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Tol Color Schemes

Qualitative, diverging, and sequential color schemes by Paul Tol.

Date Posted September 24, 2018 Last Updated July 20, 2023
Author Jason C Fisher
Reading Time 8 minutes Share


Choosing colors for a graphic is a bit like taking a trip down the rabbit hole, that is, it can take much longer than expected and be both fun and frustrating at the same time. Striking a balance between colors that look good to you and your audience is important. Keep in mind that color blindness affects many individuals throughout the world and it is incumbent on you to choose a color scheme that works in color-blind vision. Luckily there are a number of excellent R packages that address this very issue, such as the colorspace, RColorBrewer, and viridis packages. And because this is R, where diversity is king, why not offer one more function for creating color blind friendly palettes.

Let me introduce the GetTolColors function in the R-package inlmisc. This function generates a vector of colors from qualitative, diverging, and sequential color schemes by Paul Tol (2018). The original inspiration for developing this function came from Peter Carl’s blog post describing color schemes from an older issue of Paul Tol’s Technical Note (issue 2.2, released Dec. 2012). And the qualitative color schemes described in his blog post found their way into the ptol_pal function in the R-package ggthemes. My intent with this document is to exhibit the latest Tol color schemes (issue 3.0, released May 2018) and show that they are not only visually pleasing but also well thought out.

To get started, install the inlmisc package from CRAN using the command:

if (system.file(package = "inlmisc", lib.loc = .libPaths()) == "")
  utils::install.packages("inlmisc", dependencies = TRUE)

And if you’re so inclined, read through the function documentation.

utils::help("GetTolColors", package = "inlmisc")

Like almost every other R function used to create a color palette, GetTolColors takes as its first argument the number of colors to be in the returned palette (n). For example, the following command generates a palette of 10 colors using default values for function arguments.

cols <- inlmisc::GetTolColors(n = 10)
##  [1] "#E8ECFB" "#B997C7" "#824D99" "#4E78C4" "#57A2AC" "#7EB875" "#D0B541"
##  [8] "#E67F33" "#CE2220" "#521A13"
## attr(,"bad")
## [1] "#666666"
## attr(,"call")
## GetTolColors(n = 10, scheme = "smooth rainbow", alpha = NULL, 
##     start = 0, end = 1, bias = 1, reverse = FALSE, blind = NULL, 
##     gray = FALSE)
## attr(,"class")
## [1] "Tol"       "character"

Returned from the function is an object of class "Tol" that inherits behavior from the "character" class. A Tol-class object is comprised of a character vector of n colors and the following attributes: "names", the informal names assigned to colors in the palette, where a value of NULL indicates that no color names were specified for the scheme; "bad", the color meant for bad data or data gaps, where a value of NA indicates that no bad color was specified for the scheme; and "call", the unevaluated function call that can be used to reproduce the palette.

A plot method is provided for the Tol class that displays the palette of colors.

Display colors in palette.

Display colors in palette.

The main title for the plot will always indicate the n and scheme argument values used to create the palette. Where scheme is the name of the color scheme, its default value is "smooth rainbow". All other arguments are only included in the title if their specified value differs from their default value. The label positioned below each shaded rectangle gives the informal color name.

Color Schemes

Tal (2018) defines 13 color schemes: 7 for qualitative data, 3 for diverging data, and 3 for sequential data (table 1). The maximum number of colors in a generated palette is dependent on the user selected scheme. For example, the "discrete rainbow" scheme can have at most 23 colors in its palette (n ≤ 23). Whereas a continuous (or interpolated) version of the "smooth rainbow" scheme is available that has no upper limit on values of n. About half of the schemes include a color meant for bad data.

Table 1. Suggested data type for color schemes and the characteristics of generated palettes.

[Data type: is the type of data being represented, either qualitative, diverging, or sequential. Maximum n: is the maximum number of colors in a generated palette. And the maximum n value when palette colors are designed for gray-scale conversion is enclosed in parentheses. Bad data: whether a color has been provided for bad data. Abbreviations: ---, no limit placed on the number of colors in the palette]
Data typeColor schemeMaximum nBad data
Qualitativebright7 (3)no
vibrant7 (4)no
muted9 (5)yes
ground cover14no
discrete rainbow23yes
smooth rainbow---yes


Qualitative color schemes "bright", "vibrant", "muted", "pale", "dark", and "light" are appropriate for representing nominal or categorical data.

op <- graphics::par(mfrow = c(6, 1), oma = c(0, 0, 0, 0))
plot(inlmisc::GetTolColors(7, scheme = "bright"))
plot(inlmisc::GetTolColors(7, scheme = "vibrant"))
plot(inlmisc::GetTolColors(9, scheme = "muted"))
plot(inlmisc::GetTolColors(6, scheme = "pale"))
plot(inlmisc::GetTolColors(6, scheme = "dark"))
plot(inlmisc::GetTolColors(9, scheme = "light"))
Qualitative color schemes

Qualitative color schemes

And the "ground cover" scheme is a color-blind safe version of the AVHRR global land cover classification color scheme (Hansen and others, 1998).

op <- graphics::par(oma = c(1, 0, 0, 0), cex = 0.7)
plot(inlmisc::GetTolColors(14, scheme = "ground cover"))
Land cover color scheme

Land cover color scheme

Note that schemes "pale", "dark", and "ground cover" are intended to be accessed in their entirety and subset using vector element names.


