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Core API Reference

The core module contains fundamental classes and functions for working with complex functions.

Domains

::: complexplorer.core.domain options: show_root_heading: true show_source: true heading_level: 3 members: - Domain - Rectangle - Disk - Annulus

Domain Base Class

All domains inherit from the Domain base class and provide:

  • contains(z): Check if points are in the domain
  • sample(resolution): Generate grid of points for visualization
  • Proper representation and string formatting

Rectangle

Rectangular domain in the complex plane.

Example: 

import complexplorer as cp

# Square centered at origin
domain = cp.Rectangle(4, 4)

# Rectangle centered at 1+1j
domain = cp.Rectangle(re_length=6, im_length=4, center=1+1j)

Disk

Circular domain in the complex plane.

Example: 

# Unit disk
domain = cp.Disk(radius=1)

# Disk centered at 2j
domain = cp.Disk(radius=3, center=2j)

Annulus

Ring-shaped domain between two circles.

Example: 

# Annulus excluding origin
domain = cp.Annulus(inner_radius=0.5, outer_radius=3)

# Off-center annulus
domain = cp.Annulus(inner_radius=1, outer_radius=2, center=1+1j)

Colormaps

::: complexplorer.core.colormap options: show_root_heading: true show_source: true heading_level: 3 members: - Colormap - Phase - OklabPhase - PerceptualPastel - Isoluminant - CubehelixPhase - AnalogousWedge - DivergingWarmCool - InkPaper - EarthTopographic - FourQuadrant - Chessboard - PolarChessboard - LogRings

Colormap Base Class

All colormaps inherit from Colormap and provide:

  • __call__(z): Map complex values to RGB colors
  • hsv(z): Map complex values to HSV colors (internal)
  • rgb(z): Convert HSV to RGB (internal)

Classic Phase Portraits

Phase

The fundamental phase portrait colormap.

Example: 

# Basic phase portrait
cmap = cp.Phase()

# Enhanced with 6 phase sectors
cmap = cp.Phase(phase_sectors=6)

# Auto-scaled for square cells
cmap = cp.Phase(phase_sectors=6, auto_scale_r=True, scale_radius=0.8)

# With modulus contours
cmap = cp.Phase(r_linear_step=0.5)
cmap = cp.Phase(r_log_base=2.0)

Parameters: - phase_sectors: Number of angular wedges (0 = none) - r_linear_step: Linear modulus contour spacing (0 = none) - r_log_base: Logarithmic modulus base (0 = none) - v_base: Minimum brightness (default 0.5) - auto_scale_r: Auto-calculate spacing for square cells - scale_radius: Reference radius for auto-scaling - emphasize_unit_circle: Highlight |z| = 1 - unit_circle_strength: Emphasis strength

OklabPhase

Perceptually uniform phase portrait using OKLAB color space.

Example: 

# Smooth OKLAB phase
cmap = cp.OklabPhase(L=0.7, C=0.35)

# Enhanced with phase sectors
cmap = cp.OklabPhase(phase_sectors=6, auto_scale_r=True, enhanced=True)

Parameters: - L: Lightness (0 to 1, default 0.7) - C: Chroma (0 to 0.5, default 0.35) - enhanced: Enable sawtooth modulation - phase_offset: Color rotation offset - Plus all Phase parameters

Perceptually Uniform Colormaps

PerceptualPastel

Elegant OkLCh-based pastels with uniform brightness.

Example: 

cmap = cp.PerceptualPastel()
cmap = cp.PerceptualPastel(phase_sectors=6, auto_scale_r=True)
cmap = cp.PerceptualPastel(L_center=0.60, C=0.08)

Isoluminant

Constant lightness, phase encoded purely in hue.

Example: 

cmap = cp.Isoluminant()  # With contours
cmap = cp.Isoluminant(show_contours=False)  # Pure isoluminant

CubehelixPhase

Grayscale-safe colormap for scientific publishing.

Example: 

cmap = cp.CubehelixPhase()
cmap = cp.CubehelixPhase(start=0.5, rotations=1.5)

Artistic Colormaps

AnalogousWedge

Harmonious colors from compressed hue range.

