Colormaps¶

Colormaps define how complex values are transformed into colors for visualization. Complexplorer offers a rich collection of colormaps, from classic phase portraits to modern perceptually-uniform schemes.

Quick Overview¶

Colormap Family	Best For	Key Feature
Phase	General purpose	Classic HSV phase portrait
OklabPhase	Perceptual accuracy	OKLAB color space
PerceptualPastel	Print/presentations	Elegant pastels
Isoluminant	Phase structure	Constant brightness
CubehelixPhase	Scientific publishing	Grayscale-safe
AnalogousWedge	Aesthetic appeal	Harmonious hues
DivergingWarmCool	Cartographic style	Warm/cool divergence
InkPaper	Minimalist	Near-monochrome
EarthTopographic	Natural aesthetics	Terrain-inspired
FourQuadrant	Geometric clarity	Bauhaus-inspired
Chessboard	Grid visualization	Cartesian grid
PolarChessboard	Polar structure	Circular grid
LogRings	Magnitude focus	Logarithmic rings

Classic Phase Portraits¶

Phase¶

The fundamental phase portrait colormap. Maps complex phase (argument) to hue, optionally enhanced with modulus contours.

import complexplorer as cp

f = lambda z: (z**2 - 1) / (z**2 + 1)
domain = cp.Rectangle(4, 4)

# Basic phase portrait
cmap = cp.Phase()
cp.plot(domain, f, cmap=cmap)

# Enhanced with 6 phase sectors
cmap = cp.Phase(phase_sectors=6)
cp.plot(domain, f, cmap=cmap)

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

# With linear modulus rings
cmap = cp.Phase(r_linear_step=0.5)
cp.plot(domain, f, cmap=cmap)

# With logarithmic modulus rings
cmap = cp.Phase(r_log_base=2.0)
cp.plot(domain, f, cmap=cmap)

Parameters: - phase_sectors: Number of phase sectors (creates sawtooth brightness patterns) - r_linear_step: Linear modulus contour spacing - r_log_base: Logarithmic modulus contour base - v_base: Minimum brightness (0 to 1) - auto_scale_r: Auto-calculate r_linear_step for square cells - scale_radius: Reference radius for auto-scaling - emphasize_unit_circle: Highlight |z|=1 - unit_circle_strength: Strength of unit circle emphasis

Use Cases: - General purpose visualization - Teaching complex analysis - Exploring function behavior

OklabPhase¶

Perceptually uniform phase portrait using the OKLAB color space. Better color consistency than standard HSV-based Phase colormap.

# Smooth OKLAB phase (cplot-like)
cmap = cp.OklabPhase(L=0.7, C=0.35)
cp.plot(domain, f, cmap=cmap)

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

# Adjust lightness and chroma
cmap = cp.OklabPhase(L=0.6, C=0.25, phase_sectors=8)
cp.plot(domain, f, cmap=cmap)

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

Use Cases: - When color perception matters - Comparing multiple visualizations - High-quality publications

Perceptually Uniform Colormaps¶

PerceptualPastel¶

Elegant OkLCh-based pastels with uniform perceived brightness. Non-fluorescent colors ideal for print.

# Default pastels
cmap = cp.PerceptualPastel()
cp.plot(domain, f, cmap=cmap)

# Enhanced with phase sectors
cmap = cp.PerceptualPastel(phase_sectors=6, auto_scale_r=True)
cp.plot(domain, f, cmap=cmap)

# Adjust pastel intensity
cmap = cp.PerceptualPastel(L_center=0.60, C=0.08)
cp.plot(domain, f, cmap=cmap)

Key Parameters: L_center, L_range, C (chroma)

Isoluminant¶

Constant lightness with phase encoded purely in hue. Optional thin contour lines for modulus.

cmap = cp.Isoluminant()  # With contours
cmap = cp.Isoluminant(show_contours=False)  # Pure isoluminant
cmap = cp.Isoluminant(L=0.7, C_min=0.15, C_max=0.20)

Key Parameters: L, C_min, C_max, show_contours, contour_period

CubehelixPhase¶

Scientific coloring that prints well in grayscale.

cmap = cp.CubehelixPhase()
cmap = cp.CubehelixPhase(start=0.5, rotations=1.5, saturation=0.8)

Key Parameters: start, rotations, saturation, L_min, L_max

Artistic Colormaps¶

AnalogousWedge¶

Harmonious colors from compressed hue range (20-50% of wheel).

