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Definitions

• Color gradient is a set of colors arranged in a linear order ( ordered)
• A continuous colormap is a curve through a colorspace

Strict definition

A colormap² is a function which associate a real value r with point c in color space C {\displaystyle C}

f : [ r m i n , r m a x ] ⊂ R → C {\displaystyle f:[r_{min},r_{max}]\subset \mathbf {R} \to C}

which is defined by:

• a colorspace C
• an increasing sequence of sampling points r 0 < . . . < r m ∈ [ r m i n , r m a x ] {\displaystyle r_{0}<...<r_{m}\in [r_{min},r_{max}]}
• a series of values in the colorspace c 0 , . . . , c m ∈ C {\displaystyle c_{0},...,c_{m}\in C}
• the mapping f ( r i ) = c i , i = 0 , . . . , m {\displaystyle f(r_{i})=c_{i},i=0,...,m}
• a rule for interpolating the intermediate values r i − 1 < r < r i ∈ [ r m i n , r m a x ] {\displaystyle r_{i-1}<r<r_{i}\in [r_{min},r_{max}]}

where:

• r is a real number r ∈ [ r m i n , r m a x ] ⊂ R {\displaystyle r\in [r_{min},r_{max}]\subset \mathbf {R} }
• R {\displaystyle \mathbf {R} } is a set of real numbers
• c is a color = point in colorspace C

Types

Criteria for classification:

• dimension
• discrete ( classed, color scheme) ³ / continuous
• shape
• range: full or limited. Example : pastel color with limited range of saturation.
• perceptual uniformity⁴
• order
  • ordered (sequential) and non-ordered (categorical)
  • perceptual order
• readability for color-vision deficient or color-blind people ( colorblind-friendly)
• color space
• color depth

Dimension

• 1D
• 2D:⁵ Multivariate map, bivariate or trivariate
• 3D

Shapes

Axial gradients

An axial color gradient (sometimes also called a linear color gradient) is specified by two points, and a color at each point. The colors along the line through those points are calculated using linear interpolation, then extended perpendicular to that line. In digital imaging systems, colors are typically interpolated in an RGB color space, often using gamma compressed RGB color values, as opposed to linear. CSS and SVG both support linear gradients.⁶⁷

Radial gradients

A radial gradient is specified as a circle that has one color at the edge and another at the center. Colors are calculated by linear interpolation based on distance from the center. This can be used to approximate the diffuse reflection of light from a point source by a sphere. Both CSS and SVG support radial gradients.⁸⁹

Conic gradients

Conic or conical gradients are gradients with color transitions rotated around a center point (rather than radiating from the center). Example conic gradients include pie charts and color wheels.¹⁰ Conic gradients are sometimes called "sweep gradients" (for example in the OpenType specification) or angular gradients.

Other shapes

In vector graphics polygon meshes can be used, e.g., Adobe Illustrator supported gradient meshes.

Color space

Effect of color space

The appearance of a gradient not only varies by the color themselves, but also by the color space the calculation is performed in. The problem usually becomes important for two reasons:

• Gamma correction to a color space. With a typical γ of around 2, it is easy to see that a gamma-enabled color space will blend darker than a linear-intensity color space, since the sum of squares of two numbers is never more than the square of their sum. The effect is most apparent in blending complementary colors like red and green, with the middle color being a dark color instead of the expected yellow.¹¹¹² The radial and conic examples on this page clearly exhibit this error.
• Handling of other perceptual properties. In information visualization, it is undesirable to have a supposedly "flat" gradient show non-monotonic variations in lightness and saturation along the way. This is because human vision emphasizes these qualities, causing bias or confusion in interpretation.¹³

A "linear" blend would match physical light blending and has been the standard in game engines for a long time.¹⁴ On the web, however, it has long been neglected for both color gradients and image scaling.¹⁵ Such a blend still has a subtle difference from one done in a perceptually-uniform color space.¹⁶

Examples

HSV rainbow

Applications

• represent quantitative or ordinal values, like in heat maps. More precise description is in color box.¹⁷
  • data visualisation
• fill a region:¹⁸ many window managers allow the screen background to be specified as a gradient. The colors produced by a gradient vary continuously with position, producing smooth color transitions.
• visualize the progression of an extended computer operation, such as a download, file transfer, or installation. See progress bar
• Coloring cartographic maps

See also

Wikibooks has a book on the topic of: Colors/Color gradient Wikimedia Commons has media related to Color gradient.

