How to automatically generate N distinct colors

Question

I wrote the two methods below to automatically select N distinct colors  It works by defining a piecewise linear function on the RGB cube  The benefit of this is you can also get a progressive scale if that s what you want  but when N gets large the colors can start to look similar  I can also imagine evenly subdividing the RGB cube into a lattice and then drawing points  Does anyone know any other methods  I m ruling out defining a list and then just cycling through it  I should also say I don t generally care if they clash or don t look nice  they just have to be visually distinct   public static List lt Color gt  pick int num        List lt Color gt  colors   new ArrayList lt Color gt         if  num  lt  2          return colors      float dx   1 0f    float   num - 1       for  int i   0  i  lt  num  i              colors add get i   dx              return colors     public static Color get float x        float r   0 0f      float g   0 0f      float b   1 0f      if  x  gt   0 0f  amp  amp  x  lt  0 2f            x   x   0 2f          r   0 0f          g   x          b   1 0f        else if  x  gt   0 2f  amp  amp  x  lt  0 4f            x    x - 0 2f    0 2f          r   0 0f          g   1 0f          b   1 0f - x        else if  x  gt   0 4f  amp  amp  x  lt  0 6f            x    x - 0 4f    0 2f          r   x          g   1 0f          b   0 0f        else if  x  gt   0 6f  amp  amp  x  lt  0 8f            x    x - 0 6f    0 2f          r   1 0f          g   1 0f - x          b   0 0f        else if  x  gt   0 8f  amp  amp  x  lt   1 0f            x    x - 0 8f    0 2f          r   1 0f          g   0 0f          b   x            return new Color r  g  b

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HSL color model may be well suited for  sorting  colors  but if you are looking for visually distinct colors you definitively need Lab color model instead      CIELAB was designed to be perceptually uniform with respect to human color vision  meaning that the same amount of numerical change in these values corresponds to about the same amount of visually perceived change    Once you know that  finding the optimal subset of N colors from a wide range of colors is still a  NP  hard problem  kind of similar to the Travelling salesman problem and all the solutions using k-mean algorithms or something won t really help   That said  if N is not too big and if you start with a limited set of colors  you will easily find a very good subset of distincts colors according to a Lab distance with a simple random function   I ve coded such a tool for my own usage  you can find it here  https   mokole com palette html   here is what I got for N 7    It s all javascript so feel free to take a look on the source of the page and adapt it for your own needs

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If N is big enough  you re going to get some similar-looking colors   There s only so many of them in the world   Why not just evenly distribute them through the spectrum  like so   IEnumerable lt Color gt  CreateUniqueColors int nColors        int subdivision    int Math Floor Math Pow nColors  1 3d        for int r   0  r  lt  255  r    subdivision          for int g   0  g  lt  255  g    subdivision              for int b   0  b  lt  255  b    subdivision                  yield return Color FromArgb r  g  b       If you want to mix up the sequence so that similar colors aren t next to each other  you could maybe shuffle the resulting list   Am I underthinking this

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I have written a package for R called qualpalr that is designed specifically for this purpose  I recommend you look at the vignette to find out how it works  but I will try to summarize the main points   qualpalr takes a specification of colors in the HSL color space  which was described previously in this thread   projects it to the DIN99d color space  which is perceptually uniform  and find the n that maximize the minimum distance between any oif them     Create a palette of 4 colors of hues from 0 to 360  saturations between   0 1 and 0 5  and lightness from 0 6 to 0 85 pal  lt - qualpal n   4  list h   c 0  360   s   c 0 1  0 5   l   c 0 6  0 85       Look at the colors in hex format pal hex   gt   1    6F75CE    CC6B76    CAC16A    76D0D0     Create a palette using one of the predefined color subspaces pal2  lt - qualpal n   4  colorspace    pretty      Distance matrix of the DIN99d color differences pal2 de DIN99d   gt          69A3CC  6ECC6E  CA6BC4   gt  6ECC6E      22                   gt  CA6BC4      21      30           gt  CD976B      24      21      21  plot pal2

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I think this simple recursive algorithm complementes the accepted answer  in order to generate distinct hue values  I made it for hsv  but can be used for other color spaces too   It generates hues in cycles  as separate as possible to each other in each cycle          1st cycle  0  120  240    2nd cycle   60   60  180  300    3th cycle   30   30  150  270  90  210  330    4th cycle   15   15  135  255  75  195  315  45  165  285  105  225  345     public static float recursiveHue int n           if 3  alternates red  green  blue variations     float firstCycle   3          First cycle     if  n  lt  firstCycle            return n   360f   firstCycle               Each cycle has as much values as all previous cycles summed  powers of 2      else              floor of log base 2         int numCycles    int Math floor Math log n   firstCycle    Math log 2               divDown stores the larger power of 2 that is still lower than n         int divDown    int  firstCycle   Math pow 2  numCycles               same hues than previous cycle  but summing an offset  half than previous cycle          return recursiveHue n   divDown    180f   divDown            I was unable to find this kind of algorithm here  I hope it helps  it s my first post here

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Here s an idea  Imagine an HSV cylinder    Define the upper and lower limits you want for the Brightness and Saturation   This defines a square cross section ring within the space   Now  scatter N points randomly within this space   Then apply an iterative repulsion algorithm on them  either for a fixed number of iterations  or until the points stabilise   Now you should have N points representing N colours that are about as different as possible within the colour space you re interested in   Hugo

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Here s an idea  Imagine an HSV cylinder    Define the upper and lower limits you want for the Brightness and Saturation   This defines a square cross section ring within the space   Now  scatter N points randomly within this space   Then apply an iterative repulsion algorithm on them  either for a fixed number of iterations  or until the points stabilise   Now you should have N points representing N colours that are about as different as possible within the colour space you re interested in   Hugo

