Domains

A domain is the region of the plane that gets sampled. See the guide for how they compose.

complexplorer.Domain

Domain(real: tuple[float, float], imag: tuple[float, float], square: bool = True)

Bases: ABC

Abstract base class for complex domains.

A domain represents a region in the complex plane defined by a membership function. The domain can generate meshes for visualization and supports set operations (union, intersection).

Attributes:

Name	Type	Description
window_real	tuple[float, float]	Left and right bounds of the viewing window.
window_imag	tuple[float, float]	Bottom and top bounds of the viewing window.
square	bool	Whether to constrain the viewing window to be square.

Initialize domain with viewing window.

Parameters:

Name	Type	Description	Default
real	tuple[float, float]	Left and right edges of the viewing window.	required
imag	tuple[float, float]	Bottom and top edges of the viewing window.	required
square	bool	If True, constrain viewing window to be square.	True

contains abstractmethod

contains(z: ndarray) -> np.ndarray

Check if points belong to the domain.

Parameters:

Name	Type	Description	Default
z	ndarray	Complex values to test.	required

Returns:

Type	Description
ndarray	Boolean array indicating membership.

spacing

spacing(n: int) -> float

Calculate mesh point spacing.

Parameters:

Name	Type	Description	Default
n	int	Number of points along the longer axis.	required

Returns:

Type	Description
float	Distance between adjacent mesh points.

mesh

mesh(n: int = 500) -> np.ndarray

Generate complex mesh for the viewing window.

Parameters:

Name	Type	Description	Default
n	int	Number of points along the longer axis.	500

Returns:

Type	Description
ndarray	2D array of complex values.

inmask

inmask(n: int = 500) -> np.ndarray

Generate boolean mask for points inside the domain.

Parameters:

Name	Type	Description	Default
n	int	Number of points along the longer axis.	500

Returns:

Type	Description
ndarray	Boolean mask (True for points inside).

outmask

outmask(n: int = 500) -> np.ndarray

Generate boolean mask for points outside the domain.

Parameters:

Name	Type	Description	Default
n	int	Number of points along the longer axis.	500

Returns:

Type	Description
ndarray	Boolean mask (True for points outside).

domain

domain(n: int = 500) -> np.ndarray

Generate mesh with NaN outside the domain.

Parameters:

Name	Type	Description	Default
n	int	Number of points along the longer axis.	500

Returns:

Type	Description
ndarray	Complex mesh with NaN for points outside.

union

union(other: Domain) -> CompositeDomain

Create union with another domain.

Parameters:

Name	Type	Description	Default
other	Domain	Domain to union with.	required

Returns:

Type	Description
CompositeDomain	Union of the two domains.

intersection

intersection(other: Domain) -> CompositeDomain

Create intersection with another domain.

Parameters:

Name	Type	Description	Default
other	Domain	Domain to intersect with.	required

Returns:

Type	Description
CompositeDomain	Intersection of the two domains.

difference

difference(other: Domain) -> CompositeDomain

Create set difference with another domain.

Parameters:

Name	Type	Description	Default
other	Domain	Domain to subtract.	required

Returns:

Type	Description
CompositeDomain	Points in this domain but not in other.

complexplorer.Rectangle

Rectangle(re_length: float, im_length: float, center: complex = 0 + 0j, square: bool = True)

Bases: Domain

Rectangular domain in the complex plane.

Parameters:

Name	Type	Description	Default
re_length	float	Length along the real axis.	required
im_length	float	Length along the imaginary axis.	required
center	complex	Center of the rectangle.	0 + 0j
square	bool	Whether to use square viewing window.	True

Initialize rectangular domain.

contains

contains(z: ndarray) -> np.ndarray

Check if points are inside the rectangle.

Membership is defined by the rectangle's own re_length/im_length about its center — independent of any square-padding applied to the viewing window for display (so a non-square rectangle does not report the padded strips as inside).

complexplorer.Disk

Disk(radius: float, center: complex = 0 + 0j)

Bases: Domain

Circular domain in the complex plane.

Parameters:

Name	Type	Description	Default
radius	float	Radius of the disk.	required
center	complex	Center of the disk.	0 + 0j

Initialize disk domain.

contains

contains(z: ndarray) -> np.ndarray

Check if points are inside the disk.

complexplorer.Annulus

Annulus(inner_radius: float, outer_radius: float, center: complex = 0 + 0j)

Bases: Domain

Annular (ring-shaped) domain in the complex plane.

Parameters:

Name	Type	Description	Default
inner_radius	float	Inner radius of the annulus.	required
outer_radius	float	Outer radius of the annulus.	required
center	complex	Center of the annulus.	0 + 0j

Initialize annulus domain.

contains

contains(z: ndarray) -> np.ndarray

Check if points are inside the annulus.

complexplorer.CompositeDomain

CompositeDomain(domain1: Domain, domain2: Domain, operation: str)

Bases: Domain

Domain formed by set operations on other domains.

This class represents domains created by union, intersection, or difference of two existing domains.

Parameters:

Name	Type	Description	Default
domain1	Domain	First domain.	required
domain2	Domain	Second domain.	required
operation	(union, intersection, difference)	Set operation to apply.	'union'

Initialize composite domain.

tight_bounds property

tight_bounds

Get tight bounds, calculating if necessary.

contains

contains(z: ndarray) -> np.ndarray

Check if points are in the composite domain.

calculate_tight_bounds

calculate_tight_bounds(sample_density: int = 100) -> tuple[tuple[float, float], tuple[float, float]]

Calculate tight bounds by sampling the actual domain.

Parameters:

Name	Type	Description	Default
sample_density	int	Number of sample points along each axis.	100

Returns:

Type	Description
real_bounds, imag_bounds : tuple of tuple	Tight bounds for the composite domain.

mesh

mesh(n: int = 500, use_tight_bounds: bool = True) -> np.ndarray

Generate mesh grid of complex numbers.

For composite domains, can use tight bounds for better fit.

Parameters:

Name	Type	Description	Default
n	int	Number of points along the longer axis.	500
use_tight_bounds	bool	If True, use tight bounds for composite domains.	True

Returns:

Type	Description
ndarray	2D array of complex values.