Example: 

cmap = cp.AnalogousWedge(H_center=0.55, H_wedge=0.2)  # Ocean
cmap = cp.AnalogousWedge(H_center=0.05, H_wedge=0.15)  # Sunset

DivergingWarmCool

Warm/cool divergence for cartographic style.

Example: 

cmap = cp.DivergingWarmCool()

InkPaper

Minimalist near-monochrome with subtle phase tints.

Example: 

cmap = cp.InkPaper()
cmap = cp.InkPaper(C_min=0.01, C_max=0.04)

EarthTopographic

Terrain-inspired with earth tones and hillshade.

Example: 

cmap = cp.EarthTopographic()
cmap = cp.EarthTopographic(H_water=200, H_land=30)

FourQuadrant

Bauhaus-inspired with 4 color anchors.

Example: 

cmap = cp.FourQuadrant()

Grid & Pattern Colormaps

Chessboard

Black/white grid aligned with Re/Im axes.

Example: 

cmap = cp.Chessboard()
cmap = cp.Chessboard(spacing=0.5)

PolarChessboard

Black/white pattern in polar coordinates.

Example: 

cmap = cp.PolarChessboard()
cmap = cp.PolarChessboard(phase_sectors=12, spacing=0.5)
cmap = cp.PolarChessboard(phase_sectors=8, r_log=2.0)

LogRings

Logarithmic concentric black/white rings.

Example: 

cmap = cp.LogRings()
cmap = cp.LogRings(log_spacing=0.3)

Modulus Scaling

::: complexplorer.core.scaling options: show_root_heading: true show_source: true heading_level: 3

Modulus scaling functions control how |z| is mapped to height in 3D visualizations and Riemann sphere relief maps.

Available Modes

  • constant: Flat (no height variation)
  • linear: Direct |z| mapping
  • arctan: Smooth bounded scaling (recommended)
  • logarithmic: log(1 + |z|) - emphasizes poles/zeros
  • adaptive: Auto-adjust to data range
  • linear_clamp: Linear with maximum cap
  • power: |z|^p mapping
  • sigmoid: S-curve mapping
  • hybrid: Combination modes

Example: 

from complexplorer.core.scaling import apply_modulus_scaling

# Apply arctan scaling
heights = apply_modulus_scaling(z_values, mode='arctan')

# With custom parameters
heights = apply_modulus_scaling(z_values, mode='arctan',
                                params={'r_min': 0.3, 'r_max': 0.9})

Core Functions

::: complexplorer.core.functions options: show_root_heading: true show_source: true heading_level: 3

Fundamental complex function utilities.

Phase and Modulus

Functions for extracting phase (argument) and modulus (magnitude):

from complexplorer.core.functions import phase, modulus

z = 1 + 1j
arg = phase(z)  # pi/4
mag = modulus(z)  # sqrt(2)

Sawtooth Function

Used for enhanced phase portraits:

from complexplorer.core.functions import sawtooth

# Create phase sectors
brightness = sawtooth(phase_value, n_sectors=6)

Stereographic Projection

Maps complex plane to/from Riemann sphere:

from complexplorer.core.functions import stereographic_to_sphere, sphere_to_stereographic

# Map to sphere
x, y, z_coord = stereographic_to_sphere(complex_values)

# Map back to plane
w = sphere_to_stereographic(x, y, z_coord)

Color Utilities

::: complexplorer.core.color_utils options: show_root_heading: true show_source: true heading_level: 3

Color space conversions and utilities.

Color Space Conversions

from complexplorer.core.color_utils import hsv_to_rgb, oklab_to_rgb, oklch_to_rgb

# HSV to RGB
rgb = hsv_to_rgb(h, s, v)

# OKLAB to RGB
rgb = oklab_to_rgb(L, a, b)

# OkLCh to RGB
rgb = oklch_to_rgb(L, C, h)

Constants

::: complexplorer.core.constants options: show_root_heading: true show_source: true heading_level: 3

Mathematical and visualization constants.

from complexplorer.core.constants import PI, TAU, E, I

# Mathematical constants
two_pi = TAU
imaginary_unit = I
eulers_number = E

See Also