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Like Uri Cohen s answer  but is a generator instead  Will start by using colors far apart  Deterministic  Sample  left colors first      usr bin env python3 5 from typing import Iterable  Tuple import colorsys import itertools from fractions import Fraction from pprint import pprint  def zenos dichotomy   - gt  Iterable Fraction        quot  quot  quot      http   en wikipedia org wiki 1 2  2B 1 4  2B 1 8  2B 1 16  2B  C2 B7  C2 B7  C2 B7      quot  quot  quot      for k in itertools count            yield Fraction 1 2  k   def fracs   - gt  Iterable Fraction        quot  quot  quot       Fraction 0  1   Fraction 1  2   Fraction 1  4   Fraction 3  4   Fraction 1  8   Fraction 3  8   Fraction 5  8   Fraction 7  8   Fraction 1  16   Fraction 3  16             0 0  0 5  0 25  0 75  0 125  0 375  0 625  0 875  0 0625  0 1875            quot  quot  quot      yield Fraction 0      for k in zenos dichotomy            i   k denominator    1 2 4 8 16              for j in range 1 i 2               yield Fraction j i     can be used for the v in hsv to map linear values 0  1 to something that looks equidistant   bias   lambda x   math sqrt x 3  Fraction 2 3  Fraction 1 3   Fraction 6 5   HSVTuple   Tuple Fraction  Fraction  Fraction  RGBTuple   Tuple float  float  float   def hue to tones h  Fraction  - gt  Iterable HSVTuple       for s in  Fraction 6 10      optionally use range         for v in  Fraction 8 10  Fraction 5 10      could use range too             yield  h  s  v    use bias for v here if you use range  def hsv to rgb x  HSVTuple  - gt  RGBTuple      return colorsys hsv to rgb  map float  x    flatten   itertools chain from iterable  def hsvs   - gt  Iterable HSVTuple       return flatten map hue to tones  fracs      def rgbs   - gt  Iterable RGBTuple       return map hsv to rgb  hsvs     def rgb to css x  RGBTuple  - gt  str      uint8tuple   map lambda y  int y 255   x      return  quot rgb           quot  format  uint8tuple   def css colors   - gt  Iterable str       return map rgb to css  rgbs     if   name       quot   main   quot         sample 100 colors in css format     sample colors   list itertools islice css colors    100       pprint sample colors

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This is trivial in MATLAB  there is an hsv command     cmap   hsv number of colors

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This is trivial in MATLAB  there is an hsv command     cmap   hsv number of colors

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For the sake of generations to come I add here the accepted answer in Python   import numpy as np import colorsys  def  get colors num colors       colors        for i in np arange 0   360   360    num colors           hue   i 360          lightness    50   np random rand     10  100          saturation    90   np random rand     10  100          colors append colorsys hls to rgb hue  lightness  saturation       return colors

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Here s a solution to managed your  distinct  issue  which is entirely overblown   Create a unit sphere and drop points on it with repelling charges   Run a particle system until they no longer move  or the delta is  small enough     At this point  each of the points are as far away from each other as possible   Convert  x  y  z  to rgb   I mention it because for certain classes of problems  this type of solution can work better than brute force   I originally saw this approach here for tesselating a sphere   Again  the most obvious solutions of traversing HSL space or RGB space will probably work just fine

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I would try to fix saturation and lumination to maximum and focus on hue only  As I see it  H can go from 0 to 255 and then wraps around  Now if you wanted two contrasting colours you would take the opposite sides of this ring  i e  0 and 128  If you wanted 4 colours  you would take some separated by 1 4 of the 256 length of the circle  i e  0  64 128 192  And of course  as others suggested when you need N colours  you could just separate them by 256 N    What I would add to this idea is to use a reversed representation of a binary number to form this sequence  Look at this   0   00000000  after reversal is 00000000   0 1   00000001  after reversal is 10000000   128 2   00000010  after reversal is 01000000   64 3   00000011  after reversal is 11000000   192       this way if you need N different colours you could just take first N numbers  reverse them  and you get as much distant points as possible  for N being power of two  while at the same time preserving that each prefix of the sequence differs a lot   This was an important goal in my use case  as I had a chart where colors were sorted by area covered by this colour  I wanted the largest areas of the chart to have large contrast  and I was ok with some small areas to have colours similar to those from top 10  as it was obvious for the reader which one is which one by just observing the area

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Here s an idea  Imagine an HSV cylinder    Define the upper and lower limits you want for the Brightness and Saturation   This defines a square cross section ring within the space   Now  scatter N points randomly within this space   Then apply an iterative repulsion algorithm on them  either for a fixed number of iterations  or until the points stabilise   Now you should have N points representing N colours that are about as different as possible within the colour space you re interested in   Hugo

