Aleph::CA::Reproductions::gray_scott_rgb ( const Gray_Scott_Cell & cell )

inline

Convert one Gray-Scott state to an RGB colour.

Parameters

cell	concentration pair.

Returns: palette colour.

Definition at line 484 of file ca_reproduction_support.H.

References cell(), and value.

Referenced by TEST(), and write_gray_scott_png().

◆ make_gray_scott_seed()

Gray_Scott_Lattice Aleph::CA::Reproductions::make_gray_scott_seed	(	const ca_size_t	side,
		const std::uint64_t	master_seed
	)

inline

Build the deterministic finite-amplitude Gray-Scott perturbation.

Parameters

side	square lattice side length.
master_seed	seed for cell-local perturbations.

Returns: initial Gray-Scott frame.

Exceptions

std::domain_error if side < 8.

Definition at line 441 of file ca_reproduction_support.H.

References ah_domain_error_if, Aleph::blossom_maximum_cardinality_matching(), h, and r.

Referenced by run_gray_scott().

◆ mean_channel_difference()

double Aleph::CA::Reproductions::mean_channel_difference	(	const Native_Png &	lhs,
		const Native_Png &	rhs
	)

inline

Compute normalized mean absolute per-channel PNG difference.

Parameters

lhs	first decoded PNG.
rhs	second decoded PNG.

Returns: difference in [0, 1], where 0 is pixel-identical.

Exceptions

std::domain_error if dimensions differ.

Definition at line 625 of file ca_reproduction_support.H.

References ah_domain_error_if, ah_runtime_error_if, Aleph::blossom_maximum_cardinality_matching(), Aleph::CA::Reproductions::Native_Png::height, Aleph::CA::Reproductions::Native_Png::raw, row, and Aleph::CA::Reproductions::Native_Png::width.

Referenced by main(), and TEST().

◆ morans_i_binary()

template<typename Lattice >

double Aleph::CA::Reproductions::morans_i_binary	(	const Lattice &	frame,
		const typename Lattice::state_type	empty_state,
		const typename Lattice::state_type	type_a,
		const typename Lattice::state_type	type_b
	)

Compute Moran's I for two occupied Schelling cell types.

Empty cells are excluded. Occupied cells are encoded as +1 and -1; each occupied cell is connected to its four periodic Von-Neumann neighbours when those neighbours are occupied.

Template Parameters

Lattice rank-2 lattice type.

Parameters

frame	toroidal Schelling frame.
empty_state	value representing a vacancy.
type_a	value representing the first population.
type_b	value representing the second population.

Returns: Moran's I, or 0.0 when the statistic is undefined.

Complexity: O(rows * columns).

Definition at line 218 of file ca_reproduction_support.H.

References Aleph::CA::Lattice< Storage, Boundary >::at(), Aleph::blossom_maximum_cardinality_matching(), cols, k, Aleph::mean(), r, Aleph::CA::Lattice< Storage, Boundary >::rank, rows, Aleph::CA::Lattice< Storage, Boundary >::size(), Aleph::sum(), and value.

Referenced by main().

◆ read_native_png()

Native_Png Aleph::CA::Reproductions::read_native_png ( const std::filesystem::path & path )

inline

Read and decode a native Aleph PNG.

Parameters

path	input path.

Returns: decoded PNG.

Exceptions

std::runtime_error if the file cannot be read or decoded.

Definition at line 612 of file ca_reproduction_support.H.

References ah_runtime_error_if, Aleph::blossom_maximum_cardinality_matching(), and decode_native_png().

Referenced by main().

◆ run_gray_scott()

Gray_Scott_Lattice Aleph::CA::Reproductions::run_gray_scott	(	const Gray_Scott_Preset &	preset,
		const ca_size_t	side,
		const std::size_t	steps,
		const std::uint64_t	master_seed
	)

inline

Run one Gray-Scott preset from the shared deterministic seed.

