How to automatically generate N "distinct" colors?
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<Color> KellysMaxContrastSet
{
get { return _kellysMaxContrastSet.AsReadOnly(); }
}
private static readonly List<Color> _kellysMaxContrastSet = new List<Color>
{
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<Color> BoyntonOptimized
{
get { return _boyntonOptimized.AsReadOnly(); }
}
private static readonly List<Color> _boyntonOptimized = new List<Color>
{
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 >> 24);
var r = (byte)(color >> 16);
var g = (byte)(color >> 8);
var b = (byte)(color >> 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)
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 < 360; i += 360 / num_colors) {
HSLColor c;
c.hue = i;
c.saturation = 90 + randf() * 10;
c.lightness = 50 + randf() * 10;
addColor(c);
}
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
from typing import Iterable, Tuple
import colorsys
import itertools
from fractions import Fraction
from pprint import pprint
def zenos_dichotomy() -> Iterable[Fraction]:
"""
http://en.wikipedia.org/wiki/1/2_%2B_1/4_%2B_1/8_%2B_1/16_%2B_%C2%B7_%C2%B7_%C2%B7
"""
for k in itertools.count():
yield Fraction(1,2**k)
def fracs() -> Iterable[Fraction]:
"""
[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, ...]
"""
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) -> 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) -> RGBTuple:
return colorsys.hsv_to_rgb(*map(float, x))
flatten = itertools.chain.from_iterable
def hsvs() -> Iterable[HSVTuple]:
return flatten(map(hue_to_tones, fracs()))
def rgbs() -> Iterable[RGBTuple]:
return map(hsv_to_rgb, hsvs())
def rgb_to_css(x: RGBTuple) -> str:
uint8tuple = map(lambda y: int(y*255), x)
return "rgb({},{},{})".format(*uint8tuple)
def css_colors() -> Iterable[str]:
return map(rgb_to_css, rgbs())
if __name__ == "__main__":
# sample 100 colors in css format
sample_colors = list(itertools.islice(css_colors(), 100))
pprint(sample_colors)
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
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