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Everyone seems to have missed the existence of the very useful YUV color space which was designed to represent perceived color differences in the human visual system  Distances in YUV represent differences in human perception  I needed this functionality for MagicCube4D which implements 4-dimensional Rubik s cubes and an unlimited numbers of other 4D twisty puzzles having arbitrary numbers of faces    My solution starts by selecting random points in YUV and then iteratively breaking up the closest two points  and only converting to RGB when returning the result  The method is O n 3  but that doesn t matter for small numbers or ones that can be cached  It can certainly be made more efficient but the results appear to be excellent   The function allows for optional specification of brightness thresholds so as not to produce colors in which no component is brighter or darker than given amounts  IE you may not want values close to black or white  This is useful when the resulting colors will be used as base colors that are later shaded via lighting  layering  transparency  etc  and must still appear different from their base colors   import java awt Color  import java util Random          Contains a method to generate N visually distinct colors and helper methods          author Melinda Green     public class ColorUtils       private ColorUtils         To disallow instantiation      private final static float         U OFF    436f          V OFF    615f      private static final long RAND SEED   0      private static Random rand   new Random RAND SEED                      Returns an array of ncolors RGB triplets such that each is as unique from the rest as possible        and each color has at least one component greater than minComponent and one less than maxComponent         Use min    1 and max    0 to include the full RGB color range                 Warning  O N 2 algorithm blows up fast for more than 100 colors              public static Color   generateVisuallyDistinctColors int ncolors  float minComponent  float maxComponent            rand setSeed RAND SEED      So that we get consistent results for each combination of inputs          float     yuv   new float ncolors  3               initialize array with random colors         for int got   0  got  lt  ncolors                 System arraycopy randYUVinRGBRange minComponent  maxComponent   0  yuv got     0  3                        continually break up the worst-fit color pair until we get tired of searching         for int c   0  c  lt  ncolors   1000  c                  float worst   8888              int worstID   0              for int i   1  i  lt  yuv length  i                      for int j   0  j  lt  i  j                          float dist   sqrdist yuv i   yuv j                        if dist  lt  worst                            worst   dist                          worstID   i                                                                    float   best   randYUVBetterThan worst  minComponent  maxComponent  yuv               if best    null                  break              else                 yuv worstID    best                     Color   rgbs   new Color yuv length           for int i   0  i  lt  yuv length  i                  float   rgb   new float 3               yuv2rgb yuv i  0   yuv i  1   yuv i  2   rgb               rgbs i    new Color rgb 0   rgb 1   rgb 2                  System out println rgb i  0      t    rgb i  1      t    rgb i  2                       return rgbs             public static void hsv2rgb float h  float s  float v  float   rgb               H is given on  0- gt 6  or -1  S and V are given on  0- gt 1               RGB are each returned on  0- gt 1            float m  n  f          int i           float   hsv   new float 3            hsv 0    h          hsv 1    s          hsv 2    v          System out println  H      h     S      s     V     v           if hsv 0     -1                rgb 0    rgb 1    rgb 2    hsv 2               return                    i    int   Math floor hsv 0             f   hsv 0  - i          if i   2    0              f   1 - f     if i is even          m   hsv 2     1 - hsv 1            n   hsv 2     1 - hsv 1    f           switch i                case 6              case 0                  rgb 0    hsv 2                   rgb 1    n                  rgb 2    m                  break              case 1                  rgb 0    n                  rgb 1    hsv 2                   rgb 2    m                  break              case 2                  rgb 0    m                  rgb 1    hsv 2                   rgb 2    n                  break              case 3                  rgb 0    m                  rgb 1    n                  rgb 2    hsv 2                   break              case 4                  rgb 0    n                  rgb 1    m                  rgb 2    hsv 2                   break              case 5                  rgb 0    hsv 2                   rgb 1    m                  rgb 2    n                  break                           From http   en wikipedia org wiki YUV Mathematical derivations and formulas     public static void yuv2rgb float y  float u  float v  float   rgb            rgb 0    1   y   0   u   1 13983f   v          rgb 1    1   y   - 39465f   u   - 58060f   v          rgb 2    1   y   2 03211f   u   0   v             public static void rgb2yuv float r  float g  float b  float   yuv            yuv 0     299f   r    587f   g    114f   b          yuv 1    - 14713f   r   - 28886f   g    436f   b          yuv 2     615f   r   - 51499f   g   - 10001f   b             private static float   randYUVinRGBRange float minComponent  float maxComponent            while true                float y   rand nextFloat         YFRAC   1-YFRAC               float u   rand nextFloat     2   U OFF - U OFF              float v   rand nextFloat     2   V OFF - V OFF              float   rgb   new float 3               yuv2rgb y  u  v  rgb               float r   rgb 0   g   rgb 1   b   rgb 2               if 0  lt   r  amp  amp  r  lt   1  amp  amp                  0  lt   g  amp  amp  g  lt   1  amp  amp                  0  lt   b  amp  amp  b  lt   1  amp  amp                   r  gt  minComponent    g  gt  minComponent    b  gt  minComponent   amp  amp     don t want all dark components                  r  lt  maxComponent    g  lt  maxComponent    b  lt  maxComponent      don t want all light components                  return new float   y  u  v                        private static float sqrdist float   a  float   b            float sum   0          for int i   0  i  lt  a length  i                  float diff   a i  - b i               sum    diff   diff                    return sum             private static double worstFit Color   colors            float worst   8888          float   a   new float 3   b   new float 3           for int i   1  i  lt  colors length  i                  colors i  getColorComponents a               for int j   0  j  lt  i  j                      colors j  getColorComponents b                   float dist   sqrdist a  b                   if dist  lt  worst                        worst   dist                                                    return Math sqrt worst              private static float   randYUVBetterThan float bestDistSqrd  float minComponent  float maxComponent  float     in            for int attempt   1  attempt  lt  100   in length  attempt                  float   candidate   randYUVinRGBRange minComponent  maxComponent               boolean good   true              for int i   0  i  lt  in length  i                    if sqrdist candidate  in i    lt  bestDistSqrd                      good   false              if good                  return candidate                    return null     after a bunch of passes  couldn t find a candidate that beat the best                         Simple example program              public static void main String   args            final int ncolors   10          Color   colors   generateVisuallyDistinctColors ncolors   8f   3f           for int i   0  i  lt  colors length  i                  System out println colors i  toString                       System out println  Worst fit color       worstFit colors

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For the sake of generations to come I add here the accepted answer in Python   import numpy as np import colorsys  def  get colors num colors       colors        for i in np arange 0   360   360    num colors           hue   i 360          lightness    50   np random rand     10  100          saturation    90   np random rand     10  100          colors append colorsys hls to rgb hue  lightness  saturation       return colors

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Like Uri Cohen s answer  but is a generator instead  Will start by using colors far apart  Deterministic  Sample  left colors first      usr bin env python3 5 from typing import Iterable  Tuple import colorsys import itertools from fractions import Fraction from pprint import pprint  def zenos dichotomy   - gt  Iterable Fraction        quot  quot  quot      http   en wikipedia org wiki 1 2  2B 1 4  2B 1 8  2B 1 16  2B  C2 B7  C2 B7  C2 B7      quot  quot  quot      for k in itertools count            yield Fraction 1 2  k   def fracs   - gt  Iterable Fraction        quot  quot  quot       Fraction 0  1   Fraction 1  2   Fraction 1  4   Fraction 3  4   Fraction 1  8   Fraction 3  8   Fraction 5  8   Fraction 7  8   Fraction 1  16   Fraction 3  16             0 0  0 5  0 25  0 75  0 125  0 375  0 625  0 875  0 0625  0 1875            quot  quot  quot      yield Fraction 0      for k in zenos dichotomy            i   k denominator    1 2 4 8 16              for j in range 1 i 2               yield Fraction j i     can be used for the v in hsv to map linear values 0  1 to something that looks equidistant   bias   lambda x   math sqrt x 3  Fraction 2 3  Fraction 1 3   Fraction 6 5   HSVTuple   Tuple Fraction  Fraction  Fraction  RGBTuple   Tuple float  float  float   def hue to tones h  Fraction  - gt  Iterable HSVTuple       for s in  Fraction 6 10      optionally use range         for v in  Fraction 8 10  Fraction 5 10      could use range too             yield  h  s  v    use bias for v here if you use range  def hsv to rgb x  HSVTuple  - gt  RGBTuple      return colorsys hsv to rgb  map float  x    flatten   itertools chain from iterable  def hsvs   - gt  Iterable HSVTuple       return flatten map hue to tones  fracs      def rgbs   - gt  Iterable RGBTuple       return map hsv to rgb  hsvs     def rgb to css x  RGBTuple  - gt  str      uint8tuple   map lambda y  int y 255   x      return  quot rgb           quot  format  uint8tuple   def css colors   - gt  Iterable str       return map rgb to css  rgbs     if   name       quot   main   quot         sample 100 colors in css format     sample colors   list itertools islice css colors    100       pprint sample colors