Parameters

preset	feed and kill rates.
side	square lattice side length.
steps	number of synchronous steps.
master_seed	perturbation seed.

Returns: final Gray-Scott frame.

Definition at line 468 of file ca_reproduction_support.H.

References Aleph::blossom_maximum_cardinality_matching(), engine, make_gray_scott_seed(), and steps.

Referenced by main(), and TEST().

◆ write_gray_scott_png()

void Aleph::CA::Reproductions::write_gray_scott_png	(	const std::filesystem::path &	path,
		const Gray_Scott_Lattice &	frame
	)

inline

Write a Gray-Scott frame as a native Aleph RGB PNG.

Parameters

path	output path.
frame	frame to encode.

Exceptions

std::runtime_error if the output cannot be written.

Definition at line 501 of file ca_reproduction_support.H.

References ah_runtime_error_if, Aleph::blossom_maximum_cardinality_matching(), gray_scott_rgb(), out, and Aleph::CA::write_png().

Referenced by main().

◆ write_histogram_csv()

void Aleph::CA::Reproductions::write_histogram_csv	(	const std::filesystem::path &	path,
		const std::vector< std::size_t > &	samples
	)

inline

Write an exact discrete histogram as CSV.

Parameters

path	output path.
samples	integral samples to count.

Exceptions

std::runtime_error if the output cannot be written.

Complexity: O(samples.size() log samples.size()).

Definition at line 184 of file ca_reproduction_support.H.

References ah_runtime_error_if, Aleph::blossom_maximum_cardinality_matching(), Aleph::count(), Aleph::histogram(), out, and Aleph::size().

Referenced by main().

Variable Documentation

◆ gosper_gun_cells

constexpr std::array<std::array<std::int64_t, 2>, 36> Aleph::CA::Reproductions::gosper_gun_cells

inlineconstexpr

Initial value:

{{
  {{1, 5}}, {{1, 6}}, {{2, 5}}, {{2, 6}},
  {{11, 5}}, {{11, 6}}, {{11, 7}}, {{12, 4}}, {{12, 8}},
  {{13, 3}}, {{13, 9}}, {{14, 3}}, {{14, 9}},
  {{15, 6}}, {{16, 4}}, {{16, 8}},
  {{17, 5}}, {{17, 6}}, {{17, 7}}, {{18, 6}},
  {{21, 3}}, {{21, 4}}, {{21, 5}},
  {{22, 3}}, {{22, 4}}, {{22, 5}},
  {{23, 2}}, {{23, 6}},
  {{25, 1}}, {{25, 2}}, {{25, 6}}, {{25, 7}},
  {{35, 3}}, {{35, 4}}, {{36, 3}}, {{36, 4}},
}}

Canonical 36-cell Gosper glider gun.

Definition at line 646 of file ca_reproduction_support.H.

Referenced by for_each_gosper_gun_cell().

◆ gray_scott_presets

constexpr std::array<Gray_Scott_Preset, 3> Aleph::CA::Reproductions::gray_scott_presets

inlineconstexpr

Initial value:

{{
  {"spots", 0.0350, 0.0650},
  {"stripes", 0.0250, 0.0500},
  {"mitosis", 0.0367, 0.0649},
}}

Canonical visual presets used by the weekly Gray-Scott reproduction.

Definition at line 426 of file ca_reproduction_support.H.

Referenced by main(), and TEST().

Classes

Typedefs

Functions

Variables

Typedef Documentation

◆ Gray_Scott_Cell

◆ Gray_Scott_Lattice

Function Documentation

◆ decode_native_png()

◆ fit_log_log_histogram()

◆ for_each_gosper_gun_cell()

◆ gray_scott_rgb()

◆ make_gray_scott_seed()

◆ mean_channel_difference()

◆ morans_i_binary()

◆ read_native_png()

◆ run_gray_scott()

◆ write_gray_scott_png()

◆ write_histogram_csv()

Variable Documentation

◆ gosper_gun_cells

◆ gray_scott_presets