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

Key Parameters: H_center, H_wedge, S, V_base

DivergingWarmCool¶

Warm for positive phase, cool for negative.

cmap = cp.DivergingWarmCool()  # Amber to indigo

Key Parameters: H_warm, H_cool, L_center, C_min, C_max

InkPaper¶

Nearly monochrome with subtle phase tints.

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

Key Parameters: L_min, L_max, C_min, C_max

EarthTopographic¶

Terrain-inspired with earth tones and hillshade.

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

Key Parameters: H_water, H_land, add_hillshade

FourQuadrant¶

Bauhaus-inspired with 4 color anchors.

cmap = cp.FourQuadrant()  # Red, green, cyan, magenta

Key Parameters: H_anchors, C, L_min, L_max

Grid & Pattern Colormaps¶

Chessboard¶

Black/white grid aligned with Re/Im axes.

cmap = cp.Chessboard()
cmap = cp.Chessboard(spacing=0.5)  # Finer grid

Use: Visualize Cartesian grid distortion

PolarChessboard¶

Black/white pattern in polar coordinates.

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

Use: Visualize polar structure

LogRings¶

Logarithmic concentric black/white rings.

cmap = cp.LogRings()
cmap = cp.LogRings(log_spacing=0.3)  # Tighter rings

Use: Focus on magnitude structure

Enhanced Phase Portraits¶

Many colormaps support enhanced phase portraits:

Phase Sectors¶

Create sawtooth brightness in angular wedges:

cmap = cp.Phase(phase_sectors=6)

Modulus Contours¶

Brightness variations at specific |z| values:

cmap = cp.Phase(r_linear_step=0.5)  # Linear: 0.5, 1.0, 1.5, ...
cmap = cp.Phase(r_log_base=2.0)     # Log: 1, 2, 4, 8, ...

Auto-Scaled Square Cells¶

Automatically calculate spacing for square cells:

cmap = cp.Phase(phase_sectors=6, auto_scale_r=True, scale_radius=0.8)

Choosing the Right Colormap¶

By Purpose¶

Learning/Teaching: Phase, Chessboard, PolarChessboard

Publications: PerceptualPastel, CubehelixPhase, Isoluminant

Presentations: PerceptualPastel, InkPaper, AnalogousWedge

Exploration: Phase with auto_scale_r, OklabPhase, LogRings

Artistic: EarthTopographic, FourQuadrant, DivergingWarmCool

By Function Type¶

Rational (poles/zeros): Enhanced Phase, LogRings, Isoluminant

Periodic/Trig: Phase with contours, PolarChessboard, PerceptualPastel

Multi-valued: Phase with sectors, Chessboard, OklabPhase

Advanced Usage¶

Brightness Control¶

# Darker base for contrast (default 0.5)
cmap = cp.Phase(phase_sectors=6, v_base=0.3)

# Lighter base for pastel look
cmap = cp.Phase(phase_sectors=6, v_base=0.7)

Out-of-Domain Coloring¶

# Custom color for points outside domain (HSV)
cmap = cp.Phase(out_of_domain_hsv=(0.6, 0.1, 0.95))

Combining Enhancements¶

# Both phase sectors AND modulus rings
cmap = cp.Phase(phase_sectors=6, r_linear_step=0.5, v_base=0.4)

Quick Examples¶

import complexplorer as cp

f = lambda z: (z**2 - 1) / (z**2 + 1)
domain = cp.Rectangle(4, 4)

# Classic enhanced phase
cp.plot(domain, f, cmap=cp.Phase(phase_sectors=6, auto_scale_r=True))

# Perceptual pastel
cp.plot(domain, f, cmap=cp.PerceptualPastel(phase_sectors=6, auto_scale_r=True))

# Scientific
cp.plot(domain, f, cmap=cp.CubehelixPhase(phase_sectors=6, auto_scale_r=True))

# Minimalist
cp.plot(domain, f, cmap=cp.InkPaper())

# Grid
cp.plot(domain, f, cmap=cp.Chessboard(spacing=0.5))

# Magnitude
cp.plot(domain, f, cmap=cp.LogRings())

Tips¶

Start with Phase(phase_sectors=6, auto_scale_r=True) for exploration
Use PerceptualPastel for presentations and print
Use CubehelixPhase for scientific publications
Use Isoluminant to focus purely on phase structure
Use Chessboard/PolarChessboard to understand grid distortion
Adjust v_base to control contrast (lower = more contrast)
Try InkPaper for elegant, minimalist visualizations
Use OklabPhase when color perception accuracy matters

Next Steps¶

2D Plotting - Apply colormaps in 2D
3D Plotting - Use colormaps for 3D surfaces
Riemann Sphere - Colormaps on the sphere
Domains - Domain selection
Quick Start - Basic examples