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This questions appears in quite a few SO discussions    Algorithm For Generating Unique Colors Generate unique colours Generate distinctly different RGB colors in graphs How to generate n different colors for any natural number n    Different solutions are proposed  but none are optimal  Luckily  science comes to the rescue  Arbitrary N   Colour displays for categorical images  free download  A WEB SERVICE TO PERSONALISE MAP COLOURING  free download  a webservice solution should be available by next month  An Algorithm for the Selection of High-Contrast Color Sets  the authors offer a free C   implementation  High-contrast sets of colors  The first algorithm for the problem    The last 2 will be free via most university libraries   proxies    N is finite and relatively small  In this case  one could go for a list solution  A very interesting article in the subject is freely available    A Colour Alphabet and the Limits of Colour Coding   There are several color lists to consider    Boynton s list of 11 colors that are almost never confused  available in the first paper of the previous section  Kelly s 22 colors of maximum contrast  available in the paper above    I also ran into this Palette by an MIT student  Lastly  The following links may be useful in converting between different color systems   coordinates  some colors in the articles are not specified in RGB  for instance     http   chem8 org uch space-55036-do-blog-id-5333 html https   metacpan org pod Color  Library  Dictionary  NBS ISCC Color Theory  How to convert Munsell HVC to RGB HSB HSL   For Kelly s and Boynton s list  I ve already made the conversion to RGB  with the exception of white and black  which should be obvious   Some C  code     public static ReadOnlyCollection lt Color gt  KellysMaxContrastSet       get   return  kellysMaxContrastSet AsReadOnly         private static readonly List lt Color gt   kellysMaxContrastSet   new List lt Color gt        UIntToColor 0xFFFFB300     Vivid Yellow     UIntToColor 0xFF803E75     Strong Purple     UIntToColor 0xFFFF6800     Vivid Orange     UIntToColor 0xFFA6BDD7     Very Light Blue     UIntToColor 0xFFC10020     Vivid Red     UIntToColor 0xFFCEA262     Grayish Yellow     UIntToColor 0xFF817066     Medium Gray        The following will not be good for people with defective color vision     UIntToColor 0xFF007D34     Vivid Green     UIntToColor 0xFFF6768E     Strong Purplish Pink     UIntToColor 0xFF00538A     Strong Blue     UIntToColor 0xFFFF7A5C     Strong Yellowish Pink     UIntToColor 0xFF53377A     Strong Violet     UIntToColor 0xFFFF8E00     Vivid Orange Yellow     UIntToColor 0xFFB32851     Strong Purplish Red     UIntToColor 0xFFF4C800     Vivid Greenish Yellow     UIntToColor 0xFF7F180D     Strong Reddish Brown     UIntToColor 0xFF93AA00     Vivid Yellowish Green     UIntToColor 0xFF593315     Deep Yellowish Brown     UIntToColor 0xFFF13A13     Vivid Reddish Orange     UIntToColor 0xFF232C16     Dark Olive Green     public static ReadOnlyCollection lt Color gt  BoyntonOptimized       get   return  boyntonOptimized AsReadOnly         private static readonly List lt Color gt   boyntonOptimized   new List lt Color gt        Color FromArgb 0  0  255          Blue     Color FromArgb 255  0  0          Red     Color FromArgb 0  255  0          Green     Color FromArgb 255  255  0        Yellow     Color FromArgb 255  0  255        Magenta     Color FromArgb 255  128  128      Pink     Color FromArgb 128  128  128      Gray     Color FromArgb 128  0  0          Brown     Color FromArgb 255  128  0        Orange     static public Color UIntToColor uint color        var a    byte  color  gt  gt  24       var r    byte  color  gt  gt  16       var g    byte  color  gt  gt  8       var b    byte  color  gt  gt  0       return Color FromArgb a  r  g  b       And here are the RGB values in hex and 8-bit-per-channel representations     kelly colors hex         0xFFB300    Vivid Yellow     0x803E75    Strong Purple     0xFF6800    Vivid Orange     0xA6BDD7    Very Light Blue     0xC10020    Vivid Red     0xCEA262    Grayish Yellow     0x817066    Medium Gray        The following don t work well for people with defective color vision     0x007D34    Vivid Green     0xF6768E    Strong Purplish Pink     0x00538A    Strong Blue     0xFF7A5C    Strong Yellowish Pink     0x53377A    Strong Violet     0xFF8E00    Vivid Orange Yellow     0xB32851    Strong Purplish Red     0xF4C800    Vivid Greenish Yellow     0x7F180D    Strong Reddish Brown     0x93AA00    Vivid Yellowish Green     0x593315    Deep Yellowish Brown     0xF13A13    Vivid Reddish Orange     0x232C16    Dark Olive Green        kelly colors   dict vivid yellow  255  179  0                       strong purple  128  62  117                       vivid orange  255  104  0                       very light blue  166  189  215                       vivid red  193  0  32                       grayish yellow  206  162  98                       medium gray  129  112  102                          these aren t good for people with defective color vision                      vivid green  0  125  52                       strong purplish pink  246  118  142                       strong blue  0  83  138                       strong yellowish pink  255  122  92                       strong violet  83  55  122                       vivid orange yellow  255  142  0                       strong purplish red  179  40  81                       vivid greenish yellow  244  200  0                       strong reddish brown  127  24  13                       vivid yellowish green  147  170  0                       deep yellowish brown  89  51  21                       vivid reddish orange  241  58  19                       dark olive green  35  44  22     For all you Java developers  here are the JavaFX colors        Don t forget to import javafx scene paint Color   private static final Color   KELLY COLORS         Color web  0xFFB300          Vivid Yellow     Color web  0x803E75          Strong Purple     Color web  0xFF6800          Vivid Orange     Color web  0xA6BDD7          Very Light Blue     Color web  0xC10020          Vivid Red     Color web  0xCEA262          Grayish Yellow     Color web  0x817066          Medium Gray      Color web  0x007D34          Vivid Green     Color web  0xF6768E          Strong Purplish Pink     Color web  0x00538A          Strong Blue     Color web  0xFF7A5C          Strong Yellowish Pink     Color web  0x53377A          Strong Violet     Color web  0xFF8E00          Vivid Orange Yellow     Color web  0xB32851          Strong Purplish Red     Color web  0xF4C800          Vivid Greenish Yellow     Color web  0x7F180D          Strong Reddish Brown     Color web  0x93AA00          Vivid Yellowish Green     Color web  0x593315          Deep Yellowish Brown     Color web  0xF13A13          Vivid Reddish Orange     Color web  0x232C16          Dark Olive Green      the following is the unsorted kelly colors according to the order above     the following is the sorted kelly colors according to hues  note that some yellows are not very contrasting

