colormap-theory

Overview

A colormap is a visual encoding function: data value → color. Bad ones (rainbow/jet) create false structure and hide real structure; good ones are perceptually uniform and readable by everyone. This skill covers matching colormap type to data (sequential, diverging, cyclic, qualitative), perceptual uniformity, color-vision-deficiency safety, and practical selection in matplotlib, Plotly, and beyond.

When to use

• Choosing a colormap for a heatmap, contour plot, or 3D surface
• Fixing a figure that uses rainbow/jet
• Encoding signed data (anomalies, differences) with a diverging map
• Making figures readable for colorblind viewers and in grayscale
• Designing a custom colormap for a specific variable

Core concepts

• Perceptual uniformity: equal data steps should look like equal color steps — measured in CIELAB space; viridis, cividis, batlow, and ColorBrewer maps qualify; jet/rainbow emphatically don't (their sharp yellow/cyan bands invent boundaries).

• Map types: sequential (low→high, one hue ramp: viridis, plasma, Blues), diverging (two ramps around a meaningful center: RdBu, Vik, coolwarm — center must be meaningful, e.g., zero anomaly), cyclic (phase/angle: twilight, hsv — ends must match), qualitative/categorical (distinct hues: Tab10, Set2 — never a continuous map for categories).

• Lightness carries the information: the human visual system reads data primarily through lightness variation — a good sequential map is monotonic in lightness; test by converting to grayscale.

• Color-vision deficiency: ~8% of men have red–green deficiency — avoid red–green encodings for critical distinctions; cividis was designed for maximal CVD safety; simulate with CVD simulators before publishing.

• Background matters: dark-background figures need different map tuning than white-background ones; transparency/alpha encodings interact with the background color.

• The data's dynamic range: skewed data need nonlinear normalization (log, power-law, asinh) more than they need a fancy map — fix the mapping before blaming the colors.

• CIELAB and perceptual distance: professional colormap design happens in perceptually uniform spaces (CIELAB, CIECAM02) — equal steps in data become equal ΔE steps in color; RGB interpolation is not perceptually uniform.

• The rainbow's specific sins: non-monotonic lightness (bright yellow/cyan bands), false contours at hue boundaries, and high-frequency name boundaries — each creates structure the data doesn't have.

• Bivariate colormaps: encoding two variables in one map (e.g., value + uncertainty) — powerful but hard to read; use only with a clear legend and when the joint distribution is the message.

Practical workflow

1. Classify your data, then choose

Data	Map type	Examples
Sequential, zero-based	Sequential	viridis, plasma, batlow, Blues
Diverging around meaningful center	Diverging	RdBu_r, Vik, coolwarm
Phase / orientation	Cyclic	twilight, phase
Categories	Qualitative	Tab10, Set2, Okabe-Ito

2. Apply correctly

import matplotlib.pyplot as plt
from matplotlib.colors import CenteredNorm, LogNorm, PowerNorm
# Diverging data around zero: center the map explicitly
plt.imshow(anomaly, cmap="RdBu_r", norm=CenteredNorm(vcenter=0))
# Skewed positive data: log or power-law normalization
plt.imshow(counts, cmap="viridis", norm=LogNorm())

1. Set vmin/vmax (or norm) deliberately — autoscaling to outliers wastes the dynamic range; consider robust limits (percentiles) with out-of-range marking.
2. For diverging maps, center exactly on the meaningful midpoint — an off-center "diverging" map lies.
3. Always include a colorbar with labeled ticks and units — a heatmap without a scale is decoration.

3. Test accessibility

1. Convert to grayscale: is the structure still visible? (If not, the map fails its primary job.)
2. Simulate deuteranopia/protanopia/tritanopia — check that critical distinctions survive.
3. Print in black and white if the venue might — many readers still do.

4. Go beyond defaults when needed

1. For publication series, define one palette per variable and reuse it — consistency builds reader intuition.
2. Build custom maps with perceptually uniform interpolation (viscm, cmaputil) rather than hand-picking RGB stops.
3. Document the colormap and normalization in the caption or methods — reproducibility includes the visual encoding.

5. Design a custom colormap

1. Define the data mapping first (sequential/diverging/cyclic, normalization, center) — the map serves the mapping, not vice versa.
2. Build in a perceptual colorspace: interpolate in CIELAB between chosen control colors, enforcing monotonic lightness for sequential maps.
3. Test with viscm-style diagnostics: perceptual-delta plots should be flat (uniform), and test images (sine waves, wedges) should show no false banding — iterate until clean.

Common pitfalls

• Rainbow/jet: non-uniform, creates false contours, CVD-hostile — the single most common visualization error in science; replace on sight.
• Diverging map without a meaningful center: a diverging map centered at an arbitrary value implies structure that isn't there.
• Continuous map for categories: implies ordering and interpolation between classes that don't exist.
• Autoscale to outliers: one hot pixel flattens everything else — use robust limits.
• Missing colorbar: no scale, no units, no interpretation — always label.
• 3D surface + bad map: perspective distortion plus non-uniform color is double deception — prefer 2D heatmaps with good maps for quantitative reading.
• Alpha as a second encoding: transparency interacts with background color unpredictably — overlapping transparent marks create false dark spots read as data.
• Colormap applied to already-encoded data: double-encoding (e.g., contour lines + colormap of the same variable) adds ink without information — pick one encoding per variable.