Hcfyk

How can we change any of the two dots of the ddots math symbol?

I can change both of them:

documentclassarticle

usepackagexcolor

begindocument

$colorredddotcolorblackx$

enddocument

Something like:

The following uses two slightly shifted coloured dot macros. The placement is not perfect and might be really bad for some letters.

documentclass[]article

% for colours
usepackagexcolor
% for mighty interface to define new macros, it also loads the l3 kernel
usepackagexparse
% for mathrlap
usepackagemathtools

% change to the coding language of LaTeX3 (in which spaces are ignored, that why
% I can do stuff like #2 etc., also _ is a character now and can be part of
% macro names)
ExplSyntaxOn
% define a user facing macro, it takes one optional argument, which by default
% is empty and a mandatory one (neither of them can contain a par). The
% optional argument will be split at a "," once.
NewDocumentCommand cddot >SplitArgument1,O m 
 
 % pass on the now split argument #1 and the mandatory argument #2. #1 will
 % be something like #1.1 #1.2 
 __manooooh_cddot:nnn #1 #2 
 
% define a new internal macro (cs_new_protected:Npn is like protecteddef)
cs_new_protected:Npn __manooooh_cddot:nnn #1 #2 #3
 
 % start a new group
 group_begin:
 % check whether the first argument is blank (meaning it only contains spaces
 % or nothing), if it isn't blank change the color. It will be blank if you
 % don't use an optional argument or if you start your optional argument with
 % a ","
 tl_if_blank:nF #1 color #1 
 % mathrlap will print its argument without really taking any space, phantom
 % will only take the space of #3, mkern-1.5mu will move the dot slightly to
 % the left
 mathrlap mkern-1.25mu dot phantom #3 
 % end the group containing the first color
 group_end:
 % start a new group
 group_begin:
 % IfValueT will check whether the second part of the split argument was
 % available (so will result in True if there was a comma in [#1]). If there
 % was a second argument assume it is the second color
 IfValueT #2 color #2 
 % again mathrlap and a phantom #3, this time shifting the dot slightly to
 % the right by 2mu
 mathrlap mkern+2.25mu dot phantom #3 
 % end the second color's group
 group_end:
 % print #3 without further ado (since we used mathrlap previously we're
 % still on the same spot and due to the phantom #3 will only be printed
 % visible once
 #3
 
% end the LaTeX3 programming syntax
ExplSyntaxOff

begindocument
% without optional argument
$cddotx$

% with the first half of the optional argument
$cddot[blue]x$

% with the second half of the optional argument
$cddot[,green]x$

% with both halves of the optional argument
$cddot[blue,green]x$

% for comparison
$ddotx$
enddocument

Adapting from the definition of dddot in amsmath. The bottom line in the picture shows the symbol superimposed on each other; the difference is really negligible.

documentclassarticle
usepackageamsmath
usepackagexcolor

makeatletter
DeclareRobustCommandcolorddot[3]%
 % #1=color of first dot, #2=color of second dot, #3=accentee
 mathopkernz@#3limits^%
 vbox to-1.55ex@%
 kern-tw@ex@
 hboxnormalfontkern0.05emtextcolor#1.kern-0.085emtextcolor#2.
 vss
 %
 %

makeatother

begindocument

$ddotx$

$colorddotgreenbluex$

$ddotx$llap$colorddotgreenbluex$
$colorddotgreenbluex$llap$ddotx$

enddocument

Beware that the different colors will make the dots to appear misaligned.

One may just use the accents package, which was made for this.

documentclassarticle
usepackageamsmath
usepackageaccents
usepackagepgffor
usepackagexcolor
newcommandColorDots[2]accentsetforeach X in #1
textcolorXboldsymbol.#2
begindocument
$accentsetboldsymbol..x$ $ColorDotsred,bluey$ $ColorDotsredz$
$ColorDotsred,orange,blueX$
enddocument