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You can use the HSL color model to create your colors   If all you want is differing hues  likely   and slight variations on lightness or saturation  you can distribute the hues like so      assumes hue  0  360   saturation  0  100   lightness  0  100   for i   0  i  lt  360  i    360   num colors        HSLColor c      c hue   i      c saturation   90   randf     10      c lightness   50   randf     10       addColor c

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If N is big enough  you re going to get some similar-looking colors   There s only so many of them in the world   Why not just evenly distribute them through the spectrum  like so   IEnumerable lt Color gt  CreateUniqueColors int nColors        int subdivision    int Math Floor Math Pow nColors  1 3d        for int r   0  r  lt  255  r    subdivision          for int g   0  g  lt  255  g    subdivision              for int b   0  b  lt  255  b    subdivision                  yield return Color FromArgb r  g  b       If you want to mix up the sequence so that similar colors aren t next to each other  you could maybe shuffle the resulting list   Am I underthinking this

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You can use the HSL color model to create your colors   If all you want is differing hues  likely   and slight variations on lightness or saturation  you can distribute the hues like so      assumes hue  0  360   saturation  0  100   lightness  0  100   for i   0  i  lt  360  i    360   num colors        HSLColor c      c hue   i      c saturation   90   randf     10      c lightness   50   randf     10       addColor c

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If N is big enough  you re going to get some similar-looking colors   There s only so many of them in the world   Why not just evenly distribute them through the spectrum  like so   IEnumerable lt Color gt  CreateUniqueColors int nColors        int subdivision    int Math Floor Math Pow nColors  1 3d        for int r   0  r  lt  255  r    subdivision          for int g   0  g  lt  255  g    subdivision              for int b   0  b  lt  255  b    subdivision                  yield return Color FromArgb r  g  b       If you want to mix up the sequence so that similar colors aren t next to each other  you could maybe shuffle the resulting list   Am I underthinking this

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This OpenCV function uses the HSV color model to generate n evenly distributed colors around the 0 lt  H lt  360   with maximum S 1 0 and V 1 0  The function outputs the BGR colors in bgr mat   void distributed colors  int n  cv  Mat  lt cv  Vec3f gt   amp  bgr mat      cv  Mat  lt cv  Vec3f gt  hsv mat n CV 32F cv  Vec3f 0 0 1 0 1 0      double step   360 0 n    double h  0 0    cv  Vec3f value    for  int i 0 i lt n i   h  step        value   hsv mat at lt cv  Vec3f gt  i       hsv mat at lt cv  Vec3f gt  i  0    h        cv  cvtColor hsv mat  bgr mat  CV HSV2BGR     bgr mat    255

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Pretty neat with seaborn for Python users   gt  gt  gt  import seaborn as sns  gt  gt  gt  sns color palette n colors 4    it returns list of RGB tuples    0 12156862745098039  0 4666666666666667  0 7058823529411765    1 0  0 4980392156862745  0 054901960784313725    0 17254901960784313  0 6274509803921569  0 17254901960784313    0 8392156862745098  0 15294117647058825  0 1568627450980392

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Pretty neat with seaborn for Python users   gt  gt  gt  import seaborn as sns  gt  gt  gt  sns color palette n colors 4    it returns list of RGB tuples    0 12156862745098039  0 4666666666666667  0 7058823529411765    1 0  0 4980392156862745  0 054901960784313725    0 17254901960784313  0 6274509803921569  0 17254901960784313    0 8392156862745098  0 15294117647058825  0 1568627450980392

