Maximally Distinct Color Generator

Generate maximally-distinct colors in an RGB colormap.

MAXDISTCOLOR generates an RGB colormap of maximally-distinct colors. The distance between the colors is measured in a perceptually uniform colorspace, which by default is OKLab: https://en.wikipedia.org/wiki/Oklab_color_space

Optional input arguments allow the user to:

• Limit the lightness range.
• Limit the chroma range.
• Provide a colormap of colors to be excluded (e.g. background colors, existing plot colors).
• Provide a colormap of colors to be included (e.g. company colorscheme).
• Specify the class (double/single) used for the RGB calculations.
• Specify the bit/color depth to control the number of samples of each color channel.
• Sort the colormap (e.g. by hue, chroma, saturation, lightness, farthest colors, etc.).
• Use a different perceptually uniform colorspace.

See the Examples tab (HTML documentation) for explanations of the required and optional input arguments.

Warning

Requesting many colors from a large gamut can require minutes/hours/days of processing. Some option combinations are not tractable!

Examples

>> N = 5;
>> rgb = maxdistcolor(N)
rgb =
        0            0      0.80952
        1      0.38583            0
   0.8254            0            1
  0.42857            0     0.015873
        0       0.8189            0
>> axes('ColorOrder',rgb, 'NextPlot','replacechildren')
>> X = linspace(0,pi*3,1000);
>> Y = bsxfun(@(x,n)n*sin(x+2*n*pi/N), X(:), 1:N);
>> plot(X,Y, 'linewidth',4)

>> maxdistcolor(5, 'exc',[0,0,0]) % Exclude only black.
ans =
        1            1            1
        0            0            1
        0      0.67717            0
        1      0.19685            1
  0.52381            0     0.063492

>> maxdistcolor(5, 'inc',[1,0,1]) % Include magenta.
ans =
        1            0            1      <- magenta!
        0      0.85827            0
  0.11111            0            1
        0      0.26772            0
   0.8254      0.38583            0

>> [rgb,Lab] = maxdistcolor(6, 'Lmin',0.5, 'Lmax',0.7)
rgb =
  0.42857            0      0.96825
        0      0.74803            0
        1            0      0.15873
        0      0.65354            1
  0.39683      0.40157      0.30159
        1            0      0.98413
Lab =
  0.50226     0.093312     -0.27038
  0.69651     -0.18804      0.14423
   0.6297      0.23078      0.10984
  0.69962    -0.076203     -0.15295
  0.50336    -0.013163     0.036171
   0.6993      0.27502      -0.1638

Motivation

The development of MAXDISTCOLOR was prompted by:

1. Existing "distinct color" generators use inadequate colorspaces and/or algorithms, leading to suboptimal color distinctiveness.
2. The realization that 64 bit PCs with >8 GB of RAM can operate on the entire 16 million colors of 24 bit TrueColor, allowing for neat and simple vectorized MATLAB code.

These two motivations are closely linked to two non-trivial tasks that have to be solved in order to generate maximally-distinct colors:

1. An algorithm to find the best color combination requires finding the global optimum, a task which grows exponentially with the number of requested colors and with the color gamut size. In MAXDISTCOLOR I use repeated application of a simple greedy algorithm to find the maximally-distinct colors: the repeated greedy algorithm is not particularly fast and is not a general solution for finding a global optimum, but luckily it gives good results for the regularly sampled RGB cube. Note that this algorithm contains no random numbers: it is entirely deterministic and repeatable.
2. Defining a true uniform colorspace: the venerable CIELab (used by most existing tools I could find) is not really very uniform, particularly around the blues/greens. For MAXDISTCOLOR I used OKLab, a very neat perceptually uniform colorspace with a relatively simple implementation.