Diverging color schemes "sunset", "BuRd", and "PRGn" are appropriate for representing quantitative data with progressions outward from a critical midpoint of the data range.

op <- graphics::par(mfrow = c(6, 1), oma = c(0, 0, 0, 0))
plot(inlmisc::GetTolColors( 11, scheme = "sunset"))
plot(inlmisc::GetTolColors(256, scheme = "sunset"))
plot(inlmisc::GetTolColors(  9, scheme = "BuRd"))
plot(inlmisc::GetTolColors(256, scheme = "BuRd"))
plot(inlmisc::GetTolColors(  9, scheme = "PRGn"))
plot(inlmisc::GetTolColors(256, scheme = "PRGn"))
Diverging color schemes

Diverging color schemes


Sequential schemes "YlOrBr", "discrete rainbow", and "smooth rainbow" are appropriate for representing quantitative data that progress from small to large values.

op <- graphics::par(mfrow = c(5, 1), oma = c(0, 0, 0, 0))
plot(inlmisc::GetTolColors(  9, scheme = "YlOrBr"))
plot(inlmisc::GetTolColors(256, scheme = "YlOrBr"))
plot(inlmisc::GetTolColors( 23, scheme = "discrete rainbow"))
plot(inlmisc::GetTolColors( 34, scheme = "smooth rainbow"))
plot(inlmisc::GetTolColors(256, scheme = "smooth rainbow"))
Sequential color schemes

Sequential color schemes

Alpha Transparency

The transparency (or opacity) of palette colors is specified using the alpha argument. Values range from 0 (fully transparent) to 1 (fully opaque).

op <- graphics::par(mfrow = c(5, 1), oma = c(0, 0, 0, 0))
plot(inlmisc::GetTolColors(34, alpha = 1.0))
plot(inlmisc::GetTolColors(34, alpha = 0.8))
plot(inlmisc::GetTolColors(34, alpha = 0.6))
plot(inlmisc::GetTolColors(34, alpha = 0.4))
plot(inlmisc::GetTolColors(34, alpha = 0.2))
Adjust alpha transparency of colors.

Adjust alpha transparency of colors.

Color Levels

Color levels are used to limit the range of colors in a scheme—applies only to schemes that can be interpolated, which includes the "sunset", "BuRd", "PRGn", "YlOrBr", and "smooth rainbow" schemes. Starting and ending color levels are specified using the start and end arguments, respectively. Values range from 0 to 1 and represent a fraction of the scheme’s color domain.

op <- graphics::par(mfrow = c(4, 1), oma = c(0, 0, 0, 0))
plot(inlmisc::GetTolColors(256, start = 0.0, end = 1.0))
plot(inlmisc::GetTolColors(256, start = 0.0, end = 0.5))
plot(inlmisc::GetTolColors(256, start = 0.5, end = 1.0))
plot(inlmisc::GetTolColors(256, start = 0.3, end = 0.9))
Adjust starting and ending color levels.

Adjust starting and ending color levels.

Interpolation Bias

Interpolation bias is specified using the bias argument, where a value of 1 indicates no bias. Smaller values result in more widely spaced colors at the low end, and larger values result in more widely spaced colors at the high end.

op <- graphics::par(mfrow = c(7, 1), oma = c(0, 0, 0, 0))
plot(inlmisc::GetTolColors(256, bias = 0.4))
plot(inlmisc::GetTolColors(256, bias = 0.6))
plot(inlmisc::GetTolColors(256, bias = 0.8))
plot(inlmisc::GetTolColors(256, bias = 1.0))
plot(inlmisc::GetTolColors(256, bias = 1.2))
plot(inlmisc::GetTolColors(256, bias = 1.4))
plot(inlmisc::GetTolColors(256, bias = 1.6))
Adjust interpolation bias.

Adjust interpolation bias.

Reverse Colors

Reverse the order of colors in a palette by specifying the reverse argument as TRUE .

op <- graphics::par(mfrow = c(2, 1), oma = c(0, 0, 0, 0), cex = 0.7)
plot(inlmisc::GetTolColors(10, reverse = FALSE))
plot(inlmisc::GetTolColors(10, reverse = TRUE))
Reverse colors in palette.

Reverse colors in palette.