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This questions appears in quite a few SO discussions    Algorithm For Generating Unique Colors Generate unique colours Generate distinctly different RGB colors in graphs How to generate n different colors for any natural number n    Different solutions are proposed  but none are optimal  Luckily  science comes to the rescue  Arbitrary N   Colour displays for categorical images  free download  A WEB SERVICE TO PERSONALISE MAP COLOURING  free download  a webservice solution should be available by next month  An Algorithm for the Selection of High-Contrast Color Sets  the authors offer a free C   implementation  High-contrast sets of colors  The first algorithm for the problem    The last 2 will be free via most university libraries   proxies    N is finite and relatively small  In this case  one could go for a list solution  A very interesting article in the subject is freely available    A Colour Alphabet and the Limits of Colour Coding   There are several color lists to consider    Boynton s list of 11 colors that are almost never confused  available in the first paper of the previous section  Kelly s 22 colors of maximum contrast  available in the paper above    I also ran into this Palette by an MIT student  Lastly  The following links may be useful in converting between different color systems   coordinates  some colors in the articles are not specified in RGB  for instance     http   chem8 org uch space-55036-do-blog-id-5333 html https   metacpan org pod Color  Library  Dictionary  NBS ISCC Color Theory  How to convert Munsell HVC to RGB HSB HSL   For Kelly s and Boynton s list  I ve already made the conversion to RGB  with the exception of white and black  which should be obvious   Some C  code     public static ReadOnlyCollection lt Color gt  KellysMaxContrastSet       get   return  kellysMaxContrastSet AsReadOnly         private static readonly List lt Color gt   kellysMaxContrastSet   new List lt Color gt        UIntToColor 0xFFFFB300     Vivid Yellow     UIntToColor 0xFF803E75     Strong Purple     UIntToColor 0xFFFF6800     Vivid Orange     UIntToColor 0xFFA6BDD7     Very Light Blue     UIntToColor 0xFFC10020     Vivid Red     UIntToColor 0xFFCEA262     Grayish Yellow     UIntToColor 0xFF817066     Medium Gray        The following will not be good for people with defective color vision     UIntToColor 0xFF007D34     Vivid Green     UIntToColor 0xFFF6768E     Strong Purplish Pink     UIntToColor 0xFF00538A     Strong Blue     UIntToColor 0xFFFF7A5C     Strong Yellowish Pink     UIntToColor 0xFF53377A     Strong Violet     UIntToColor 0xFFFF8E00     Vivid Orange Yellow     UIntToColor 0xFFB32851     Strong Purplish Red     UIntToColor 0xFFF4C800     Vivid Greenish Yellow     UIntToColor 0xFF7F180D     Strong Reddish Brown     UIntToColor 0xFF93AA00     Vivid Yellowish Green     UIntToColor 0xFF593315     Deep Yellowish Brown     UIntToColor 0xFFF13A13     Vivid Reddish Orange     UIntToColor 0xFF232C16     Dark Olive Green     public static ReadOnlyCollection lt Color gt  BoyntonOptimized       get   return  boyntonOptimized AsReadOnly         private static readonly List lt Color gt   boyntonOptimized   new List lt Color gt        Color FromArgb 0  0  255          Blue     Color FromArgb 255  0  0          Red     Color FromArgb 0  255  0          Green     Color FromArgb 255  255  0        Yellow     Color FromArgb 255  0  255        Magenta     Color FromArgb 255  128  128      Pink     Color FromArgb 128  128  128      Gray     Color FromArgb 128  0  0          Brown     Color FromArgb 255  128  0        Orange     static public Color UIntToColor uint color        var a    byte  color  gt  gt  24       var r    byte  color  gt  gt  16       var g    byte  color  gt  gt  8       var b    byte  color  gt  gt  0       return Color FromArgb a  r  g  b       And here are the RGB values in hex and 8-bit-per-channel representations     kelly colors hex         0xFFB300    Vivid Yellow     0x803E75    Strong Purple     0xFF6800    Vivid Orange     0xA6BDD7    Very Light Blue     0xC10020    Vivid Red     0xCEA262    Grayish Yellow     0x817066    Medium Gray        The following don t work well for people with defective color vision     0x007D34    Vivid Green     0xF6768E    Strong Purplish Pink     0x00538A    Strong Blue     0xFF7A5C    Strong Yellowish Pink     0x53377A    Strong Violet     0xFF8E00    Vivid Orange Yellow     0xB32851    Strong Purplish Red     0xF4C800    Vivid Greenish Yellow     0x7F180D    Strong Reddish Brown     0x93AA00    Vivid Yellowish Green     0x593315    Deep Yellowish Brown     0xF13A13    Vivid Reddish Orange     0x232C16    Dark Olive Green        kelly colors   dict vivid yellow  255  179  0                       strong purple  128  62  117                       vivid orange  255  104  0                       very light blue  166  189  215                       vivid red  193  0  32                       grayish yellow  206  162  98                       medium gray  129  112  102                          these aren t good for people with defective color vision                      vivid green  0  125  52                       strong purplish pink  246  118  142                       strong blue  0  83  138                       strong yellowish pink  255  122  92                       strong violet  83  55  122                       vivid orange yellow  255  142  0                       strong purplish red  179  40  81                       vivid greenish yellow  244  200  0                       strong reddish brown  127  24  13                       vivid yellowish green  147  170  0                       deep yellowish brown  89  51  21                       vivid reddish orange  241  58  19                       dark olive green  35  44  22     For all you Java developers  here are the JavaFX colors        Don t forget to import javafx scene paint Color   private static final Color   KELLY COLORS         Color web  0xFFB300          Vivid Yellow     Color web  0x803E75          Strong Purple     Color web  0xFF6800          Vivid Orange     Color web  0xA6BDD7          Very Light Blue     Color web  0xC10020          Vivid Red     Color web  0xCEA262          Grayish Yellow     Color web  0x817066          Medium Gray      Color web  0x007D34          Vivid Green     Color web  0xF6768E          Strong Purplish Pink     Color web  0x00538A          Strong Blue     Color web  0xFF7A5C          Strong Yellowish Pink     Color web  0x53377A          Strong Violet     Color web  0xFF8E00          Vivid Orange Yellow     Color web  0xB32851          Strong Purplish Red     Color web  0xF4C800          Vivid Greenish Yellow     Color web  0x7F180D          Strong Reddish Brown     Color web  0x93AA00          Vivid Yellowish Green     Color web  0x593315          Deep Yellowish Brown     Color web  0xF13A13          Vivid Reddish Orange     Color web  0x232C16          Dark Olive Green      the following is the unsorted kelly colors according to the order above     the following is the sorted kelly colors according to hues  note that some yellows are not very contrasting

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Here s an idea  Imagine an HSV cylinder    Define the upper and lower limits you want for the Brightness and Saturation   This defines a square cross section ring within the space   Now  scatter N points randomly within this space   Then apply an iterative repulsion algorithm on them  either for a fixed number of iterations  or until the points stabilise   Now you should have N points representing N colours that are about as different as possible within the colour space you re interested in   Hugo

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Here s a solution to managed your  distinct  issue  which is entirely overblown   Create a unit sphere and drop points on it with repelling charges   Run a particle system until they no longer move  or the delta is  small enough     At this point  each of the points are as far away from each other as possible   Convert  x  y  z  to rgb   I mention it because for certain classes of problems  this type of solution can work better than brute force   I originally saw this approach here for tesselating a sphere   Again  the most obvious solutions of traversing HSL space or RGB space will probably work just fine

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Here s a solution to managed your  distinct  issue  which is entirely overblown   Create a unit sphere and drop points on it with repelling charges   Run a particle system until they no longer move  or the delta is  small enough     At this point  each of the points are as far away from each other as possible   Convert  x  y  z  to rgb   I mention it because for certain classes of problems  this type of solution can work better than brute force   I originally saw this approach here for tesselating a sphere   Again  the most obvious solutions of traversing HSL space or RGB space will probably work just fine

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You can use the HSL color model to create your colors   If all you want is differing hues  likely   and slight variations on lightness or saturation  you can distribute the hues like so      assumes hue  0  360   saturation  0  100   lightness  0  100   for i   0  i  lt  360  i    360   num colors        HSLColor c      c hue   i      c saturation   90   randf     10      c lightness   50   randf     10       addColor c

