Plotting: 2D

matplotlib-backed. All of these return matplotlib objects, so you can keep styling them.

complexplorer.plot

plot(domain: Domain | None = None, func: Callable | None = None, z: ndarray | None = None, f: ndarray | None = None, resolution: int = 400, cmap: Colormap | None = None, ax: Axes | None = None, title: str | None = None, filename: str | None = None, legend: bool = False) -> Axes

Plot complex function as domain coloring.

This function provides a convenient interface for plotting complex functions using domain coloring. Either provide a domain and function, or directly provide the mesh arrays z and f.

Parameters:

Name	Type	Description	Default
domain	Domain	Domain object. If None, z must be provided.	None
func	callable	Complex function. If None, f must be provided.	None
z	ndarray	2D array of complex domain values.	None
f	ndarray	2D array of complex codomain values.	None
resolution	int	Resolution (number of points along longest edge).	400
cmap	Colormap	Colormap to use. Defaults to enhanced phase portrait.	None
ax	Axes	Matplotlib axes to plot on.	None
title	str	Plot title.	None
filename	str	If provided, save the figure to this file (honored whether or not ax is supplied).	None
legend	bool	If True, draw a phase-wheel legend inset (the unit disk colored by the active colormap) in the upper-right corner.	False

Returns:

Type	Description
Axes	The matplotlib axes drawn on (always returned).

Examples:

>>> # Using domain and function
>>> domain = Rectangle(4, 4)
>>> plot(domain, lambda z: z**2, resolution=200)

>>> # Using pre-computed arrays
>>> z = domain.mesh(200)
>>> f = z**2
>>> plot(z=z, f=f)

complexplorer.pair_plot

pair_plot(domain: Domain | None = None, func: Callable | None = None, z: ndarray | None = None, f: ndarray | None = None, resolution: int = 400, cmap: Colormap | None = None, title: str | None = None, figsize: tuple[float, float] = (10, 5), filename: str | None = None, legend: bool = False) -> Figure

Plot domain and codomain side by side.

Parameters:

Name	Type	Description	Default
domain	Domain	Domain object. If None, z must be provided.	None
func	callable	Complex function. If None, f must be provided.	None
z	ndarray	2D array of complex domain values.	None
f	ndarray	2D array of complex codomain values.	None
resolution	int	Resolution (number of points along longest edge).	400
cmap	Colormap	Colormap to use. Defaults to enhanced phase portrait.	None
title	str	Overall figure title.	None
figsize	tuple	Figure size (width, height).	(10, 5)
filename	str	If provided, save figure to this file.	None
legend	bool	If True, draw a phase-wheel legend inset on the codomain panel.	False

Returns:

Type	Description
Figure	The matplotlib figure.

complexplorer.riemann_chart

riemann_chart(func: Callable, domain: Domain | None = None, resolution: int = 100, show_south_hemisphere: bool = True, project_from_north: bool = True, cmap: Colormap | None = None, ax: Axes | None = None, margin: float = 0.05, unit_circle_width: float = 1.0) -> Axes

Plot phase portrait on Riemann hemisphere.

This function visualizes a complex function on either hemisphere of the Riemann sphere using stereographic projection.

Parameters:

Name	Type	Description	Default
func	callable	Complex function to visualize.	required
domain	Domain	If provided, chart samples outside this domain are painted with the colormap's out-of-domain color.	None
resolution	int	Resolution for the mesh.	100
show_south_hemisphere	bool	If True, show lower hemisphere; else upper.	True
project_from_north	bool	If True, use north pole projection (standard).	True
cmap	Colormap	Colormap to use.	None
ax	Axes	Matplotlib axes to plot on.	None
margin	float	Margin around unit disk (0 to 0.5).	0.05
unit_circle_width	float	Width of unit circle highlight.	1.0

Returns:

Type	Description
Axes	The matplotlib axes used.

complexplorer.riemann_hemispheres

riemann_hemispheres(func: Callable, title: str | None = None, resolution: int = 400, margin: float = 0.05, unit_circle_width: float = 1.0, figsize: tuple[float, float] = (12, 4), filename: str | None = None) -> Figure

Plot both hemispheres of the Riemann sphere.

Parameters:

Name	Type	Description	Default
func	callable	Complex function to visualize.	required
title	str	Overall figure title.	None
resolution	int	Resolution for the mesh.	400
margin	float	Margin around unit disk.	0.05
unit_circle_width	float	Width of unit circle highlight.	1.0
figsize	tuple	Figure size (width, height).	(12, 4)
filename	str	If provided, save figure to this file.	None

Returns:

Type	Description
Figure	The matplotlib figure.