R help - Dec 2004 - Creating a vector of colours that are as different from one another as possible

Hi

I want to create a vector of colors that are as different from one
another as possible.  ?rainbow states "Conceptually, all of these
functions actually use (parts of) a line cut out of the 3-dimensional
color space...".  This suggests to me that the resulting colors are all
placed on this "line" and are equi-distant along it.  The resulting
color palette is a range of colours where adjacent colours are actually
quite similar, especially when n (the number of colours) is high.

Conceptually I guess what I want is colors from a 3D polygon in 3D
colour space, where the number of vertices in the polygon is n,
resulting in a color palette where the colors are all quite different
from one another.  Is this possible or am I talking crap? (I've only had
one coffee this morning)

Thanks in advance
Mick

On 21-Dec-04 michael watson \(IAH-C\) wrote:
> Hi
> 
> I want to create a vector of colors that are as different
> from one another as possible.  ?rainbow states "Conceptually,
> all of these functions actually use (parts of) a line cut out
> of the 3-dimensional color space...".  This suggests to me
> that the resulting colors are all placed on this "line" and
> are equi-distant along it.  The resulting color palette is
> a range of colours where adjacent colours are actually quite
> similar, especially when n (the number of colours) is high.
> 
> Conceptually I guess what I want is colors from a 3D polygon
> in 3D colour space, where the number of vertices in the polygon
> is n, resulting in a color palette where the colors are all
> quite different from one another.  Is this possible or am I
> talking crap? (I've only had one coffee this morning)
One is not enough, by a long way, in my experience ...

How large is n? It's not easy to select more than a few clearly
distinct colours. Also, "distinct" is context-dependent, because:

What will be the spatial relationships of the different colours
in your output? You can successfully have fairly similar
colours adjacent to each other, since the contrast is more
obvious when they're adjacent. However, if you want to use
colours to track identity and difference across scttered points
or patches, then you need bigger separations between colours,
since you want to be able to see easily that patch "A" here is
of the same kind as patch "A" there and different from patch
"B"
somwehere else, when mingled with patches of other kinds.

And size matters. Big patches of similar colour (as on a map)
can look quite distinct, while the same colours used to plot
filled circular blobs on a graph might be barely distinguishable,
and totally undistinguishable if used to plot coloured "."s
or "+"s.

It depends too on what you will be using to render the colours.
Monitor screens vary in their aility to render different
colours distinctly, and so do colour printers.

It's all very psycho-visual and success usually requires
experimentation!

Cheers,
Ted.


--------------------------------------------------------------------
E-Mail: (Ted Harding) <Ted.Harding at nessie.mcc.ac.uk>
Fax-to-email: +44 (0)870 094 0861  [NB: New number!]
Date: 21-Dec-04                                       Time: 13:02:10
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On 21 Dec 2004 at 11:05, michael watson (IAH-C) wrote:
> Hi
> 
> I want to create a vector of colors that are as different from one
> another as possible.  ?rainbow states "Conceptually, all of these
> functions actually use (parts of) a line cut out of the 3-dimensional
> color space...".  This suggests to me that the resulting colors are
> all placed on this "line" and are equi-distant along it.  The
> resulting color palette is a range of colours where adjacent colours
> are actually quite similar, especially when n (the number of colours)
> is high.
> 
> Conceptually I guess what I want is colors from a 3D polygon in 3D
> colour space, where the number of vertices in the polygon is n,
> resulting in a color palette where the colors are all quite different
> from one another.  Is this possible or am I talking crap? (I've only
> had one coffee this morning)
Hi Micheal

With increased number of colors you always end with neighbour 
colors quite similar. If I understand the rainbow function correctly 
it sets saturation to 1 (maximum) value to 1 (maximum) and divide 
the third component hue to equally spaced intervals to get the most 
different colours from given range of hues.

You can also experiment with hsv() function
> plot(1:11, col = hsv(h = seq(0,1,.1), s=1, v=0)) #all black
> plot(1:11, col = hsv(h = seq(0,1,.1), s=1, v=1)) # different colours
You can imagine hue as a circle from 0 to 360 and if you want to 
have neighbouring colours to be the most different you have to 
choose them from oposit parts of a circle e.g. 0,180 or 90,270.

So

barvy<-rainbow(12)
vyber<-c(1,7,3,9,5,11,2,8,4,10,6,12)
plot(1:12,col=rainbow(12)[vyber])

will give you a sequence of 12 colours which are by my opinion 
most different.

Cheers
Petr

> 
> Thanks in advance
> Mick
> 
> ______________________________________________
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Petr Pikal
petr.pikal at precheza.cz

On Tue, 21 Dec 2004, michael watson (IAH-C) wrote:
>
> Conceptually I guess what I want is colors from a 3D polygon in 3D
> colour space, where the number of vertices in the polygon is n,
> resulting in a color palette where the colors are all quite different
> from one another.  Is this possible or am I talking crap? (I've only
had
> one coffee this morning)
>
It depends on whether you need the colors to be different colors or 
whether lightness and saturation differences are ok.  For example, a cube 
with edges parallel to the axes in RGB space will have quite strong 
lightness differences, and will probably have visible saturation 
differences (depending on exactly which cube it is).  Often this is a Bad 
Thing.


It's hard to get a large number of colours that are all obviously 
different.  The ColorBrewer palettes (which are optimised for map 
coloring) go up to 11, but some of these are sets of light/dark pairs. If 
you wanted small plotting symbols it would be even more difficult, since 
blue-yellow distinctions are less visible in small things and since you 
probably want higher saturation.

 	-thomas

 	-thomas

michael watson (IAH-C) wrote:
> Hi
> 
> I want to create a vector of colors that are as different from one
> another as possible.  ?rainbow states "Conceptually, all of these
> functions actually use (parts of) a line cut out of the 3-dimensional
> color space...".  This suggests to me that the resulting colors are
all
> placed on this "line" and are equi-distant along it.  The
resulting
> color palette is a range of colours where adjacent colours are actually
> quite similar, especially when n (the number of colours) is high.
> 
> Conceptually I guess what I want is colors from a 3D polygon in 3D
> colour space, where the number of vertices in the polygon is n,
> resulting in a color palette where the colors are all quite different
> from one another.  Is this possible or am I talking crap? (I've only
had
> one coffee this morning)
First, you want to be using a color space where distance corresponds
to perception of similarity/difference.  There are a number of
perceptually based spaces which approximate this (CIELUV, CIELAB
and Munsell).  You could put your points in one of these spaces
and them move them about until they are as far from each other
as possible.

Second, it's generally considered bad practice to use more that
six colors in a single display.  Given the approximate nature of
the uniformity of the perceptual color spaces you could consider
placing this many points "by hand."

How much sense this makes depends on what it is you are trying to do.

(I found reading some of what Munsell had to say pretty informative.)

-- 
Ross Ihaka                         Email:  ihaka at stat.auckland.ac.nz
Department of Statistics           Phone:  (64-9) 373-7599 x 85054
University of Auckland             Fax:    (64-9) 373-7018
Private Bag 92019, Auckland
New Zealand