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I have written a package for R called qualpalr that is designed specifically for this purpose  I recommend you look at the vignette to find out how it works  but I will try to summarize the main points   qualpalr takes a specification of colors in the HSL color space  which was described previously in this thread   projects it to the DIN99d color space  which is perceptually uniform  and find the n that maximize the minimum distance between any oif them     Create a palette of 4 colors of hues from 0 to 360  saturations between   0 1 and 0 5  and lightness from 0 6 to 0 85 pal  lt - qualpal n   4  list h   c 0  360   s   c 0 1  0 5   l   c 0 6  0 85       Look at the colors in hex format pal hex   gt   1    6F75CE    CC6B76    CAC16A    76D0D0     Create a palette using one of the predefined color subspaces pal2  lt - qualpal n   4  colorspace    pretty      Distance matrix of the DIN99d color differences pal2 de DIN99d   gt          69A3CC  6ECC6E  CA6BC4   gt  6ECC6E      22                   gt  CA6BC4      21      30           gt  CD976B      24      21      21  plot pal2

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You can use the HSL color model to create your colors   If all you want is differing hues  likely   and slight variations on lightness or saturation  you can distribute the hues like so      assumes hue  0  360   saturation  0  100   lightness  0  100   for i   0  i  lt  360  i    360   num colors        HSLColor c      c hue   i      c saturation   90   randf     10      c lightness   50   randf     10       addColor c

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I think this simple recursive algorithm complementes the accepted answer  in order to generate distinct hue values  I made it for hsv  but can be used for other color spaces too   It generates hues in cycles  as separate as possible to each other in each cycle          1st cycle  0  120  240    2nd cycle   60   60  180  300    3th cycle   30   30  150  270  90  210  330    4th cycle   15   15  135  255  75  195  315  45  165  285  105  225  345     public static float recursiveHue int n           if 3  alternates red  green  blue variations     float firstCycle   3          First cycle     if  n  lt  firstCycle            return n   360f   firstCycle               Each cycle has as much values as all previous cycles summed  powers of 2      else              floor of log base 2         int numCycles    int Math floor Math log n   firstCycle    Math log 2               divDown stores the larger power of 2 that is still lower than n         int divDown    int  firstCycle   Math pow 2  numCycles               same hues than previous cycle  but summing an offset  half than previous cycle          return recursiveHue n   divDown    180f   divDown            I was unable to find this kind of algorithm here  I hope it helps  it s my first post here

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HSL color model may be well suited for  sorting  colors  but if you are looking for visually distinct colors you definitively need Lab color model instead      CIELAB was designed to be perceptually uniform with respect to human color vision  meaning that the same amount of numerical change in these values corresponds to about the same amount of visually perceived change    Once you know that  finding the optimal subset of N colors from a wide range of colors is still a  NP  hard problem  kind of similar to the Travelling salesman problem and all the solutions using k-mean algorithms or something won t really help   That said  if N is not too big and if you start with a limited set of colors  you will easily find a very good subset of distincts colors according to a Lab distance with a simple random function   I ve coded such a tool for my own usage  you can find it here  https   mokole com palette html   here is what I got for N 7    It s all javascript so feel free to take a look on the source of the page and adapt it for your own needs