Color Blindness

Different types of color blindness can be simulated using the blind argument: specify "deutan" for green-blind vision, "protan" for red-blind vision, "tritan" for green-blue-blind vision, and "monochromacy" for total-color blindness.

op <- graphics::par(mfrow = c(5, 1), oma = c(0, 0, 0, 0))
plot(inlmisc::GetTolColors(34, blind = NULL))
plot(inlmisc::GetTolColors(34, blind = "deutan"))
plot(inlmisc::GetTolColors(34, blind = "protan"))
plot(inlmisc::GetTolColors(34, blind = "tritan"))
plot(inlmisc::GetTolColors(34, blind = "monochromacy"))
Adjust for color blindness.

Adjust for color blindness.

With the exception of total-color blindness, the "smooth rainbow" scheme is well suited for the variants of color-vision deficiency.

Gray-Scale Preparation

Subset the qualitative schemes "bright", "vibrant", and "muted" to work after conversion to gray scale by specifying the gray argument as TRUE.

op <- graphics::par(mfrow = c(6, 1), oma = c(0, 0, 0, 0))
plot(inlmisc::GetTolColors(3, "bright",  gray = TRUE))
plot(inlmisc::GetTolColors(3, "bright",  gray = TRUE, blind = "m"))
plot(inlmisc::GetTolColors(4, "vibrant", gray = TRUE))
plot(inlmisc::GetTolColors(4, "vibrant", gray = TRUE, blind = "m"))
plot(inlmisc::GetTolColors(5, "muted",   gray = TRUE))
plot(inlmisc::GetTolColors(5, "muted",   gray = TRUE, blind = "m"))
Prepare qualitative schemes for gray-scale conversion.

Prepare qualitative schemes for gray-scale conversion.

Note that the sequential scheme "YlOrBr" works well for conversion to gray scale.

op <- graphics::par(mfrow = c(2, 1), oma = c(0, 0, 0, 0), cex = 0.7)
plot(inlmisc::GetTolColors(256, "YlOrBr"))
plot(inlmisc::GetTolColors(256, "YlOrBr", blind = "monochromacy"))
Prepare YlOrBr scheme for gray-scale conversion.

Prepare YlOrBr scheme for gray-scale conversion.

References Cited

Hansen, M., DeFries, R., Townshend, J.R.G., and Sohlberg, R., 1998, UMD Global Land Cover Classification, 1 Kilometer, 1.0: Department of Geography, University of Maryland, College Park, Maryland, 1981-1994.

Tol, Paul, 2018, Colour Schemes: SRON Technical Note, doc. no. SRON/EPS/TN/09-002, issue 3.0, 17 p., accessed August 29, 2018 at


R-session information for content in this document is as follows:

##  setting  value                       
##  version  R version 3.5.1 (2018-07-02)
##  system   x86_64, mingw32             
##  ui       Rgui                        
##  language (EN)                        
##  collate  English_United States.1252  
##  tz       America/Los_Angeles         
##  date     2018-09-12                  
##  package    * version date       source        
##  backports    1.1.2   2017-12-13 CRAN (R 3.5.0)
##  base       * 3.5.1   2018-07-02 local         
##  checkmate    1.8.5   2017-10-24 CRAN (R 3.5.1)
##  compiler     3.5.1   2018-07-02 local         
##  datasets   * 3.5.1   2018-07-02 local         
##  devtools     1.13.6  2018-06-27 CRAN (R 3.5.1)
##  dichromat    2.0-0   2013-01-24 CRAN (R 3.5.0)
##  digest       0.6.16  2018-08-22 CRAN (R 3.5.1)
##  evaluate     0.11    2018-07-17 CRAN (R 3.5.1)
##  graphics   * 3.5.1   2018-07-02 local         
##  grDevices  * 3.5.1   2018-07-02 local         
##  grid         3.5.1   2018-07-02 local         
##  highr        0.7     2018-06-09 CRAN (R 3.5.1)
##  igraph       1.2.2   2018-07-27 CRAN (R 3.5.1)
##  inlmisc      0.4.3   2018-09-10 CRAN (R 3.5.1)
##  knitr        1.20    2018-02-20 CRAN (R 3.5.1)
##  lattice      0.20-35 2017-03-25 CRAN (R 3.5.1)
##  magrittr     1.5     2014-11-22 CRAN (R 3.5.1)
##  memoise      1.1.0   2017-04-21 CRAN (R 3.5.1)
##  methods    * 3.5.1   2018-07-02 local         
##  pkgconfig    2.0.2   2018-08-16 CRAN (R 3.5.1)
##  rgdal        1.3-4   2018-08-03 CRAN (R 3.5.1)
##  rstudioapi   0.7     2017-09-07 CRAN (R 3.5.1)
##  sp           1.3-1   2018-06-05 CRAN (R 3.5.1)
##  stats      * 3.5.1   2018-07-02 local         
##  stringi      1.2.4   2018-07-20 CRAN (R 3.5.1)
##  stringr      1.3.1   2018-05-10 CRAN (R 3.5.1)
##  tools        3.5.1   2018-07-02 local         
##  utils      * 3.5.1   2018-07-02 local         
##  withr        2.1.2   2018-03-15 CRAN (R 3.5.1)




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