Frances belatedly to Michael...
You asked how in Peircean philosophy the notion or process of
mapping is developed and explained, where you assume mapping to
be the correlating of one idea with another, or of an idea with
an external object. You stated Peirce was a cartographer for the
American Geodetic Survey, and also developed a quincuncial
projection system using a map of the whole earth, but that you
are interested in the mental or conceptual process of associating
two things such that one represents the other and "is mapped
onto" the other. In philosophy today there is among other studies
"logical argument mapping" and "computer supported argument
visualization" and "dialogue mapping" and in science today there
is "topological mapping" of the brain. In Peircean pragmatism
there is "existential graphing" but no mention of mapping at all,
at least that could be found by me. The science of psychology in
his day was usually held to be a branch of philosophy, which may
explain the absence of psychical mapping in his writings. If his
logical graphing is held to be somewhat equivalent to psychical
mapping, then something might be made of this. It would all turn
on signs and especially on icons. Perhaps other members might
shed some light on this question.