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Everyone seems to have missed the existence of the very useful YUV color space which was designed to represent perceived color differences in the human visual system  Distances in YUV represent differences in human perception  I needed this functionality for MagicCube4D which implements 4-dimensional Rubik s cubes and an unlimited numbers of other 4D twisty puzzles having arbitrary numbers of faces    My solution starts by selecting random points in YUV and then iteratively breaking up the closest two points  and only converting to RGB when returning the result  The method is O n 3  but that doesn t matter for small numbers or ones that can be cached  It can certainly be made more efficient but the results appear to be excellent   The function allows for optional specification of brightness thresholds so as not to produce colors in which no component is brighter or darker than given amounts  IE you may not want values close to black or white  This is useful when the resulting colors will be used as base colors that are later shaded via lighting  layering  transparency  etc  and must still appear different from their base colors   import java awt Color  import java util Random          Contains a method to generate N visually distinct colors and helper methods          author Melinda Green     public class ColorUtils       private ColorUtils         To disallow instantiation      private final static float         U OFF    436f          V OFF    615f      private static final long RAND SEED   0      private static Random rand   new Random RAND SEED                      Returns an array of ncolors RGB triplets such that each is as unique from the rest as possible        and each color has at least one component greater than minComponent and one less than maxComponent         Use min    1 and max    0 to include the full RGB color range                 Warning  O N 2 algorithm blows up fast for more than 100 colors              public static Color   generateVisuallyDistinctColors int ncolors  float minComponent  float maxComponent            rand setSeed RAND SEED      So that we get consistent results for each combination of inputs          float     yuv   new float ncolors  3               initialize array with random colors         for int got   0  got  lt  ncolors                 System arraycopy randYUVinRGBRange minComponent  maxComponent   0  yuv got     0  3                        continually break up the worst-fit color pair until we get tired of searching         for int c   0  c  lt  ncolors   1000  c                  float worst   8888              int worstID   0              for int i   1  i  lt  yuv length  i                      for int j   0  j  lt  i  j                          float dist   sqrdist yuv i   yuv j                        if dist  lt  worst                            worst   dist                          worstID   i                                                                    float   best   randYUVBetterThan worst  minComponent  maxComponent  yuv               if best    null                  break              else                 yuv worstID    best                     Color   rgbs   new Color yuv length           for int i   0  i  lt  yuv length  i                  float   rgb   new float 3               yuv2rgb yuv i  0   yuv i  1   yuv i  2   rgb               rgbs i    new Color rgb 0   rgb 1   rgb 2                  System out println rgb i  0      t    rgb i  1      t    rgb i  2                       return rgbs             public static void hsv2rgb float h  float s  float v  float   rgb               H is given on  0- gt 6  or -1  S and V are given on  0- gt 1               RGB are each returned on  0- gt 1            float m  n  f          int i           float   hsv   new float 3            hsv 0    h          hsv 1    s          hsv 2    v          System out println  H      h     S      s     V     v           if hsv 0     -1                rgb 0    rgb 1    rgb 2    hsv 2               return                    i    int   Math floor hsv 0             f   hsv 0  - i          if i   2    0              f   1 - f     if i is even          m   hsv 2     1 - hsv 1            n   hsv 2     1 - hsv 1    f           switch i                case 6              case 0                  rgb 0    hsv 2                   rgb 1    n                  rgb 2    m                  break              case 1                  rgb 0    n                  rgb 1    hsv 2                   rgb 2    m                  break              case 2                  rgb 0    m                  rgb 1    hsv 2                   rgb 2    n                  break              case 3                  rgb 0    m                  rgb 1    n                  rgb 2    hsv 2                   break              case 4                  rgb 0    n                  rgb 1    m                  rgb 2    hsv 2                   break              case 5                  rgb 0    hsv 2                   rgb 1    m                  rgb 2    n                  break                           From http   en wikipedia org wiki YUV Mathematical derivations and formulas     public static void yuv2rgb float y  float u  float v  float   rgb            rgb 0    1   y   0   u   1 13983f   v          rgb 1    1   y   - 39465f   u   - 58060f   v          rgb 2    1   y   2 03211f   u   0   v             public static void rgb2yuv float r  float g  float b  float   yuv            yuv 0     299f   r    587f   g    114f   b          yuv 1    - 14713f   r   - 28886f   g    436f   b          yuv 2     615f   r   - 51499f   g   - 10001f   b             private static float   randYUVinRGBRange float minComponent  float maxComponent            while true                float y   rand nextFloat         YFRAC   1-YFRAC               float u   rand nextFloat     2   U OFF - U OFF              float v   rand nextFloat     2   V OFF - V OFF              float   rgb   new float 3               yuv2rgb y  u  v  rgb               float r   rgb 0   g   rgb 1   b   rgb 2               if 0  lt   r  amp  amp  r  lt   1  amp  amp                  0  lt   g  amp  amp  g  lt   1  amp  amp                  0  lt   b  amp  amp  b  lt   1  amp  amp                   r  gt  minComponent    g  gt  minComponent    b  gt  minComponent   amp  amp     don t want all dark components                  r  lt  maxComponent    g  lt  maxComponent    b  lt  maxComponent      don t want all light components                  return new float   y  u  v                        private static float sqrdist float   a  float   b            float sum   0          for int i   0  i  lt  a length  i                  float diff   a i  - b i               sum    diff   diff                    return sum             private static double worstFit Color   colors            float worst   8888          float   a   new float 3   b   new float 3           for int i   1  i  lt  colors length  i                  colors i  getColorComponents a               for int j   0  j  lt  i  j                      colors j  getColorComponents b                   float dist   sqrdist a  b                   if dist  lt  worst                        worst   dist                                                    return Math sqrt worst              private static float   randYUVBetterThan float bestDistSqrd  float minComponent  float maxComponent  float     in            for int attempt   1  attempt  lt  100   in length  attempt                  float   candidate   randYUVinRGBRange minComponent  maxComponent               boolean good   true              for int i   0  i  lt  in length  i                    if sqrdist candidate  in i    lt  bestDistSqrd                      good   false              if good                  return candidate                    return null     after a bunch of passes  couldn t find a candidate that beat the best                         Simple example program              public static void main String   args            final int ncolors   10          Color   colors   generateVisuallyDistinctColors ncolors   8f   3f           for int i   0  i  lt  colors length  i                  System out println colors i  toString                       System out println  Worst fit color       worstFit colors

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This OpenCV function uses the HSV color model to generate n evenly distributed colors around the 0 lt  H lt  360   with maximum S 1 0 and V 1 0  The function outputs the BGR colors in bgr mat   void distributed colors  int n  cv  Mat  lt cv  Vec3f gt   amp  bgr mat      cv  Mat  lt cv  Vec3f gt  hsv mat n CV 32F cv  Vec3f 0 0 1 0 1 0      double step   360 0 n    double h  0 0    cv  Vec3f value    for  int i 0 i lt n i   h  step        value   hsv mat at lt cv  Vec3f gt  i       hsv mat at lt cv  Vec3f gt  i  0    h        cv  cvtColor hsv mat  bgr mat  CV HSV2BGR     bgr mat    255

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If N is big enough  you re going to get some similar-looking colors   There s only so many of them in the world   Why not just evenly distribute them through the spectrum  like so   IEnumerable lt Color gt  CreateUniqueColors int nColors        int subdivision    int Math Floor Math Pow nColors  1 3d        for int r   0  r  lt  255  r    subdivision          for int g   0  g  lt  255  g    subdivision              for int b   0  b  lt  255  b    subdivision                  yield return Color FromArgb r  g  b       If you want to mix up the sequence so that similar colors aren t next to each other  you could maybe shuffle the resulting list   Am I underthinking this

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Here s a solution to managed your  distinct  issue  which is entirely overblown   Create a unit sphere and drop points on it with repelling charges   Run a particle system until they no longer move  or the delta is  small enough     At this point  each of the points are as far away from each other as possible   Convert  x  y  z  to rgb   I mention it because for certain classes of problems  this type of solution can work better than brute force   I originally saw this approach here for tesselating a sphere   Again  the most obvious solutions of traversing HSL space or RGB space will probably work just fine

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I would try to fix saturation and lumination to maximum and focus on hue only  As I see it  H can go from 0 to 255 and then wraps around  Now if you wanted two contrasting colours you would take the opposite sides of this ring  i e  0 and 128  If you wanted 4 colours  you would take some separated by 1 4 of the 256 length of the circle  i e  0  64 128 192  And of course  as others suggested when you need N colours  you could just separate them by 256 N    What I would add to this idea is to use a reversed representation of a binary number to form this sequence  Look at this   0   00000000  after reversal is 00000000   0 1   00000001  after reversal is 10000000   128 2   00000010  after reversal is 01000000   64 3   00000011  after reversal is 11000000   192       this way if you need N different colours you could just take first N numbers  reverse them  and you get as much distant points as possible  for N being power of two  while at the same time preserving that each prefix of the sequence differs a lot   This was an important goal in my use case  as I had a chart where colors were sorted by area covered by this colour  I wanted the largest areas of the chart to have large contrast  and I was ok with some small areas to have colours similar to those from top 10  as it was obvious for the reader which one is which one by just observing the area

[java] How to automatically generate N "distinct" colors?

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