• Bokashi (printing)
• Color banding
• Color difference
• Color grading
• Color mapping; a function that maps (transforms) the colors of one image to the colors of another image
• Diffusion curve
• dithering
• Image gradient
• Mach banding
• Ombré
• Palette; a finite set of colors in no particular order
• Perceptually uniform color spaces
• Posterization
• Color chart
• swatch books ( like in Paper color swatch book or RAL CLASSIC K5 colour fan or Pantone color guides)

References

1. cssgradient: CSS Gradient Swatches https://cssgradient.io/swatches/ ↩

2. The Good, the Bad, and the Ugly: A Theoretical Framework for the Assessment of Continuous Colormaps by Roxana Bujack, Terece L. Turton, Francesca Samsel, Colin Ware https://datascience.dsscale.org/wp-content/uploads/2017/10/TheGoodtheBadandtheUgly.pdf ↩

3. which-color-scale-to-use-in-data-vis by Lisa Charlotte Rost https://blog.datawrapper.de/which-color-scale-to-use-in-data-vis/ ↩

4. Fabio Crameri: Scientific colour maps https://www.fabiocrameri.ch/visualisation/#ws-block-features-with-aside-icons-3-cols-mQE9rwEn ↩

5. A survey and task-based quality assessment of static 2D colormaps Author(s): Bernard, Jürgen; Steiger, Martin; Mittelstädt, Sebastian; Thum, Simon; Keim, Daniel; Kohlhammer, Jörn, In Kao, David L. (Ed.) ; Society for Imaging Science and Technology -IS&T-; Society of Photo-Optical Instrumentation Engineers -SPIE-, Bellingham/Wash.: Visualization and Data Analysis 2015 : 9–11 February 2015, San Francisco, California Bellingham, WA: SPIE, 2015 (Proceedings of SPIE 9397) ISBN 9781628414875 http://publica.fraunhofer.de/documents/N-337230.html ↩

6. Linear Gradients in "CSS Image Values and Replaced Content Module Level 3", W3C Candidate Recommendation, April 2012 http://www.w3.org/TR/2012/CR-css3-images-20120417/#linear-gradients ↩

7. Linear Gradients in "SVG 1.1 (Second Edition)", W3C Recommendation, August 2011 http://www.w3.org/TR/2011/REC-SVG11-20110816/pservers.html#LinearGradients ↩

8. Radial Gradients in "CSS Image Values and Replaced Content Module Level 3", W3C Candidate Recommendation, April 2012 http://www.w3.org/TR/2012/CR-css3-images-20120417/#radial-gradients ↩

9. Radial Gradients in "SVG 1.1 (Second Edition)", W3C Recommendation, August 2011 http://www.w3.org/TR/2011/REC-SVG11-20110816/pservers.html#RadialGradients ↩

10. mozilla docs: CSS conic-gradient https://developer.mozilla.org/en-US/docs/Web/CSS/conic-gradient ↩

11. Minute Physics (March 20, 2015). "Computer Color is Broken". YouTube. Archived from the original on December 21, 2021. https://www.youtube.com/watch?v=LKnqECcg6Gw ↩

12. Novak, John (September 21, 2016). "What every coder should know about gamma". https://blog.johnnovak.net/2016/09/21/what-every-coder-should-know-about-gamma/ ↩

13. Zeileis, Achim; Fisher, Jason C.; Hornik, Kurt; Ihaka, Ross; McWhite, Claire D.; Murrell, Paul; Stauffer, Reto; Wilke, Claus O. (2019). "colorspace: A Toolbox for Manipulating and Assessing Colors and Palettes". Journal of Statistical Software. 96. arXiv:1903.06490. doi:10.18637/jss.v096.i01. https://doi.org/10.18637%2Fjss.v096.i01 ↩

14. "Chapter 24. The Importance of Being Linear". NVIDIA Developer. https://developer.nvidia.com/gpugems/gpugems3/part-iv-image-effects/chapter-24-importance-being-linear ↩

15. "Web color is still broken". https://webcolorisstillbroken.com ↩

16. "How software gets color wrong". bottosson.github.io. December 3, 2020. https://bottosson.github.io/posts/colorwrong/ ↩

17. gnuplot docs 4.2 node167: Color box[permanent dead link‍] https://gnuplot.sourceforge.net/docs%204.2/node167.html ↩

18. Eisenberg, J. David (2002). SVG Essentials. O'Reilly Media. p. 107. ISBN 0-596-00223-8. 0-596-00223-8 ↩